wolf SSL
wolfSSL SSL/TLS library, support up to TLS1.3
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wolfcrypt/src/sp_c32.c
- Committer:
- wolfSSL
- Date:
- 2020-06-05
- Revision:
- 17:a5f916481144
- Parent:
- 16:8e0d178b1d1e
File content as of revision 17:a5f916481144:
/* sp.c
*
* Copyright (C) 2006-2020 wolfSSL Inc.
*
* This file is part of wolfSSL.
*
* wolfSSL is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* wolfSSL is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
*/
/* Implementation by Sean Parkinson. */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <wolfssl/wolfcrypt/settings.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/cpuid.h>
#ifdef NO_INLINE
#include <wolfssl/wolfcrypt/misc.h>
#else
#define WOLFSSL_MISC_INCLUDED
#include <wolfcrypt/src/misc.c>
#endif
#if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH) || \
defined(WOLFSSL_HAVE_SP_ECC)
#ifdef RSA_LOW_MEM
#ifndef SP_RSA_PRIVATE_EXP_D
#define SP_RSA_PRIVATE_EXP_D
#endif
#ifndef WOLFSSL_SP_SMALL
#define WOLFSSL_SP_SMALL
#endif
#endif
#include <wolfssl/wolfcrypt/sp.h>
#ifndef WOLFSSL_SP_ASM
#if SP_WORD_SIZE == 32
#if (defined(WOLFSSL_SP_CACHE_RESISTANT) || defined(WOLFSSL_SP_SMALL)) && (defined(WOLFSSL_HAVE_SP_ECC) || !defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Mask for address to obfuscate which of the two address will be used. */
static const size_t addr_mask[2] = { 0, (size_t)-1 };
#endif
#if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)
#ifndef WOLFSSL_SP_NO_2048
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_2048_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 15U) {
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_2048_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 23
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 23
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 23U) <= (word32)DIGIT_BIT) {
s += 23U;
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 23) {
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
s = 23 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 256
*
* r A single precision integer.
* a Byte array.
*/
static void sp_2048_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<89; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
j = 2048 / 8 - 1;
a[j] = 0;
for (i=0; i<90 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); /*lint !e9033*/
b += 8 - s;
if (j < 0) {
break;
}
while (b < 23) {
a[j--] = (byte)(r[i] >> b);
b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 23);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
#ifndef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int64_t t0 = ((int64_t)a[ 0]) * b[ 0];
int64_t t1 = ((int64_t)a[ 0]) * b[ 1]
+ ((int64_t)a[ 1]) * b[ 0];
int64_t t2 = ((int64_t)a[ 0]) * b[ 2]
+ ((int64_t)a[ 1]) * b[ 1]
+ ((int64_t)a[ 2]) * b[ 0];
int64_t t3 = ((int64_t)a[ 0]) * b[ 3]
+ ((int64_t)a[ 1]) * b[ 2]
+ ((int64_t)a[ 2]) * b[ 1]
+ ((int64_t)a[ 3]) * b[ 0];
int64_t t4 = ((int64_t)a[ 0]) * b[ 4]
+ ((int64_t)a[ 1]) * b[ 3]
+ ((int64_t)a[ 2]) * b[ 2]
+ ((int64_t)a[ 3]) * b[ 1]
+ ((int64_t)a[ 4]) * b[ 0];
int64_t t5 = ((int64_t)a[ 0]) * b[ 5]
+ ((int64_t)a[ 1]) * b[ 4]
+ ((int64_t)a[ 2]) * b[ 3]
+ ((int64_t)a[ 3]) * b[ 2]
+ ((int64_t)a[ 4]) * b[ 1]
+ ((int64_t)a[ 5]) * b[ 0];
int64_t t6 = ((int64_t)a[ 0]) * b[ 6]
+ ((int64_t)a[ 1]) * b[ 5]
+ ((int64_t)a[ 2]) * b[ 4]
+ ((int64_t)a[ 3]) * b[ 3]
+ ((int64_t)a[ 4]) * b[ 2]
+ ((int64_t)a[ 5]) * b[ 1]
+ ((int64_t)a[ 6]) * b[ 0];
int64_t t7 = ((int64_t)a[ 0]) * b[ 7]
+ ((int64_t)a[ 1]) * b[ 6]
+ ((int64_t)a[ 2]) * b[ 5]
+ ((int64_t)a[ 3]) * b[ 4]
+ ((int64_t)a[ 4]) * b[ 3]
+ ((int64_t)a[ 5]) * b[ 2]
+ ((int64_t)a[ 6]) * b[ 1]
+ ((int64_t)a[ 7]) * b[ 0];
int64_t t8 = ((int64_t)a[ 0]) * b[ 8]
+ ((int64_t)a[ 1]) * b[ 7]
+ ((int64_t)a[ 2]) * b[ 6]
+ ((int64_t)a[ 3]) * b[ 5]
+ ((int64_t)a[ 4]) * b[ 4]
+ ((int64_t)a[ 5]) * b[ 3]
+ ((int64_t)a[ 6]) * b[ 2]
+ ((int64_t)a[ 7]) * b[ 1]
+ ((int64_t)a[ 8]) * b[ 0];
int64_t t9 = ((int64_t)a[ 0]) * b[ 9]
+ ((int64_t)a[ 1]) * b[ 8]
+ ((int64_t)a[ 2]) * b[ 7]
+ ((int64_t)a[ 3]) * b[ 6]
+ ((int64_t)a[ 4]) * b[ 5]
+ ((int64_t)a[ 5]) * b[ 4]
+ ((int64_t)a[ 6]) * b[ 3]
+ ((int64_t)a[ 7]) * b[ 2]
+ ((int64_t)a[ 8]) * b[ 1]
+ ((int64_t)a[ 9]) * b[ 0];
int64_t t10 = ((int64_t)a[ 0]) * b[10]
+ ((int64_t)a[ 1]) * b[ 9]
+ ((int64_t)a[ 2]) * b[ 8]
+ ((int64_t)a[ 3]) * b[ 7]
+ ((int64_t)a[ 4]) * b[ 6]
+ ((int64_t)a[ 5]) * b[ 5]
+ ((int64_t)a[ 6]) * b[ 4]
+ ((int64_t)a[ 7]) * b[ 3]
+ ((int64_t)a[ 8]) * b[ 2]
+ ((int64_t)a[ 9]) * b[ 1]
+ ((int64_t)a[10]) * b[ 0];
int64_t t11 = ((int64_t)a[ 0]) * b[11]
+ ((int64_t)a[ 1]) * b[10]
+ ((int64_t)a[ 2]) * b[ 9]
+ ((int64_t)a[ 3]) * b[ 8]
+ ((int64_t)a[ 4]) * b[ 7]
+ ((int64_t)a[ 5]) * b[ 6]
+ ((int64_t)a[ 6]) * b[ 5]
+ ((int64_t)a[ 7]) * b[ 4]
+ ((int64_t)a[ 8]) * b[ 3]
+ ((int64_t)a[ 9]) * b[ 2]
+ ((int64_t)a[10]) * b[ 1]
+ ((int64_t)a[11]) * b[ 0];
int64_t t12 = ((int64_t)a[ 0]) * b[12]
+ ((int64_t)a[ 1]) * b[11]
+ ((int64_t)a[ 2]) * b[10]
+ ((int64_t)a[ 3]) * b[ 9]
+ ((int64_t)a[ 4]) * b[ 8]
+ ((int64_t)a[ 5]) * b[ 7]
+ ((int64_t)a[ 6]) * b[ 6]
+ ((int64_t)a[ 7]) * b[ 5]
+ ((int64_t)a[ 8]) * b[ 4]
+ ((int64_t)a[ 9]) * b[ 3]
+ ((int64_t)a[10]) * b[ 2]
+ ((int64_t)a[11]) * b[ 1]
+ ((int64_t)a[12]) * b[ 0];
int64_t t13 = ((int64_t)a[ 0]) * b[13]
+ ((int64_t)a[ 1]) * b[12]
+ ((int64_t)a[ 2]) * b[11]
+ ((int64_t)a[ 3]) * b[10]
+ ((int64_t)a[ 4]) * b[ 9]
+ ((int64_t)a[ 5]) * b[ 8]
+ ((int64_t)a[ 6]) * b[ 7]
+ ((int64_t)a[ 7]) * b[ 6]
+ ((int64_t)a[ 8]) * b[ 5]
+ ((int64_t)a[ 9]) * b[ 4]
+ ((int64_t)a[10]) * b[ 3]
+ ((int64_t)a[11]) * b[ 2]
+ ((int64_t)a[12]) * b[ 1]
+ ((int64_t)a[13]) * b[ 0];
int64_t t14 = ((int64_t)a[ 0]) * b[14]
+ ((int64_t)a[ 1]) * b[13]
+ ((int64_t)a[ 2]) * b[12]
+ ((int64_t)a[ 3]) * b[11]
+ ((int64_t)a[ 4]) * b[10]
+ ((int64_t)a[ 5]) * b[ 9]
+ ((int64_t)a[ 6]) * b[ 8]
+ ((int64_t)a[ 7]) * b[ 7]
+ ((int64_t)a[ 8]) * b[ 6]
+ ((int64_t)a[ 9]) * b[ 5]
+ ((int64_t)a[10]) * b[ 4]
+ ((int64_t)a[11]) * b[ 3]
+ ((int64_t)a[12]) * b[ 2]
+ ((int64_t)a[13]) * b[ 1]
+ ((int64_t)a[14]) * b[ 0];
int64_t t15 = ((int64_t)a[ 1]) * b[14]
+ ((int64_t)a[ 2]) * b[13]
+ ((int64_t)a[ 3]) * b[12]
+ ((int64_t)a[ 4]) * b[11]
+ ((int64_t)a[ 5]) * b[10]
+ ((int64_t)a[ 6]) * b[ 9]
+ ((int64_t)a[ 7]) * b[ 8]
+ ((int64_t)a[ 8]) * b[ 7]
+ ((int64_t)a[ 9]) * b[ 6]
+ ((int64_t)a[10]) * b[ 5]
+ ((int64_t)a[11]) * b[ 4]
+ ((int64_t)a[12]) * b[ 3]
+ ((int64_t)a[13]) * b[ 2]
+ ((int64_t)a[14]) * b[ 1];
int64_t t16 = ((int64_t)a[ 2]) * b[14]
+ ((int64_t)a[ 3]) * b[13]
+ ((int64_t)a[ 4]) * b[12]
+ ((int64_t)a[ 5]) * b[11]
+ ((int64_t)a[ 6]) * b[10]
+ ((int64_t)a[ 7]) * b[ 9]
+ ((int64_t)a[ 8]) * b[ 8]
+ ((int64_t)a[ 9]) * b[ 7]
+ ((int64_t)a[10]) * b[ 6]
+ ((int64_t)a[11]) * b[ 5]
+ ((int64_t)a[12]) * b[ 4]
+ ((int64_t)a[13]) * b[ 3]
+ ((int64_t)a[14]) * b[ 2];
int64_t t17 = ((int64_t)a[ 3]) * b[14]
+ ((int64_t)a[ 4]) * b[13]
+ ((int64_t)a[ 5]) * b[12]
+ ((int64_t)a[ 6]) * b[11]
+ ((int64_t)a[ 7]) * b[10]
+ ((int64_t)a[ 8]) * b[ 9]
+ ((int64_t)a[ 9]) * b[ 8]
+ ((int64_t)a[10]) * b[ 7]
+ ((int64_t)a[11]) * b[ 6]
+ ((int64_t)a[12]) * b[ 5]
+ ((int64_t)a[13]) * b[ 4]
+ ((int64_t)a[14]) * b[ 3];
int64_t t18 = ((int64_t)a[ 4]) * b[14]
+ ((int64_t)a[ 5]) * b[13]
+ ((int64_t)a[ 6]) * b[12]
+ ((int64_t)a[ 7]) * b[11]
+ ((int64_t)a[ 8]) * b[10]
+ ((int64_t)a[ 9]) * b[ 9]
+ ((int64_t)a[10]) * b[ 8]
+ ((int64_t)a[11]) * b[ 7]
+ ((int64_t)a[12]) * b[ 6]
+ ((int64_t)a[13]) * b[ 5]
+ ((int64_t)a[14]) * b[ 4];
int64_t t19 = ((int64_t)a[ 5]) * b[14]
+ ((int64_t)a[ 6]) * b[13]
+ ((int64_t)a[ 7]) * b[12]
+ ((int64_t)a[ 8]) * b[11]
+ ((int64_t)a[ 9]) * b[10]
+ ((int64_t)a[10]) * b[ 9]
+ ((int64_t)a[11]) * b[ 8]
+ ((int64_t)a[12]) * b[ 7]
+ ((int64_t)a[13]) * b[ 6]
+ ((int64_t)a[14]) * b[ 5];
int64_t t20 = ((int64_t)a[ 6]) * b[14]
+ ((int64_t)a[ 7]) * b[13]
+ ((int64_t)a[ 8]) * b[12]
+ ((int64_t)a[ 9]) * b[11]
+ ((int64_t)a[10]) * b[10]
+ ((int64_t)a[11]) * b[ 9]
+ ((int64_t)a[12]) * b[ 8]
+ ((int64_t)a[13]) * b[ 7]
+ ((int64_t)a[14]) * b[ 6];
int64_t t21 = ((int64_t)a[ 7]) * b[14]
+ ((int64_t)a[ 8]) * b[13]
+ ((int64_t)a[ 9]) * b[12]
+ ((int64_t)a[10]) * b[11]
+ ((int64_t)a[11]) * b[10]
+ ((int64_t)a[12]) * b[ 9]
+ ((int64_t)a[13]) * b[ 8]
+ ((int64_t)a[14]) * b[ 7];
int64_t t22 = ((int64_t)a[ 8]) * b[14]
+ ((int64_t)a[ 9]) * b[13]
+ ((int64_t)a[10]) * b[12]
+ ((int64_t)a[11]) * b[11]
+ ((int64_t)a[12]) * b[10]
+ ((int64_t)a[13]) * b[ 9]
+ ((int64_t)a[14]) * b[ 8];
int64_t t23 = ((int64_t)a[ 9]) * b[14]
+ ((int64_t)a[10]) * b[13]
+ ((int64_t)a[11]) * b[12]
+ ((int64_t)a[12]) * b[11]
+ ((int64_t)a[13]) * b[10]
+ ((int64_t)a[14]) * b[ 9];
int64_t t24 = ((int64_t)a[10]) * b[14]
+ ((int64_t)a[11]) * b[13]
+ ((int64_t)a[12]) * b[12]
+ ((int64_t)a[13]) * b[11]
+ ((int64_t)a[14]) * b[10];
int64_t t25 = ((int64_t)a[11]) * b[14]
+ ((int64_t)a[12]) * b[13]
+ ((int64_t)a[13]) * b[12]
+ ((int64_t)a[14]) * b[11];
int64_t t26 = ((int64_t)a[12]) * b[14]
+ ((int64_t)a[13]) * b[13]
+ ((int64_t)a[14]) * b[12];
int64_t t27 = ((int64_t)a[13]) * b[14]
+ ((int64_t)a[14]) * b[13];
int64_t t28 = ((int64_t)a[14]) * b[14];
t1 += t0 >> 23; r[ 0] = t0 & 0x7fffff;
t2 += t1 >> 23; r[ 1] = t1 & 0x7fffff;
t3 += t2 >> 23; r[ 2] = t2 & 0x7fffff;
t4 += t3 >> 23; r[ 3] = t3 & 0x7fffff;
t5 += t4 >> 23; r[ 4] = t4 & 0x7fffff;
t6 += t5 >> 23; r[ 5] = t5 & 0x7fffff;
t7 += t6 >> 23; r[ 6] = t6 & 0x7fffff;
t8 += t7 >> 23; r[ 7] = t7 & 0x7fffff;
t9 += t8 >> 23; r[ 8] = t8 & 0x7fffff;
t10 += t9 >> 23; r[ 9] = t9 & 0x7fffff;
t11 += t10 >> 23; r[10] = t10 & 0x7fffff;
t12 += t11 >> 23; r[11] = t11 & 0x7fffff;
t13 += t12 >> 23; r[12] = t12 & 0x7fffff;
t14 += t13 >> 23; r[13] = t13 & 0x7fffff;
t15 += t14 >> 23; r[14] = t14 & 0x7fffff;
t16 += t15 >> 23; r[15] = t15 & 0x7fffff;
t17 += t16 >> 23; r[16] = t16 & 0x7fffff;
t18 += t17 >> 23; r[17] = t17 & 0x7fffff;
t19 += t18 >> 23; r[18] = t18 & 0x7fffff;
t20 += t19 >> 23; r[19] = t19 & 0x7fffff;
t21 += t20 >> 23; r[20] = t20 & 0x7fffff;
t22 += t21 >> 23; r[21] = t21 & 0x7fffff;
t23 += t22 >> 23; r[22] = t22 & 0x7fffff;
t24 += t23 >> 23; r[23] = t23 & 0x7fffff;
t25 += t24 >> 23; r[24] = t24 & 0x7fffff;
t26 += t25 >> 23; r[25] = t25 & 0x7fffff;
t27 += t26 >> 23; r[26] = t26 & 0x7fffff;
t28 += t27 >> 23; r[27] = t27 & 0x7fffff;
r[29] = (sp_digit)(t28 >> 23);
r[28] = t28 & 0x7fffff;
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_15(sp_digit* r, const sp_digit* a)
{
int64_t t0 = ((int64_t)a[ 0]) * a[ 0];
int64_t t1 = (((int64_t)a[ 0]) * a[ 1]) * 2;
int64_t t2 = (((int64_t)a[ 0]) * a[ 2]) * 2
+ ((int64_t)a[ 1]) * a[ 1];
int64_t t3 = (((int64_t)a[ 0]) * a[ 3]
+ ((int64_t)a[ 1]) * a[ 2]) * 2;
int64_t t4 = (((int64_t)a[ 0]) * a[ 4]
+ ((int64_t)a[ 1]) * a[ 3]) * 2
+ ((int64_t)a[ 2]) * a[ 2];
int64_t t5 = (((int64_t)a[ 0]) * a[ 5]
+ ((int64_t)a[ 1]) * a[ 4]
+ ((int64_t)a[ 2]) * a[ 3]) * 2;
int64_t t6 = (((int64_t)a[ 0]) * a[ 6]
+ ((int64_t)a[ 1]) * a[ 5]
+ ((int64_t)a[ 2]) * a[ 4]) * 2
+ ((int64_t)a[ 3]) * a[ 3];
int64_t t7 = (((int64_t)a[ 0]) * a[ 7]
+ ((int64_t)a[ 1]) * a[ 6]
+ ((int64_t)a[ 2]) * a[ 5]
+ ((int64_t)a[ 3]) * a[ 4]) * 2;
int64_t t8 = (((int64_t)a[ 0]) * a[ 8]
+ ((int64_t)a[ 1]) * a[ 7]
+ ((int64_t)a[ 2]) * a[ 6]
+ ((int64_t)a[ 3]) * a[ 5]) * 2
+ ((int64_t)a[ 4]) * a[ 4];
int64_t t9 = (((int64_t)a[ 0]) * a[ 9]
+ ((int64_t)a[ 1]) * a[ 8]
+ ((int64_t)a[ 2]) * a[ 7]
+ ((int64_t)a[ 3]) * a[ 6]
+ ((int64_t)a[ 4]) * a[ 5]) * 2;
int64_t t10 = (((int64_t)a[ 0]) * a[10]
+ ((int64_t)a[ 1]) * a[ 9]
+ ((int64_t)a[ 2]) * a[ 8]
+ ((int64_t)a[ 3]) * a[ 7]
+ ((int64_t)a[ 4]) * a[ 6]) * 2
+ ((int64_t)a[ 5]) * a[ 5];
int64_t t11 = (((int64_t)a[ 0]) * a[11]
+ ((int64_t)a[ 1]) * a[10]
+ ((int64_t)a[ 2]) * a[ 9]
+ ((int64_t)a[ 3]) * a[ 8]
+ ((int64_t)a[ 4]) * a[ 7]
+ ((int64_t)a[ 5]) * a[ 6]) * 2;
int64_t t12 = (((int64_t)a[ 0]) * a[12]
+ ((int64_t)a[ 1]) * a[11]
+ ((int64_t)a[ 2]) * a[10]
+ ((int64_t)a[ 3]) * a[ 9]
+ ((int64_t)a[ 4]) * a[ 8]
+ ((int64_t)a[ 5]) * a[ 7]) * 2
+ ((int64_t)a[ 6]) * a[ 6];
int64_t t13 = (((int64_t)a[ 0]) * a[13]
+ ((int64_t)a[ 1]) * a[12]
+ ((int64_t)a[ 2]) * a[11]
+ ((int64_t)a[ 3]) * a[10]
+ ((int64_t)a[ 4]) * a[ 9]
+ ((int64_t)a[ 5]) * a[ 8]
+ ((int64_t)a[ 6]) * a[ 7]) * 2;
int64_t t14 = (((int64_t)a[ 0]) * a[14]
+ ((int64_t)a[ 1]) * a[13]
+ ((int64_t)a[ 2]) * a[12]
+ ((int64_t)a[ 3]) * a[11]
+ ((int64_t)a[ 4]) * a[10]
+ ((int64_t)a[ 5]) * a[ 9]
+ ((int64_t)a[ 6]) * a[ 8]) * 2
+ ((int64_t)a[ 7]) * a[ 7];
int64_t t15 = (((int64_t)a[ 1]) * a[14]
+ ((int64_t)a[ 2]) * a[13]
+ ((int64_t)a[ 3]) * a[12]
+ ((int64_t)a[ 4]) * a[11]
+ ((int64_t)a[ 5]) * a[10]
+ ((int64_t)a[ 6]) * a[ 9]
+ ((int64_t)a[ 7]) * a[ 8]) * 2;
int64_t t16 = (((int64_t)a[ 2]) * a[14]
+ ((int64_t)a[ 3]) * a[13]
+ ((int64_t)a[ 4]) * a[12]
+ ((int64_t)a[ 5]) * a[11]
+ ((int64_t)a[ 6]) * a[10]
+ ((int64_t)a[ 7]) * a[ 9]) * 2
+ ((int64_t)a[ 8]) * a[ 8];
int64_t t17 = (((int64_t)a[ 3]) * a[14]
+ ((int64_t)a[ 4]) * a[13]
+ ((int64_t)a[ 5]) * a[12]
+ ((int64_t)a[ 6]) * a[11]
+ ((int64_t)a[ 7]) * a[10]
+ ((int64_t)a[ 8]) * a[ 9]) * 2;
int64_t t18 = (((int64_t)a[ 4]) * a[14]
+ ((int64_t)a[ 5]) * a[13]
+ ((int64_t)a[ 6]) * a[12]
+ ((int64_t)a[ 7]) * a[11]
+ ((int64_t)a[ 8]) * a[10]) * 2
+ ((int64_t)a[ 9]) * a[ 9];
int64_t t19 = (((int64_t)a[ 5]) * a[14]
+ ((int64_t)a[ 6]) * a[13]
+ ((int64_t)a[ 7]) * a[12]
+ ((int64_t)a[ 8]) * a[11]
+ ((int64_t)a[ 9]) * a[10]) * 2;
int64_t t20 = (((int64_t)a[ 6]) * a[14]
+ ((int64_t)a[ 7]) * a[13]
+ ((int64_t)a[ 8]) * a[12]
+ ((int64_t)a[ 9]) * a[11]) * 2
+ ((int64_t)a[10]) * a[10];
int64_t t21 = (((int64_t)a[ 7]) * a[14]
+ ((int64_t)a[ 8]) * a[13]
+ ((int64_t)a[ 9]) * a[12]
+ ((int64_t)a[10]) * a[11]) * 2;
int64_t t22 = (((int64_t)a[ 8]) * a[14]
+ ((int64_t)a[ 9]) * a[13]
+ ((int64_t)a[10]) * a[12]) * 2
+ ((int64_t)a[11]) * a[11];
int64_t t23 = (((int64_t)a[ 9]) * a[14]
+ ((int64_t)a[10]) * a[13]
+ ((int64_t)a[11]) * a[12]) * 2;
int64_t t24 = (((int64_t)a[10]) * a[14]
+ ((int64_t)a[11]) * a[13]) * 2
+ ((int64_t)a[12]) * a[12];
int64_t t25 = (((int64_t)a[11]) * a[14]
+ ((int64_t)a[12]) * a[13]) * 2;
int64_t t26 = (((int64_t)a[12]) * a[14]) * 2
+ ((int64_t)a[13]) * a[13];
int64_t t27 = (((int64_t)a[13]) * a[14]) * 2;
int64_t t28 = ((int64_t)a[14]) * a[14];
t1 += t0 >> 23; r[ 0] = t0 & 0x7fffff;
t2 += t1 >> 23; r[ 1] = t1 & 0x7fffff;
t3 += t2 >> 23; r[ 2] = t2 & 0x7fffff;
t4 += t3 >> 23; r[ 3] = t3 & 0x7fffff;
t5 += t4 >> 23; r[ 4] = t4 & 0x7fffff;
t6 += t5 >> 23; r[ 5] = t5 & 0x7fffff;
t7 += t6 >> 23; r[ 6] = t6 & 0x7fffff;
t8 += t7 >> 23; r[ 7] = t7 & 0x7fffff;
t9 += t8 >> 23; r[ 8] = t8 & 0x7fffff;
t10 += t9 >> 23; r[ 9] = t9 & 0x7fffff;
t11 += t10 >> 23; r[10] = t10 & 0x7fffff;
t12 += t11 >> 23; r[11] = t11 & 0x7fffff;
t13 += t12 >> 23; r[12] = t12 & 0x7fffff;
t14 += t13 >> 23; r[13] = t13 & 0x7fffff;
t15 += t14 >> 23; r[14] = t14 & 0x7fffff;
t16 += t15 >> 23; r[15] = t15 & 0x7fffff;
t17 += t16 >> 23; r[16] = t16 & 0x7fffff;
t18 += t17 >> 23; r[17] = t17 & 0x7fffff;
t19 += t18 >> 23; r[18] = t18 & 0x7fffff;
t20 += t19 >> 23; r[19] = t19 & 0x7fffff;
t21 += t20 >> 23; r[20] = t20 & 0x7fffff;
t22 += t21 >> 23; r[21] = t21 & 0x7fffff;
t23 += t22 >> 23; r[22] = t22 & 0x7fffff;
t24 += t23 >> 23; r[23] = t23 & 0x7fffff;
t25 += t24 >> 23; r[24] = t24 & 0x7fffff;
t26 += t25 >> 23; r[25] = t25 & 0x7fffff;
t27 += t26 >> 23; r[26] = t26 & 0x7fffff;
t28 += t27 >> 23; r[27] = t27 & 0x7fffff;
r[29] = (sp_digit)(t28 >> 23);
r[28] = t28 & 0x7fffff;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] + b[ 0];
r[ 1] = a[ 1] + b[ 1];
r[ 2] = a[ 2] + b[ 2];
r[ 3] = a[ 3] + b[ 3];
r[ 4] = a[ 4] + b[ 4];
r[ 5] = a[ 5] + b[ 5];
r[ 6] = a[ 6] + b[ 6];
r[ 7] = a[ 7] + b[ 7];
r[ 8] = a[ 8] + b[ 8];
r[ 9] = a[ 9] + b[ 9];
r[10] = a[10] + b[10];
r[11] = a[11] + b[11];
r[12] = a[12] + b[12];
r[13] = a[13] + b[13];
r[14] = a[14] + b[14];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_30(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 24; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[24] = a[24] - b[24];
r[25] = a[25] - b[25];
r[26] = a[26] - b[26];
r[27] = a[27] - b[27];
r[28] = a[28] - b[28];
r[29] = a[29] - b[29];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_30(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 24; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[24] = a[24] + b[24];
r[25] = a[25] + b[25];
r[26] = a[26] + b[26];
r[27] = a[27] + b[27];
r[28] = a[28] + b[28];
r[29] = a[29] + b[29];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit p0[30];
sp_digit p1[30];
sp_digit p2[30];
sp_digit p3[30];
sp_digit p4[30];
sp_digit p5[30];
sp_digit t0[30];
sp_digit t1[30];
sp_digit t2[30];
sp_digit a0[15];
sp_digit a1[15];
sp_digit a2[15];
sp_digit b0[15];
sp_digit b1[15];
sp_digit b2[15];
(void)sp_2048_add_15(a0, a, &a[15]);
(void)sp_2048_add_15(b0, b, &b[15]);
(void)sp_2048_add_15(a1, &a[15], &a[30]);
(void)sp_2048_add_15(b1, &b[15], &b[30]);
(void)sp_2048_add_15(a2, a0, &a[30]);
(void)sp_2048_add_15(b2, b0, &b[30]);
sp_2048_mul_15(p0, a, b);
sp_2048_mul_15(p2, &a[15], &b[15]);
sp_2048_mul_15(p4, &a[30], &b[30]);
sp_2048_mul_15(p1, a0, b0);
sp_2048_mul_15(p3, a1, b1);
sp_2048_mul_15(p5, a2, b2);
XMEMSET(r, 0, sizeof(*r)*2U*45U);
(void)sp_2048_sub_30(t0, p3, p2);
(void)sp_2048_sub_30(t1, p1, p2);
(void)sp_2048_sub_30(t2, p5, t0);
(void)sp_2048_sub_30(t2, t2, t1);
(void)sp_2048_sub_30(t0, t0, p4);
(void)sp_2048_sub_30(t1, t1, p0);
(void)sp_2048_add_30(r, r, p0);
(void)sp_2048_add_30(&r[15], &r[15], t1);
(void)sp_2048_add_30(&r[30], &r[30], t2);
(void)sp_2048_add_30(&r[45], &r[45], t0);
(void)sp_2048_add_30(&r[60], &r[60], p4);
}
/* Square a into r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_45(sp_digit* r, const sp_digit* a)
{
sp_digit p0[30];
sp_digit p1[30];
sp_digit p2[30];
sp_digit p3[30];
sp_digit p4[30];
sp_digit p5[30];
sp_digit t0[30];
sp_digit t1[30];
sp_digit t2[30];
sp_digit a0[15];
sp_digit a1[15];
sp_digit a2[15];
(void)sp_2048_add_15(a0, a, &a[15]);
(void)sp_2048_add_15(a1, &a[15], &a[30]);
(void)sp_2048_add_15(a2, a0, &a[30]);
sp_2048_sqr_15(p0, a);
sp_2048_sqr_15(p2, &a[15]);
sp_2048_sqr_15(p4, &a[30]);
sp_2048_sqr_15(p1, a0);
sp_2048_sqr_15(p3, a1);
sp_2048_sqr_15(p5, a2);
XMEMSET(r, 0, sizeof(*r)*2U*45U);
(void)sp_2048_sub_30(t0, p3, p2);
(void)sp_2048_sub_30(t1, p1, p2);
(void)sp_2048_sub_30(t2, p5, t0);
(void)sp_2048_sub_30(t2, t2, t1);
(void)sp_2048_sub_30(t0, t0, p4);
(void)sp_2048_sub_30(t1, t1, p0);
(void)sp_2048_add_30(r, r, p0);
(void)sp_2048_add_30(&r[15], &r[15], t1);
(void)sp_2048_add_30(&r[30], &r[30], t2);
(void)sp_2048_add_30(&r[45], &r[45], t0);
(void)sp_2048_add_30(&r[60], &r[60], p4);
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[40] = a[40] + b[40];
r[41] = a[41] + b[41];
r[42] = a[42] + b[42];
r[43] = a[43] + b[43];
r[44] = a[44] + b[44];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[88] = a[88] + b[88];
r[89] = a[89] + b[89];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[88] = a[88] - b[88];
r[89] = a[89] - b[89];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit* z0 = r;
sp_digit z1[90];
sp_digit* a1 = z1;
sp_digit b1[45];
sp_digit* z2 = r + 90;
(void)sp_2048_add_45(a1, a, &a[45]);
(void)sp_2048_add_45(b1, b, &b[45]);
sp_2048_mul_45(z2, &a[45], &b[45]);
sp_2048_mul_45(z0, a, b);
sp_2048_mul_45(z1, a1, b1);
(void)sp_2048_sub_90(z1, z1, z2);
(void)sp_2048_sub_90(z1, z1, z0);
(void)sp_2048_add_90(r + 45, r + 45, z1);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_90(sp_digit* r, const sp_digit* a)
{
sp_digit* z0 = r;
sp_digit z1[90];
sp_digit* a1 = z1;
sp_digit* z2 = r + 90;
(void)sp_2048_add_45(a1, a, &a[45]);
sp_2048_sqr_45(z2, &a[45]);
sp_2048_sqr_45(z0, a);
sp_2048_sqr_45(z1, a1);
(void)sp_2048_sub_90(z1, z1, z2);
(void)sp_2048_sub_90(z1, z1, z0);
(void)sp_2048_add_90(r + 45, r + 45, z1);
}
#endif /* !WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[89]) * b[89];
r[179] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 177; k >= 0; k--) {
for (i = 89; i >= 0; i--) {
j = k - i;
if (j >= 90) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_90(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[89]) * a[89];
r[179] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 177; k >= 0; k--) {
for (i = 89; i >= 0; i--) {
j = k - i;
if (j >= 90 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[40] = a[40] - b[40];
r[41] = a[41] - b[41];
r[42] = a[42] - b[42];
r[43] = a[43] - b[43];
r[44] = a[44] - b[44];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_2048_mul_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[44]) * b[44];
r[89] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 87; k >= 0; k--) {
for (i = 44; i >= 0; i--) {
j = k - i;
if (j >= 45) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_2048_sqr_45(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[44]) * a[44];
r[89] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 87; k >= 0; k--) {
for (i = 44; i >= 0; i--) {
j = k - i;
if (j >= 45 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* Caclulate the bottom digit of -1/a mod 2^n.
*
* a A single precision number.
* rho Bottom word of inverse.
*/
static void sp_2048_mont_setup(const sp_digit* a, sp_digit* rho)
{
sp_digit x, b;
b = a[0];
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
x &= 0x7fffff;
/* rho = -1/m mod b */
*rho = (1L << 23) - x;
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_d_90(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 90; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[90] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 88; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[89];
r[89] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
r[90] = (sp_digit)(t[1] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 2048 bits, just need to subtract.
*
* r A single precision number.
* m A single precision number.
*/
static void sp_2048_mont_norm_45(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<44; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[40] = 0x7fffff;
r[41] = 0x7fffff;
r[42] = 0x7fffff;
r[43] = 0x7fffff;
#endif
r[44] = 0xfffL;
/* r = (2^n - 1) mod n */
(void)sp_2048_sub_45(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_2048_cmp_45(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=44; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[44] - b[44]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[43] - b[43]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[42] - b[42]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[41] - b[41]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[40] - b[40]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 32; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_2048_cond_sub_45(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[40] = a[40] - (b[40] & m);
r[41] = a[41] - (b[41] & m);
r[42] = a[42] - (b[42] & m);
r[43] = a[43] - (b[43] & m);
r[44] = a[44] - (b[44] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_add_45(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 45; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[45] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += (sp_digit)(t[0] & 0x7fffff);
for (i = 0; i < 40; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[i+2];
r[i+2] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
t[3] = tb * a[i+3];
r[i+3] += (sp_digit)((t[2] >> 23) + (t[3] & 0x7fffff));
t[4] = tb * a[i+4];
r[i+4] += (sp_digit)((t[3] >> 23) + (t[4] & 0x7fffff));
t[5] = tb * a[i+5];
r[i+5] += (sp_digit)((t[4] >> 23) + (t[5] & 0x7fffff));
t[6] = tb * a[i+6];
r[i+6] += (sp_digit)((t[5] >> 23) + (t[6] & 0x7fffff));
t[7] = tb * a[i+7];
r[i+7] += (sp_digit)((t[6] >> 23) + (t[7] & 0x7fffff));
t[0] = tb * a[i+8];
r[i+8] += (sp_digit)((t[7] >> 23) + (t[0] & 0x7fffff));
}
t[1] = tb * a[41]; r[41] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[42]; r[42] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
t[3] = tb * a[43]; r[43] += (sp_digit)((t[2] >> 23) + (t[3] & 0x7fffff));
t[4] = tb * a[44]; r[44] += (sp_digit)((t[3] >> 23) + (t[4] & 0x7fffff));
r[45] += (sp_digit)(t[4] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_2048_norm_45(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 44; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 40; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[40+1] += a[40] >> 23;
a[40] &= 0x7fffff;
a[41+1] += a[41] >> 23;
a[41] &= 0x7fffff;
a[42+1] += a[42] >> 23;
a[42] &= 0x7fffff;
a[43+1] += a[43] >> 23;
a[43] &= 0x7fffff;
#endif
}
/* Shift the result in the high 1024 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_2048_mont_shift_45(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[44] >> 12;
n += ((int64_t)a[45]) << 11;
for (i = 0; i < 44; i++) {
r[i] = n & 0x7fffff;
n >>= 23;
n += ((int64_t)a[46 + i]) << 11;
}
r[44] = (sp_digit)n;
#else
int i;
int64_t n = a[44] >> 12;
n += ((int64_t)a[45]) << 11;
for (i = 0; i < 40; i += 8) {
r[i + 0] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 46]) << 11;
r[i + 1] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 47]) << 11;
r[i + 2] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 48]) << 11;
r[i + 3] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 49]) << 11;
r[i + 4] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 50]) << 11;
r[i + 5] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 51]) << 11;
r[i + 6] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 52]) << 11;
r[i + 7] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 53]) << 11;
}
r[40] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[86]) << 11;
r[41] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[87]) << 11;
r[42] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[88]) << 11;
r[43] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[89]) << 11;
r[44] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[45], 0, sizeof(*r) * 45U);
}
/* Reduce the number back to 2048 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_2048_mont_reduce_45(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_2048_norm_45(a + 45);
for (i=0; i<44; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_2048_mul_add_45(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0xfffL;
sp_2048_mul_add_45(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
sp_2048_mont_shift_45(a, a);
sp_2048_cond_sub_45(a, a, m, 0 - (((a[44] >> 12) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_45(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_mul_45(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_2048_mul_45(r, a, b);
sp_2048_mont_reduce_45(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_sqr_45(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_2048_sqr_45(r, a);
sp_2048_mont_reduce_45(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_d_45(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 45; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[45] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 40; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[41];
r[41] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[42];
r[42] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[43];
r[43] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[44];
r[44] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
r[45] = (sp_digit)(t[4] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_2048_cond_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 40; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[40] = a[40] + (b[40] & m);
r[41] = a[41] + (b[41] & m);
r[42] = a[42] + (b[42] & m);
r[43] = a[43] + (b[43] & m);
r[44] = a[44] + (b[44] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_45(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 45; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_2048_rshift_45(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<44; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (23 - n))) & 0x7fffff;
}
#else
for (i=0; i<40; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (23 - n))) & 0x7fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (23 - n))) & 0x7fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (23 - n))) & 0x7fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (23 - n))) & 0x7fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (23 - n))) & 0x7fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (23 - n))) & 0x7fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (23 - n))) & 0x7fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (23 - n))) & 0x7fffff;
}
r[40] = ((a[40] >> n) | (a[41] << (23 - n))) & 0x7fffff;
r[41] = ((a[41] >> n) | (a[42] << (23 - n))) & 0x7fffff;
r[42] = ((a[42] >> n) | (a[43] << (23 - n))) & 0x7fffff;
r[43] = ((a[43] >> n) | (a[44] << (23 - n))) & 0x7fffff;
#endif
r[44] = a[44] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_2048_div_word_45(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_div_45(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[90 + 1], t2d[45 + 1], sdd[45 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 45 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
(void)m;
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 90 + 1;
sd = t2 + 45 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_2048_mul_d_45(sd, d, 1L << 11);
sp_2048_mul_d_90(t1, a, 1L << 11);
dv = sd[44];
for (i=45; i>=0; i--) {
t1[45 + i] += t1[45 + i - 1] >> 23;
t1[45 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[45 + i];
d1 <<= 23;
d1 += t1[45 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_2048_div_word_45(t1[45 + i], t1[45 + i - 1], dv);
#endif
sp_2048_mul_d_45(t2, sd, r1);
(void)sp_2048_sub_45(&t1[i], &t1[i], t2);
t1[45 + i] -= t2[45];
t1[45 + i] += t1[45 + i - 1] >> 23;
t1[45 + i - 1] &= 0x7fffff;
r1 = (((-t1[45 + i]) << 23) - t1[45 + i - 1]) / dv;
r1 -= t1[45 + i];
sp_2048_mul_d_45(t2, sd, r1);
(void)sp_2048_add_45(&t1[i], &t1[i], t2);
t1[45 + i] += t1[45 + i - 1] >> 23;
t1[45 + i - 1] &= 0x7fffff;
}
t1[45 - 1] += t1[45 - 2] >> 23;
t1[45 - 2] &= 0x7fffff;
r1 = t1[45 - 1] / dv;
sp_2048_mul_d_45(t2, sd, r1);
sp_2048_sub_45(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 45U);
for (i=0; i<43; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_2048_cond_add_45(r, r, sd, 0 - ((r[44] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_45(r);
sp_2048_rshift_45(r, r, 11);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_mod_45(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_2048_div_45(a, m, NULL, r);
}
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_2048_mod_exp_45(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 45 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 45U * 2U);
norm = t[0] = td;
t[1] = &td[45 * 2];
t[2] = &td[2 * 45 * 2];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_45(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_45(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 45U);
}
}
if (err == MP_OKAY) {
sp_2048_mul_45(t[1], t[1], norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_45(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 45 * 2);
sp_2048_mont_sqr_45(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 45 * 2);
}
sp_2048_mont_reduce_45(t[0], m, mp);
n = sp_2048_cmp_45(t[0], m);
sp_2048_cond_sub_45(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 45 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][90];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 45 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[45 * 2];
t[2] = &td[2 * 45 * 2];
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_45(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_45(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_45(t[1], t[1], norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
else {
sp_2048_mul_45(t[1], a, norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_45(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_2048_mont_sqr_45(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_2048_mont_reduce_45(t[0], m, mp);
n = sp_2048_cmp_45(t[0], m);
sp_2048_cond_sub_45(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][90];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[90];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 90, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 90;
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_45(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_45(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_45(t[1], t[1], norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
else {
sp_2048_mul_45(t[1], a, norm);
err = sp_2048_mod_45(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_2048_mont_sqr_45(t[ 2], t[ 1], m, mp);
sp_2048_mont_mul_45(t[ 3], t[ 2], t[ 1], m, mp);
sp_2048_mont_sqr_45(t[ 4], t[ 2], m, mp);
sp_2048_mont_mul_45(t[ 5], t[ 3], t[ 2], m, mp);
sp_2048_mont_sqr_45(t[ 6], t[ 3], m, mp);
sp_2048_mont_mul_45(t[ 7], t[ 4], t[ 3], m, mp);
sp_2048_mont_sqr_45(t[ 8], t[ 4], m, mp);
sp_2048_mont_mul_45(t[ 9], t[ 5], t[ 4], m, mp);
sp_2048_mont_sqr_45(t[10], t[ 5], m, mp);
sp_2048_mont_mul_45(t[11], t[ 6], t[ 5], m, mp);
sp_2048_mont_sqr_45(t[12], t[ 6], m, mp);
sp_2048_mont_mul_45(t[13], t[ 7], t[ 6], m, mp);
sp_2048_mont_sqr_45(t[14], t[ 7], m, mp);
sp_2048_mont_mul_45(t[15], t[ 8], t[ 7], m, mp);
sp_2048_mont_sqr_45(t[16], t[ 8], m, mp);
sp_2048_mont_mul_45(t[17], t[ 9], t[ 8], m, mp);
sp_2048_mont_sqr_45(t[18], t[ 9], m, mp);
sp_2048_mont_mul_45(t[19], t[10], t[ 9], m, mp);
sp_2048_mont_sqr_45(t[20], t[10], m, mp);
sp_2048_mont_mul_45(t[21], t[11], t[10], m, mp);
sp_2048_mont_sqr_45(t[22], t[11], m, mp);
sp_2048_mont_mul_45(t[23], t[12], t[11], m, mp);
sp_2048_mont_sqr_45(t[24], t[12], m, mp);
sp_2048_mont_mul_45(t[25], t[13], t[12], m, mp);
sp_2048_mont_sqr_45(t[26], t[13], m, mp);
sp_2048_mont_mul_45(t[27], t[14], t[13], m, mp);
sp_2048_mont_sqr_45(t[28], t[14], m, mp);
sp_2048_mont_mul_45(t[29], t[15], t[14], m, mp);
sp_2048_mont_sqr_45(t[30], t[15], m, mp);
sp_2048_mont_mul_45(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 45) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_sqr_45(rt, rt, m, mp);
sp_2048_mont_mul_45(rt, rt, t[y], m, mp);
}
sp_2048_mont_reduce_45(rt, m, mp);
n = sp_2048_cmp_45(rt, m);
sp_2048_cond_sub_45(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 2048 bits, just need to subtract.
*
* r A single precision number.
* m A single precision number.
*/
static void sp_2048_mont_norm_90(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<89; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[88] = 0x7fffff;
#endif
r[89] = 0x1L;
/* r = (2^n - 1) mod n */
(void)sp_2048_sub_90(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_2048_cmp_90(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=89; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[89] - b[89]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[88] - b[88]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 80; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_2048_cond_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[88] = a[88] - (b[88] & m);
r[89] = a[89] - (b[89] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_add_90(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 90; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[90] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += (sp_digit)(t[0] & 0x7fffff);
for (i = 0; i < 88; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[i+2];
r[i+2] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
t[3] = tb * a[i+3];
r[i+3] += (sp_digit)((t[2] >> 23) + (t[3] & 0x7fffff));
t[4] = tb * a[i+4];
r[i+4] += (sp_digit)((t[3] >> 23) + (t[4] & 0x7fffff));
t[5] = tb * a[i+5];
r[i+5] += (sp_digit)((t[4] >> 23) + (t[5] & 0x7fffff));
t[6] = tb * a[i+6];
r[i+6] += (sp_digit)((t[5] >> 23) + (t[6] & 0x7fffff));
t[7] = tb * a[i+7];
r[i+7] += (sp_digit)((t[6] >> 23) + (t[7] & 0x7fffff));
t[0] = tb * a[i+8];
r[i+8] += (sp_digit)((t[7] >> 23) + (t[0] & 0x7fffff));
}
t[1] = tb * a[89]; r[89] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
r[90] += (sp_digit)(t[1] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_2048_norm_90(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 89; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 88; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[88+1] += a[88] >> 23;
a[88] &= 0x7fffff;
#endif
}
/* Shift the result in the high 2048 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_2048_mont_shift_90(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[89] >> 1;
n += ((int64_t)a[90]) << 22;
for (i = 0; i < 89; i++) {
r[i] = n & 0x7fffff;
n >>= 23;
n += ((int64_t)a[91 + i]) << 22;
}
r[89] = (sp_digit)n;
#else
int i;
int64_t n = a[89] >> 1;
n += ((int64_t)a[90]) << 22;
for (i = 0; i < 88; i += 8) {
r[i + 0] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 91]) << 22;
r[i + 1] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 92]) << 22;
r[i + 2] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 93]) << 22;
r[i + 3] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 94]) << 22;
r[i + 4] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 95]) << 22;
r[i + 5] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 96]) << 22;
r[i + 6] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 97]) << 22;
r[i + 7] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 98]) << 22;
}
r[88] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[179]) << 22;
r[89] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[90], 0, sizeof(*r) * 90U);
}
/* Reduce the number back to 2048 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_2048_mont_reduce_90(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_2048_norm_90(a + 90);
#ifdef WOLFSSL_SP_DH
if (mp != 1) {
for (i=0; i<89; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1L;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
else {
for (i=0; i<89; i++) {
mu = a[i] & 0x7fffff;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = a[i] & 0x1L;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
for (i=0; i<89; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1L;
sp_2048_mul_add_90(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
#endif
sp_2048_mont_shift_90(a, a);
sp_2048_cond_sub_90(a, a, m, 0 - (((a[89] >> 1) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_90(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_mul_90(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_2048_mul_90(r, a, b);
sp_2048_mont_reduce_90(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_2048_mont_sqr_90(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_2048_sqr_90(r, a);
sp_2048_mont_reduce_90(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_2048_mul_d_180(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 180; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[180] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 176; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[177];
r[177] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[178];
r[178] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[179];
r[179] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
r[180] = (sp_digit)(t[3] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_2048_cond_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 88; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[88] = a[88] + (b[88] & m);
r[89] = a[89] + (b[89] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_sub_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_2048_add_90(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 90; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_2048_rshift_90(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<89; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (23 - n))) & 0x7fffff;
}
#else
for (i=0; i<88; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (23 - n))) & 0x7fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (23 - n))) & 0x7fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (23 - n))) & 0x7fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (23 - n))) & 0x7fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (23 - n))) & 0x7fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (23 - n))) & 0x7fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (23 - n))) & 0x7fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (23 - n))) & 0x7fffff;
}
r[88] = ((a[88] >> n) | (a[89] << (23 - n))) & 0x7fffff;
#endif
r[89] = a[89] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_2048_div_word_90(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_div_90(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[180 + 1], t2d[90 + 1], sdd[90 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 90 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
(void)m;
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 180 + 1;
sd = t2 + 90 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_2048_mul_d_90(sd, d, 1L << 22);
sp_2048_mul_d_180(t1, a, 1L << 22);
dv = sd[89];
for (i=90; i>=0; i--) {
t1[90 + i] += t1[90 + i - 1] >> 23;
t1[90 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[90 + i];
d1 <<= 23;
d1 += t1[90 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_2048_div_word_90(t1[90 + i], t1[90 + i - 1], dv);
#endif
sp_2048_mul_d_90(t2, sd, r1);
(void)sp_2048_sub_90(&t1[i], &t1[i], t2);
t1[90 + i] -= t2[90];
t1[90 + i] += t1[90 + i - 1] >> 23;
t1[90 + i - 1] &= 0x7fffff;
r1 = (((-t1[90 + i]) << 23) - t1[90 + i - 1]) / dv;
r1 -= t1[90 + i];
sp_2048_mul_d_90(t2, sd, r1);
(void)sp_2048_add_90(&t1[i], &t1[i], t2);
t1[90 + i] += t1[90 + i - 1] >> 23;
t1[90 + i - 1] &= 0x7fffff;
}
t1[90 - 1] += t1[90 - 2] >> 23;
t1[90 - 2] &= 0x7fffff;
r1 = t1[90 - 1] / dv;
sp_2048_mul_d_90(t2, sd, r1);
sp_2048_sub_90(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 90U);
for (i=0; i<88; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_2048_cond_add_90(r, r, sd, 0 - ((r[89] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_2048_norm_90(r);
sp_2048_rshift_90(r, r, 22);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_2048_mod_90(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_2048_div_90(a, m, NULL, r);
}
#if (defined(WOLFSSL_HAVE_SP_RSA) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)) || \
defined(WOLFSSL_HAVE_SP_DH)
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_2048_mod_exp_90(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 90 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 90U * 2U);
norm = t[0] = td;
t[1] = &td[90 * 2];
t[2] = &td[2 * 90 * 2];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_90(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 90U);
}
}
if (err == MP_OKAY) {
sp_2048_mul_90(t[1], t[1], norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_90(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 90 * 2);
sp_2048_mont_sqr_90(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 90 * 2);
}
sp_2048_mont_reduce_90(t[0], m, mp);
n = sp_2048_cmp_90(t[0], m);
sp_2048_cond_sub_90(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 90 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][180];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 90 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[90 * 2];
t[2] = &td[2 * 90 * 2];
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_90(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_90(t[1], t[1], norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
else {
sp_2048_mul_90(t[1], a, norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_2048_mont_mul_90(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_2048_mont_sqr_90(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_2048_mont_reduce_90(t[0], m, mp);
n = sp_2048_cmp_90(t[0], m);
sp_2048_cond_sub_90(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][180];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[180];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 180, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 180;
#endif
norm = t[0];
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
if (reduceA != 0) {
err = sp_2048_mod_90(t[1], a, m);
if (err == MP_OKAY) {
sp_2048_mul_90(t[1], t[1], norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
else {
sp_2048_mul_90(t[1], a, norm);
err = sp_2048_mod_90(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_2048_mont_sqr_90(t[ 2], t[ 1], m, mp);
sp_2048_mont_mul_90(t[ 3], t[ 2], t[ 1], m, mp);
sp_2048_mont_sqr_90(t[ 4], t[ 2], m, mp);
sp_2048_mont_mul_90(t[ 5], t[ 3], t[ 2], m, mp);
sp_2048_mont_sqr_90(t[ 6], t[ 3], m, mp);
sp_2048_mont_mul_90(t[ 7], t[ 4], t[ 3], m, mp);
sp_2048_mont_sqr_90(t[ 8], t[ 4], m, mp);
sp_2048_mont_mul_90(t[ 9], t[ 5], t[ 4], m, mp);
sp_2048_mont_sqr_90(t[10], t[ 5], m, mp);
sp_2048_mont_mul_90(t[11], t[ 6], t[ 5], m, mp);
sp_2048_mont_sqr_90(t[12], t[ 6], m, mp);
sp_2048_mont_mul_90(t[13], t[ 7], t[ 6], m, mp);
sp_2048_mont_sqr_90(t[14], t[ 7], m, mp);
sp_2048_mont_mul_90(t[15], t[ 8], t[ 7], m, mp);
sp_2048_mont_sqr_90(t[16], t[ 8], m, mp);
sp_2048_mont_mul_90(t[17], t[ 9], t[ 8], m, mp);
sp_2048_mont_sqr_90(t[18], t[ 9], m, mp);
sp_2048_mont_mul_90(t[19], t[10], t[ 9], m, mp);
sp_2048_mont_sqr_90(t[20], t[10], m, mp);
sp_2048_mont_mul_90(t[21], t[11], t[10], m, mp);
sp_2048_mont_sqr_90(t[22], t[11], m, mp);
sp_2048_mont_mul_90(t[23], t[12], t[11], m, mp);
sp_2048_mont_sqr_90(t[24], t[12], m, mp);
sp_2048_mont_mul_90(t[25], t[13], t[12], m, mp);
sp_2048_mont_sqr_90(t[26], t[13], m, mp);
sp_2048_mont_mul_90(t[27], t[14], t[13], m, mp);
sp_2048_mont_sqr_90(t[28], t[14], m, mp);
sp_2048_mont_mul_90(t[29], t[15], t[14], m, mp);
sp_2048_mont_sqr_90(t[30], t[15], m, mp);
sp_2048_mont_mul_90(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 90) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_sqr_90(rt, rt, m, mp);
sp_2048_mont_mul_90(rt, rt, t[y], m, mp);
}
sp_2048_mont_reduce_90(rt, m, mp);
n = sp_2048_cmp_90(rt, m);
sp_2048_cond_sub_90(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) || */
/* WOLFSSL_HAVE_SP_DH */
#ifdef WOLFSSL_HAVE_SP_RSA
/* RSA public key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* em Public exponent.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 256 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPublic_2048(const byte* in, word32 inLen, mp_int* em, mp_int* mm,
byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* d = NULL;
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit* norm;
sp_digit e[1] = {0};
sp_digit mp;
int i;
int err = MP_OKAY;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 90 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
a = d;
r = a + 90 * 2;
m = r + 90 * 2;
norm = r;
sp_2048_from_bin(a, 90, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_mp(m, 90, mm);
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
}
if (err == MP_OKAY) {
sp_2048_mul_90(a, a, norm);
err = sp_2048_mod_90(a, a, m);
}
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 90 * 2);
for (i--; i>=0; i--) {
sp_2048_mont_sqr_90(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_2048_mont_mul_90(r, r, a, m, mp);
}
}
sp_2048_mont_reduce_90(r, m, mp);
mp = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0)- 1);
sp_2048_to_bin(r, out);
*outLen = 256;
}
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit ad[180], md[90], rd[180];
#else
sp_digit* d = NULL;
#endif
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit e[1] = {0};
int err = MP_OKAY;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 90 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d;
r = a + 90 * 2;
m = r + 90 * 2;
}
#else
a = ad;
m = md;
r = rd;
#endif
if (err == MP_OKAY) {
sp_2048_from_bin(a, 90, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_mp(m, 90, mm);
if (e[0] == 0x3) {
sp_2048_sqr_90(r, a);
err = sp_2048_mod_90(r, r, m);
if (err == MP_OKAY) {
sp_2048_mul_90(r, a, r);
err = sp_2048_mod_90(r, r, m);
}
}
else {
sp_digit* norm = r;
int i;
sp_digit mp;
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
sp_2048_mul_90(a, a, norm);
err = sp_2048_mod_90(a, a, m);
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 180U);
for (i--; i>=0; i--) {
sp_2048_mont_sqr_90(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_2048_mont_mul_90(r, r, a, m, mp);
}
}
sp_2048_mont_reduce_90(r, m, mp);
mp = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
}
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
#endif
return err;
#endif /* WOLFSSL_SP_SMALL */
}
#ifndef WOLFSSL_RSA_PUBLIC_ONLY
#if !defined(SP_RSA_PRIVATE_EXP_D) && !defined(RSA_LOW_MEM)
#endif /* !SP_RSA_PRIVATE_EXP_D && !RSA_LOW_MEM */
/* RSA private key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* dm Private exponent.
* pm First prime.
* qm Second prime.
* dpm First prime's CRT exponent.
* dqm Second prime's CRT exponent.
* qim Inverse of second prime mod p.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 256 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPrivate_2048(const byte* in, word32 inLen, mp_int* dm,
mp_int* pm, mp_int* qm, mp_int* dpm, mp_int* dqm, mp_int* qim, mp_int* mm,
byte* out, word32* outLen)
{
#if defined(SP_RSA_PRIVATE_EXP_D) || defined(RSA_LOW_MEM)
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* a;
sp_digit* d = NULL;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 2048) {
err = MP_READ_E;
}
if (inLen > 256) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 90 * 4, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d + 90;
m = a + 180;
r = a;
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(d, 90, dm);
sp_2048_from_mp(m, 90, mm);
err = sp_2048_mod_exp_90(r, a, d, 2048, m, 0);
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
}
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 90);
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[180], d[90], m[90];
sp_digit* r = a;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 2048) {
err = MP_READ_E;
}
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(d, 90, dm);
sp_2048_from_mp(m, 90, mm);
err = sp_2048_mod_exp_90(r, a, d, 2048, m, 0);
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
}
XMEMSET(d, 0, sizeof(sp_digit) * 90);
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#else
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* t = NULL;
sp_digit* a;
sp_digit* p;
sp_digit* q;
sp_digit* dp;
sp_digit* dq;
sp_digit* qi;
sp_digit* tmpa;
sp_digit* tmpb;
sp_digit* r;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 256) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 45 * 11, NULL,
DYNAMIC_TYPE_RSA);
if (t == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = t;
p = a + 90 * 2;
q = p + 45;
qi = dq = dp = q + 45;
tmpa = qi + 45;
tmpb = tmpa + 90;
r = t + 90;
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(p, 45, pm);
sp_2048_from_mp(q, 45, qm);
sp_2048_from_mp(dp, 45, dpm);
err = sp_2048_mod_exp_45(tmpa, a, dp, 1024, p, 1);
}
if (err == MP_OKAY) {
sp_2048_from_mp(dq, 45, dqm);
err = sp_2048_mod_exp_45(tmpb, a, dq, 1024, q, 1);
}
if (err == MP_OKAY) {
(void)sp_2048_sub_45(tmpa, tmpa, tmpb);
sp_2048_cond_add_45(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[44] >> 31));
sp_2048_cond_add_45(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[44] >> 31));
sp_2048_from_mp(qi, 45, qim);
sp_2048_mul_45(tmpa, tmpa, qi);
err = sp_2048_mod_45(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_2048_mul_45(tmpa, q, tmpa);
(void)sp_2048_add_90(r, tmpb, tmpa);
sp_2048_norm_90(r);
sp_2048_to_bin(r, out);
*outLen = 256;
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_digit) * 45 * 11);
XFREE(t, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[90 * 2];
sp_digit p[45], q[45], dp[45], dq[45], qi[45];
sp_digit tmpa[90], tmpb[90];
sp_digit* r = a;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 256U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 256U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_2048_from_bin(a, 90, in, inLen);
sp_2048_from_mp(p, 45, pm);
sp_2048_from_mp(q, 45, qm);
sp_2048_from_mp(dp, 45, dpm);
sp_2048_from_mp(dq, 45, dqm);
sp_2048_from_mp(qi, 45, qim);
err = sp_2048_mod_exp_45(tmpa, a, dp, 1024, p, 1);
}
if (err == MP_OKAY) {
err = sp_2048_mod_exp_45(tmpb, a, dq, 1024, q, 1);
}
if (err == MP_OKAY) {
(void)sp_2048_sub_45(tmpa, tmpa, tmpb);
sp_2048_cond_add_45(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[44] >> 31));
sp_2048_cond_add_45(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[44] >> 31));
sp_2048_mul_45(tmpa, tmpa, qi);
err = sp_2048_mod_45(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_2048_mul_45(tmpa, tmpa, q);
(void)sp_2048_add_90(r, tmpb, tmpa);
sp_2048_norm_90(r);
sp_2048_to_bin(r, out);
*outLen = 256;
}
XMEMSET(tmpa, 0, sizeof(tmpa));
XMEMSET(tmpb, 0, sizeof(tmpb));
XMEMSET(p, 0, sizeof(p));
XMEMSET(q, 0, sizeof(q));
XMEMSET(dp, 0, sizeof(dp));
XMEMSET(dq, 0, sizeof(dq));
XMEMSET(qi, 0, sizeof(qi));
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#endif /* SP_RSA_PRIVATE_EXP_D || RSA_LOW_MEM */
}
#endif /* !WOLFSSL_RSA_PUBLIC_ONLY */
#endif /* WOLFSSL_HAVE_SP_RSA */
#if defined(WOLFSSL_HAVE_SP_DH) || (defined(WOLFSSL_HAVE_SP_RSA) && \
!defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_2048_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (2048 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 23
XMEMCPY(r->dp, a, sizeof(sp_digit) * 90);
r->used = 90;
mp_clamp(r);
#elif DIGIT_BIT < 23
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 90; i++) {
r->dp[j] |= (mp_digit)(a[i] << s);
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = (mp_digit)(a[i] >> s);
while (s + DIGIT_BIT <= 23) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = (mp_digit)(a[i] >> s);
}
}
s = 23 - s;
}
r->used = (2048 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 90; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 23 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 23 - s;
}
else {
s += 23;
}
}
r->used = (2048 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_2048(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
sp_2048_from_mp(b, 90, base);
sp_2048_from_mp(e, 90, exp);
sp_2048_from_mp(m, 90, mod);
err = sp_2048_mod_exp_90(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
err = sp_2048_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[180], ed[90], md[90];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_2048_from_mp(b, 90, base);
sp_2048_from_mp(e, 90, exp);
sp_2048_from_mp(m, 90, mod);
err = sp_2048_mod_exp_90(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
err = sp_2048_to_mp(r, res);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
#endif
return err;
#endif
}
#ifdef WOLFSSL_HAVE_SP_DH
#ifdef HAVE_FFDHE_2048
SP_NOINLINE static void sp_2048_lshift_90(sp_digit* r, sp_digit* a, byte n)
{
#ifdef WOLFSSL_SP_SMALL
int i;
r[90] = a[89] >> (23 - n);
for (i=89; i>0; i--) {
r[i] = ((a[i] << n) | (a[i-1] >> (23 - n))) & 0x7fffff;
}
#else
sp_int_digit s, t;
s = (sp_int_digit)a[89];
r[90] = s >> (23U - n);
s = (sp_int_digit)(a[89]); t = (sp_int_digit)(a[88]);
r[89] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[88]); t = (sp_int_digit)(a[87]);
r[88] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[87]); t = (sp_int_digit)(a[86]);
r[87] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[86]); t = (sp_int_digit)(a[85]);
r[86] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[85]); t = (sp_int_digit)(a[84]);
r[85] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[84]); t = (sp_int_digit)(a[83]);
r[84] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[83]); t = (sp_int_digit)(a[82]);
r[83] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[82]); t = (sp_int_digit)(a[81]);
r[82] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[81]); t = (sp_int_digit)(a[80]);
r[81] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[80]); t = (sp_int_digit)(a[79]);
r[80] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[79]); t = (sp_int_digit)(a[78]);
r[79] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[78]); t = (sp_int_digit)(a[77]);
r[78] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[77]); t = (sp_int_digit)(a[76]);
r[77] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[76]); t = (sp_int_digit)(a[75]);
r[76] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[75]); t = (sp_int_digit)(a[74]);
r[75] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[74]); t = (sp_int_digit)(a[73]);
r[74] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[73]); t = (sp_int_digit)(a[72]);
r[73] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[72]); t = (sp_int_digit)(a[71]);
r[72] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[71]); t = (sp_int_digit)(a[70]);
r[71] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[70]); t = (sp_int_digit)(a[69]);
r[70] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[69]); t = (sp_int_digit)(a[68]);
r[69] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[68]); t = (sp_int_digit)(a[67]);
r[68] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[67]); t = (sp_int_digit)(a[66]);
r[67] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[66]); t = (sp_int_digit)(a[65]);
r[66] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[65]); t = (sp_int_digit)(a[64]);
r[65] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[64]); t = (sp_int_digit)(a[63]);
r[64] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[63]); t = (sp_int_digit)(a[62]);
r[63] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[62]); t = (sp_int_digit)(a[61]);
r[62] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[61]); t = (sp_int_digit)(a[60]);
r[61] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[60]); t = (sp_int_digit)(a[59]);
r[60] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[59]); t = (sp_int_digit)(a[58]);
r[59] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[58]); t = (sp_int_digit)(a[57]);
r[58] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[57]); t = (sp_int_digit)(a[56]);
r[57] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[56]); t = (sp_int_digit)(a[55]);
r[56] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[55]); t = (sp_int_digit)(a[54]);
r[55] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[54]); t = (sp_int_digit)(a[53]);
r[54] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[53]); t = (sp_int_digit)(a[52]);
r[53] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[52]); t = (sp_int_digit)(a[51]);
r[52] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[51]); t = (sp_int_digit)(a[50]);
r[51] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[50]); t = (sp_int_digit)(a[49]);
r[50] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[49]); t = (sp_int_digit)(a[48]);
r[49] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[48]); t = (sp_int_digit)(a[47]);
r[48] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[47]); t = (sp_int_digit)(a[46]);
r[47] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[46]); t = (sp_int_digit)(a[45]);
r[46] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[45]); t = (sp_int_digit)(a[44]);
r[45] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[44]); t = (sp_int_digit)(a[43]);
r[44] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[43]); t = (sp_int_digit)(a[42]);
r[43] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[42]); t = (sp_int_digit)(a[41]);
r[42] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[41]); t = (sp_int_digit)(a[40]);
r[41] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[40]); t = (sp_int_digit)(a[39]);
r[40] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[39]); t = (sp_int_digit)(a[38]);
r[39] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[38]); t = (sp_int_digit)(a[37]);
r[38] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[37]); t = (sp_int_digit)(a[36]);
r[37] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[36]); t = (sp_int_digit)(a[35]);
r[36] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[35]); t = (sp_int_digit)(a[34]);
r[35] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[34]); t = (sp_int_digit)(a[33]);
r[34] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[33]); t = (sp_int_digit)(a[32]);
r[33] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[32]); t = (sp_int_digit)(a[31]);
r[32] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[31]); t = (sp_int_digit)(a[30]);
r[31] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[30]); t = (sp_int_digit)(a[29]);
r[30] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[29]); t = (sp_int_digit)(a[28]);
r[29] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[28]); t = (sp_int_digit)(a[27]);
r[28] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[27]); t = (sp_int_digit)(a[26]);
r[27] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[26]); t = (sp_int_digit)(a[25]);
r[26] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[25]); t = (sp_int_digit)(a[24]);
r[25] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[24]); t = (sp_int_digit)(a[23]);
r[24] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[23]); t = (sp_int_digit)(a[22]);
r[23] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[22]); t = (sp_int_digit)(a[21]);
r[22] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[21]); t = (sp_int_digit)(a[20]);
r[21] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[20]); t = (sp_int_digit)(a[19]);
r[20] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[19]); t = (sp_int_digit)(a[18]);
r[19] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[18]); t = (sp_int_digit)(a[17]);
r[18] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[17]); t = (sp_int_digit)(a[16]);
r[17] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[16]); t = (sp_int_digit)(a[15]);
r[16] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[15]); t = (sp_int_digit)(a[14]);
r[15] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[14]); t = (sp_int_digit)(a[13]);
r[14] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[13]); t = (sp_int_digit)(a[12]);
r[13] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[12]); t = (sp_int_digit)(a[11]);
r[12] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[11]); t = (sp_int_digit)(a[10]);
r[11] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[10]); t = (sp_int_digit)(a[9]);
r[10] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[9]); t = (sp_int_digit)(a[8]);
r[9] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[8]); t = (sp_int_digit)(a[7]);
r[8] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[7]); t = (sp_int_digit)(a[6]);
r[7] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[6]); t = (sp_int_digit)(a[5]);
r[6] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[5]); t = (sp_int_digit)(a[4]);
r[5] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[4]); t = (sp_int_digit)(a[3]);
r[4] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[3]); t = (sp_int_digit)(a[2]);
r[3] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[2]); t = (sp_int_digit)(a[1]);
r[2] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[1]); t = (sp_int_digit)(a[0]);
r[1] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
#endif
r[0] = (a[0] << n) & 0x7fffff;
}
/* Modular exponentiate 2 to the e mod m. (r = 2^e mod m)
*
* r A single precision number that is the result of the operation.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_2048_mod_exp_2_90(sp_digit* r, const sp_digit* e, int bits, const sp_digit* m)
{
#ifndef WOLFSSL_SMALL_STACK
sp_digit nd[180];
sp_digit td[91];
#else
sp_digit* td;
#endif
sp_digit* norm;
sp_digit* tmp;
sp_digit mp = 1;
sp_digit n, o;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 271, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
norm = td;
tmp = td + 180;
XMEMSET(td, 0, sizeof(sp_digit) * 271);
#else
norm = nd;
tmp = td;
XMEMSET(td, 0, sizeof(td));
#endif
sp_2048_mont_setup(m, &mp);
sp_2048_mont_norm_90(norm, m);
bits = ((bits + 3) / 4) * 4;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 90) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_2048_lshift_90(r, norm, y);
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_mont_sqr_90(r, r, m, mp);
sp_2048_lshift_90(r, r, y);
sp_2048_mul_d_90(tmp, norm, (r[90] << 22) + (r[89] >> 1));
r[90] = 0;
r[89] &= 0x1L;
(void)sp_2048_add_90(r, r, tmp);
sp_2048_norm_90(r);
o = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((o < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
sp_2048_mont_reduce_90(r, m, mp);
n = sp_2048_cmp_90(r, m);
sp_2048_cond_sub_90(r, r, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
#endif /* HAVE_FFDHE_2048 */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base.
* exp Array of bytes that is the exponent.
* expLen Length of data, in bytes, in exponent.
* mod Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 256 bytes long.
* outLen Length, in bytes, of exponentiation result.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_DhExp_2048(mp_int* base, const byte* exp, word32 expLen,
mp_int* mod, byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 256) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
sp_2048_from_mp(b, 90, base);
sp_2048_from_bin(e, 90, exp, expLen);
sp_2048_from_mp(m, 90, mod);
#ifdef HAVE_FFDHE_2048
if (base->used == 1 && base->dp[0] == 2 &&
((m[89] << 15) | (m[88] >> 8)) == 0xffffL) {
err = sp_2048_mod_exp_2_90(r, e, expLen * 8, m);
}
else
#endif
err = sp_2048_mod_exp_90(r, b, e, expLen * 8, m, 0);
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
for (i=0; i<256 && out[i] == 0; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[180], ed[90], md[90];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
int err = MP_OKAY;
if (mp_count_bits(base) > 2048) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 256U) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 2048) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 90 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 90 * 2;
m = e + 90;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_2048_from_mp(b, 90, base);
sp_2048_from_bin(e, 90, exp, expLen);
sp_2048_from_mp(m, 90, mod);
#ifdef HAVE_FFDHE_2048
if (base->used == 1 && base->dp[0] == 2U &&
((m[89] << 15) | (m[88] >> 8)) == 0xffffL) {
err = sp_2048_mod_exp_2_90(r, e, expLen * 8U, m);
}
else {
#endif
err = sp_2048_mod_exp_90(r, b, e, expLen * 8U, m, 0);
#ifdef HAVE_FFDHE_2048
}
#endif
}
if (err == MP_OKAY) {
sp_2048_to_bin(r, out);
*outLen = 256;
for (i=0; i<256U && out[i] == 0U; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 90U);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_1024(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1024) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1024) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1024) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 45 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 45 * 2;
m = e + 45;
r = b;
sp_2048_from_mp(b, 45, base);
sp_2048_from_mp(e, 45, exp);
sp_2048_from_mp(m, 45, mod);
err = sp_2048_mod_exp_45(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 45, 0, sizeof(*r) * 45U);
err = sp_2048_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 45U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[90], ed[45], md[45];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1024) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1024) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1024) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 45 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 45 * 2;
m = e + 45;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_2048_from_mp(b, 45, base);
sp_2048_from_mp(e, 45, exp);
sp_2048_from_mp(m, 45, mod);
err = sp_2048_mod_exp_45(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 45, 0, sizeof(*r) * 45U);
err = sp_2048_to_mp(r, res);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 45U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 45U);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH || (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) */
#endif /* !WOLFSSL_SP_NO_2048 */
#ifndef WOLFSSL_SP_NO_3072
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_3072_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 15U) {
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_3072_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 23
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 23
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x7fffff;
s = 23U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 23U) <= (word32)DIGIT_BIT) {
s += 23U;
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 23) {
r[j] &= 0x7fffff;
if (j + 1 >= size) {
break;
}
s = 23 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 384
*
* r A single precision integer.
* a Byte array.
*/
static void sp_3072_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<133; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
j = 3072 / 8 - 1;
a[j] = 0;
for (i=0; i<134 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); /*lint !e9033*/
b += 8 - s;
if (j < 0) {
break;
}
while (b < 23) {
a[j--] = (byte)(r[i] >> b);
b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 23);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
#ifndef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j;
int64_t t[134];
XMEMSET(t, 0, sizeof(t));
for (i=0; i<67; i++) {
for (j=0; j<67; j++) {
t[i+j] += ((int64_t)a[i]) * b[j];
}
}
for (i=0; i<133; i++) {
r[i] = t[i] & 0x7fffff;
t[i+1] += t[i] >> 23;
}
r[133] = (sp_digit)t[133];
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_67(sp_digit* r, const sp_digit* a)
{
int i, j;
int64_t t[134];
XMEMSET(t, 0, sizeof(t));
for (i=0; i<67; i++) {
for (j=0; j<i; j++) {
t[i+j] += (((int64_t)a[i]) * a[j]) * 2;
}
t[i+i] += ((int64_t)a[i]) * a[i];
}
for (i=0; i<133; i++) {
r[i] = t[i] & 0x7fffff;
t[i+1] += t[i] >> 23;
}
r[133] = (sp_digit)t[133];
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[64] = a[64] + b[64];
r[65] = a[65] + b[65];
r[66] = a[66] + b[66];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[128] = a[128] + b[128];
r[129] = a[129] + b[129];
r[130] = a[130] + b[130];
r[131] = a[131] + b[131];
r[132] = a[132] + b[132];
r[133] = a[133] + b[133];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[128] = a[128] - b[128];
r[129] = a[129] - b[129];
r[130] = a[130] - b[130];
r[131] = a[131] - b[131];
r[132] = a[132] - b[132];
r[133] = a[133] - b[133];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit* z0 = r;
sp_digit z1[134];
sp_digit* a1 = z1;
sp_digit b1[67];
sp_digit* z2 = r + 134;
(void)sp_3072_add_67(a1, a, &a[67]);
(void)sp_3072_add_67(b1, b, &b[67]);
sp_3072_mul_67(z2, &a[67], &b[67]);
sp_3072_mul_67(z0, a, b);
sp_3072_mul_67(z1, a1, b1);
(void)sp_3072_sub_134(z1, z1, z2);
(void)sp_3072_sub_134(z1, z1, z0);
(void)sp_3072_add_134(r + 67, r + 67, z1);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_134(sp_digit* r, const sp_digit* a)
{
sp_digit* z0 = r;
sp_digit z1[134];
sp_digit* a1 = z1;
sp_digit* z2 = r + 134;
(void)sp_3072_add_67(a1, a, &a[67]);
sp_3072_sqr_67(z2, &a[67]);
sp_3072_sqr_67(z0, a);
sp_3072_sqr_67(z1, a1);
(void)sp_3072_sub_134(z1, z1, z2);
(void)sp_3072_sub_134(z1, z1, z0);
(void)sp_3072_add_134(r + 67, r + 67, z1);
}
#endif /* !WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[133]) * b[133];
r[267] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 265; k >= 0; k--) {
for (i = 133; i >= 0; i--) {
j = k - i;
if (j >= 134) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_134(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[133]) * a[133];
r[267] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 265; k >= 0; k--) {
for (i = 133; i >= 0; i--) {
j = k - i;
if (j >= 134 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[64] = a[64] - b[64];
r[65] = a[65] - b[65];
r[66] = a[66] - b[66];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_3072_mul_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[66]) * b[66];
r[133] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 131; k >= 0; k--) {
for (i = 66; i >= 0; i--) {
j = k - i;
if (j >= 67) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_3072_sqr_67(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[66]) * a[66];
r[133] = (sp_digit)(c >> 23);
c = (c & 0x7fffff) << 23;
for (k = 131; k >= 0; k--) {
for (i = 66; i >= 0; i--) {
j = k - i;
if (j >= 67 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 46;
r[k + 1] = (c >> 23) & 0x7fffff;
c = (c & 0x7fffff) << 23;
}
r[0] = (sp_digit)(c >> 23);
}
#endif /* WOLFSSL_SP_SMALL */
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* Caclulate the bottom digit of -1/a mod 2^n.
*
* a A single precision number.
* rho Bottom word of inverse.
*/
static void sp_3072_mont_setup(const sp_digit* a, sp_digit* rho)
{
sp_digit x, b;
b = a[0];
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
x &= 0x7fffff;
/* rho = -1/m mod b */
*rho = (1L << 23) - x;
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_d_134(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 134; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[134] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 128; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[129];
r[129] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[130];
r[130] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[131];
r[131] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[132];
r[132] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[133];
r[133] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
r[134] = (sp_digit)(t[5] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 3072 bits, just need to subtract.
*
* r A single precision number.
* m A single precision number.
*/
static void sp_3072_mont_norm_67(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<66; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[64] = 0x7fffff;
r[65] = 0x7fffff;
#endif
r[66] = 0x3ffffL;
/* r = (2^n - 1) mod n */
(void)sp_3072_sub_67(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_3072_cmp_67(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=66; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[66] - b[66]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[65] - b[65]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[64] - b[64]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 56; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_3072_cond_sub_67(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[64] = a[64] - (b[64] & m);
r[65] = a[65] - (b[65] & m);
r[66] = a[66] - (b[66] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_add_67(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 67; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[67] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += (sp_digit)(t[0] & 0x7fffff);
for (i = 0; i < 64; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[i+2];
r[i+2] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
t[3] = tb * a[i+3];
r[i+3] += (sp_digit)((t[2] >> 23) + (t[3] & 0x7fffff));
t[4] = tb * a[i+4];
r[i+4] += (sp_digit)((t[3] >> 23) + (t[4] & 0x7fffff));
t[5] = tb * a[i+5];
r[i+5] += (sp_digit)((t[4] >> 23) + (t[5] & 0x7fffff));
t[6] = tb * a[i+6];
r[i+6] += (sp_digit)((t[5] >> 23) + (t[6] & 0x7fffff));
t[7] = tb * a[i+7];
r[i+7] += (sp_digit)((t[6] >> 23) + (t[7] & 0x7fffff));
t[0] = tb * a[i+8];
r[i+8] += (sp_digit)((t[7] >> 23) + (t[0] & 0x7fffff));
}
t[1] = tb * a[65]; r[65] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[66]; r[66] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
r[67] += (sp_digit)(t[2] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_3072_norm_67(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 66; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 64; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[64+1] += a[64] >> 23;
a[64] &= 0x7fffff;
a[65+1] += a[65] >> 23;
a[65] &= 0x7fffff;
#endif
}
/* Shift the result in the high 1536 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_3072_mont_shift_67(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
sp_digit n, s;
s = a[67];
n = a[66] >> 18;
for (i = 0; i < 66; i++) {
n += (s & 0x7fffff) << 5;
r[i] = n & 0x7fffff;
n >>= 23;
s = a[68 + i] + (s >> 23);
}
n += s << 5;
r[66] = n;
#else
sp_digit n, s;
int i;
s = a[67]; n = a[66] >> 18;
for (i = 0; i < 64; i += 8) {
n += (s & 0x7fffff) << 5; r[i+0] = n & 0x7fffff;
n >>= 23; s = a[i+68] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+1] = n & 0x7fffff;
n >>= 23; s = a[i+69] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+2] = n & 0x7fffff;
n >>= 23; s = a[i+70] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+3] = n & 0x7fffff;
n >>= 23; s = a[i+71] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+4] = n & 0x7fffff;
n >>= 23; s = a[i+72] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+5] = n & 0x7fffff;
n >>= 23; s = a[i+73] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+6] = n & 0x7fffff;
n >>= 23; s = a[i+74] + (s >> 23);
n += (s & 0x7fffff) << 5; r[i+7] = n & 0x7fffff;
n >>= 23; s = a[i+75] + (s >> 23);
}
n += (s & 0x7fffff) << 5; r[64] = n & 0x7fffff;
n >>= 23; s = a[132] + (s >> 23);
n += (s & 0x7fffff) << 5; r[65] = n & 0x7fffff;
n >>= 23; s = a[133] + (s >> 23);
n += s << 5; r[66] = n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[67], 0, sizeof(*r) * 67U);
}
/* Reduce the number back to 3072 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_3072_mont_reduce_67(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_3072_norm_67(a + 67);
for (i=0; i<66; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_3072_mul_add_67(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x3ffffL;
sp_3072_mul_add_67(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
sp_3072_mont_shift_67(a, a);
sp_3072_cond_sub_67(a, a, m, 0 - (((a[66] >> 18) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_3072_norm_67(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_mul_67(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_3072_mul_67(r, a, b);
sp_3072_mont_reduce_67(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_sqr_67(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_3072_sqr_67(r, a);
sp_3072_mont_reduce_67(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_d_67(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 67; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[67] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 64; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[65];
r[65] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[66];
r[66] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
r[67] = (sp_digit)(t[2] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_3072_cond_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 64; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[64] = a[64] + (b[64] & m);
r[65] = a[65] + (b[65] & m);
r[66] = a[66] + (b[66] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_67(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 67; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_3072_div_word_67(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Number to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_div_67(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[134], t2d[67 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (3 * 67 + 1), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 2 * 67;
#else
t1 = t1d;
t2 = t2d;
#endif
dv = d[66];
XMEMCPY(t1, a, sizeof(*t1) * 2U * 67U);
for (i=66; i>=0; i--) {
t1[67 + i] += t1[67 + i - 1] >> 23;
t1[67 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[67 + i];
d1 <<= 23;
d1 += t1[67 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_3072_div_word_67(t1[67 + i], t1[67 + i - 1], dv);
#endif
sp_3072_mul_d_67(t2, d, r1);
(void)sp_3072_sub_67(&t1[i], &t1[i], t2);
t1[67 + i] -= t2[67];
t1[67 + i] += t1[67 + i - 1] >> 23;
t1[67 + i - 1] &= 0x7fffff;
r1 = (((-t1[67 + i]) << 23) - t1[67 + i - 1]) / dv;
r1++;
sp_3072_mul_d_67(t2, d, r1);
(void)sp_3072_add_67(&t1[i], &t1[i], t2);
t1[67 + i] += t1[67 + i - 1] >> 23;
t1[67 + i - 1] &= 0x7fffff;
}
t1[67 - 1] += t1[67 - 2] >> 23;
t1[67 - 2] &= 0x7fffff;
r1 = t1[67 - 1] / dv;
sp_3072_mul_d_67(t2, d, r1);
(void)sp_3072_sub_67(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 67U);
for (i=0; i<65; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_3072_cond_add_67(r, r, d, 0 - ((r[66] < 0) ?
(sp_digit)1 : (sp_digit)0));
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_mod_67(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_3072_div_67(a, m, NULL, r);
}
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_3072_mod_exp_67(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 67 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 67U * 2U);
norm = t[0] = td;
t[1] = &td[67 * 2];
t[2] = &td[2 * 67 * 2];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_67(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_67(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 67U);
}
}
if (err == MP_OKAY) {
sp_3072_mul_67(t[1], t[1], norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_67(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 67 * 2);
sp_3072_mont_sqr_67(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 67 * 2);
}
sp_3072_mont_reduce_67(t[0], m, mp);
n = sp_3072_cmp_67(t[0], m);
sp_3072_cond_sub_67(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 67 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][134];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 67 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[67 * 2];
t[2] = &td[2 * 67 * 2];
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_67(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_67(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_67(t[1], t[1], norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
else {
sp_3072_mul_67(t[1], a, norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_67(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_3072_mont_sqr_67(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_3072_mont_reduce_67(t[0], m, mp);
n = sp_3072_cmp_67(t[0], m);
sp_3072_cond_sub_67(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][134];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[134];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 134, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 134;
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_67(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_67(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_67(t[1], t[1], norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
else {
sp_3072_mul_67(t[1], a, norm);
err = sp_3072_mod_67(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_3072_mont_sqr_67(t[ 2], t[ 1], m, mp);
sp_3072_mont_mul_67(t[ 3], t[ 2], t[ 1], m, mp);
sp_3072_mont_sqr_67(t[ 4], t[ 2], m, mp);
sp_3072_mont_mul_67(t[ 5], t[ 3], t[ 2], m, mp);
sp_3072_mont_sqr_67(t[ 6], t[ 3], m, mp);
sp_3072_mont_mul_67(t[ 7], t[ 4], t[ 3], m, mp);
sp_3072_mont_sqr_67(t[ 8], t[ 4], m, mp);
sp_3072_mont_mul_67(t[ 9], t[ 5], t[ 4], m, mp);
sp_3072_mont_sqr_67(t[10], t[ 5], m, mp);
sp_3072_mont_mul_67(t[11], t[ 6], t[ 5], m, mp);
sp_3072_mont_sqr_67(t[12], t[ 6], m, mp);
sp_3072_mont_mul_67(t[13], t[ 7], t[ 6], m, mp);
sp_3072_mont_sqr_67(t[14], t[ 7], m, mp);
sp_3072_mont_mul_67(t[15], t[ 8], t[ 7], m, mp);
sp_3072_mont_sqr_67(t[16], t[ 8], m, mp);
sp_3072_mont_mul_67(t[17], t[ 9], t[ 8], m, mp);
sp_3072_mont_sqr_67(t[18], t[ 9], m, mp);
sp_3072_mont_mul_67(t[19], t[10], t[ 9], m, mp);
sp_3072_mont_sqr_67(t[20], t[10], m, mp);
sp_3072_mont_mul_67(t[21], t[11], t[10], m, mp);
sp_3072_mont_sqr_67(t[22], t[11], m, mp);
sp_3072_mont_mul_67(t[23], t[12], t[11], m, mp);
sp_3072_mont_sqr_67(t[24], t[12], m, mp);
sp_3072_mont_mul_67(t[25], t[13], t[12], m, mp);
sp_3072_mont_sqr_67(t[26], t[13], m, mp);
sp_3072_mont_mul_67(t[27], t[14], t[13], m, mp);
sp_3072_mont_sqr_67(t[28], t[14], m, mp);
sp_3072_mont_mul_67(t[29], t[15], t[14], m, mp);
sp_3072_mont_sqr_67(t[30], t[15], m, mp);
sp_3072_mont_mul_67(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 67) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_sqr_67(rt, rt, m, mp);
sp_3072_mont_mul_67(rt, rt, t[y], m, mp);
}
sp_3072_mont_reduce_67(rt, m, mp);
n = sp_3072_cmp_67(rt, m);
sp_3072_cond_sub_67(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 3072 bits, just need to subtract.
*
* r A single precision number.
* m A single precision number.
*/
static void sp_3072_mont_norm_134(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<133; i++) {
r[i] = 0x7fffff;
}
#else
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = 0x7fffff;
r[i + 1] = 0x7fffff;
r[i + 2] = 0x7fffff;
r[i + 3] = 0x7fffff;
r[i + 4] = 0x7fffff;
r[i + 5] = 0x7fffff;
r[i + 6] = 0x7fffff;
r[i + 7] = 0x7fffff;
}
r[128] = 0x7fffff;
r[129] = 0x7fffff;
r[130] = 0x7fffff;
r[131] = 0x7fffff;
r[132] = 0x7fffff;
#endif
r[133] = 0x1fffL;
/* r = (2^n - 1) mod n */
(void)sp_3072_sub_134(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_3072_cmp_134(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=133; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[133] - b[133]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[132] - b[132]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[131] - b[131]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[130] - b[130]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[129] - b[129]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[128] - b[128]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 120; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_3072_cond_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[128] = a[128] - (b[128] & m);
r[129] = a[129] - (b[129] & m);
r[130] = a[130] - (b[130] & m);
r[131] = a[131] - (b[131] & m);
r[132] = a[132] - (b[132] & m);
r[133] = a[133] - (b[133] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_add_134(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 134; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[134] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += (sp_digit)(t[0] & 0x7fffff);
for (i = 0; i < 128; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[i+2];
r[i+2] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
t[3] = tb * a[i+3];
r[i+3] += (sp_digit)((t[2] >> 23) + (t[3] & 0x7fffff));
t[4] = tb * a[i+4];
r[i+4] += (sp_digit)((t[3] >> 23) + (t[4] & 0x7fffff));
t[5] = tb * a[i+5];
r[i+5] += (sp_digit)((t[4] >> 23) + (t[5] & 0x7fffff));
t[6] = tb * a[i+6];
r[i+6] += (sp_digit)((t[5] >> 23) + (t[6] & 0x7fffff));
t[7] = tb * a[i+7];
r[i+7] += (sp_digit)((t[6] >> 23) + (t[7] & 0x7fffff));
t[0] = tb * a[i+8];
r[i+8] += (sp_digit)((t[7] >> 23) + (t[0] & 0x7fffff));
}
t[1] = tb * a[129]; r[129] += (sp_digit)((t[0] >> 23) + (t[1] & 0x7fffff));
t[2] = tb * a[130]; r[130] += (sp_digit)((t[1] >> 23) + (t[2] & 0x7fffff));
t[3] = tb * a[131]; r[131] += (sp_digit)((t[2] >> 23) + (t[3] & 0x7fffff));
t[4] = tb * a[132]; r[132] += (sp_digit)((t[3] >> 23) + (t[4] & 0x7fffff));
t[5] = tb * a[133]; r[133] += (sp_digit)((t[4] >> 23) + (t[5] & 0x7fffff));
r[134] += (sp_digit)(t[5] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 23.
*
* a Array of sp_digit to normalize.
*/
static void sp_3072_norm_134(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 133; i++) {
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
int i;
for (i = 0; i < 128; i += 8) {
a[i+1] += a[i+0] >> 23; a[i+0] &= 0x7fffff;
a[i+2] += a[i+1] >> 23; a[i+1] &= 0x7fffff;
a[i+3] += a[i+2] >> 23; a[i+2] &= 0x7fffff;
a[i+4] += a[i+3] >> 23; a[i+3] &= 0x7fffff;
a[i+5] += a[i+4] >> 23; a[i+4] &= 0x7fffff;
a[i+6] += a[i+5] >> 23; a[i+5] &= 0x7fffff;
a[i+7] += a[i+6] >> 23; a[i+6] &= 0x7fffff;
a[i+8] += a[i+7] >> 23; a[i+7] &= 0x7fffff;
a[i+9] += a[i+8] >> 23; a[i+8] &= 0x7fffff;
}
a[128+1] += a[128] >> 23;
a[128] &= 0x7fffff;
a[129+1] += a[129] >> 23;
a[129] &= 0x7fffff;
a[130+1] += a[130] >> 23;
a[130] &= 0x7fffff;
a[131+1] += a[131] >> 23;
a[131] &= 0x7fffff;
a[132+1] += a[132] >> 23;
a[132] &= 0x7fffff;
#endif
}
/* Shift the result in the high 3072 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_3072_mont_shift_134(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[133] >> 13;
n += ((int64_t)a[134]) << 10;
for (i = 0; i < 133; i++) {
r[i] = n & 0x7fffff;
n >>= 23;
n += ((int64_t)a[135 + i]) << 10;
}
r[133] = (sp_digit)n;
#else
int i;
int64_t n = a[133] >> 13;
n += ((int64_t)a[134]) << 10;
for (i = 0; i < 128; i += 8) {
r[i + 0] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 135]) << 10;
r[i + 1] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 136]) << 10;
r[i + 2] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 137]) << 10;
r[i + 3] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 138]) << 10;
r[i + 4] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 139]) << 10;
r[i + 5] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 140]) << 10;
r[i + 6] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 141]) << 10;
r[i + 7] = n & 0x7fffff;
n >>= 23; n += ((int64_t)a[i + 142]) << 10;
}
r[128] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[263]) << 10;
r[129] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[264]) << 10;
r[130] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[265]) << 10;
r[131] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[266]) << 10;
r[132] = n & 0x7fffff; n >>= 23; n += ((int64_t)a[267]) << 10;
r[133] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[134], 0, sizeof(*r) * 134U);
}
/* Reduce the number back to 3072 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_3072_mont_reduce_134(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_3072_norm_134(a + 134);
#ifdef WOLFSSL_SP_DH
if (mp != 1) {
for (i=0; i<133; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1fffL;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
else {
for (i=0; i<133; i++) {
mu = a[i] & 0x7fffff;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = a[i] & 0x1fffL;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
}
#else
for (i=0; i<133; i++) {
mu = (a[i] * mp) & 0x7fffff;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
}
mu = (a[i] * mp) & 0x1fffL;
sp_3072_mul_add_134(a+i, m, mu);
a[i+1] += a[i] >> 23;
a[i] &= 0x7fffff;
#endif
sp_3072_mont_shift_134(a, a);
sp_3072_cond_sub_134(a, a, m, 0 - (((a[133] >> 13) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_3072_norm_134(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_mul_134(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_3072_mul_134(r, a, b);
sp_3072_mont_reduce_134(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_3072_mont_sqr_134(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_3072_sqr_134(r, a);
sp_3072_mont_reduce_134(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_3072_mul_d_268(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 268; i++) {
t += tb * a[i];
r[i] = t & 0x7fffff;
t >>= 23;
}
r[268] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x7fffff;
for (i = 0; i < 264; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 23) + (t[4] & 0x7fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 23) + (t[5] & 0x7fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 23) + (t[6] & 0x7fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 23) + (t[7] & 0x7fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 23) + (t[0] & 0x7fffff);
}
t[1] = tb * a[265];
r[265] = (sp_digit)(t[0] >> 23) + (t[1] & 0x7fffff);
t[2] = tb * a[266];
r[266] = (sp_digit)(t[1] >> 23) + (t[2] & 0x7fffff);
t[3] = tb * a[267];
r[267] = (sp_digit)(t[2] >> 23) + (t[3] & 0x7fffff);
r[268] = (sp_digit)(t[3] >> 23);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_3072_cond_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 128; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[128] = a[128] + (b[128] & m);
r[129] = a[129] + (b[129] & m);
r[130] = a[130] + (b[130] & m);
r[131] = a[131] + (b[131] & m);
r[132] = a[132] + (b[132] & m);
r[133] = a[133] + (b[133] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_sub_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_3072_add_134(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 134; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_3072_rshift_134(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<133; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (23 - n))) & 0x7fffff;
}
#else
for (i=0; i<128; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (23 - n))) & 0x7fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (23 - n))) & 0x7fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (23 - n))) & 0x7fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (23 - n))) & 0x7fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (23 - n))) & 0x7fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (23 - n))) & 0x7fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (23 - n))) & 0x7fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (23 - n))) & 0x7fffff;
}
r[128] = ((a[128] >> n) | (a[129] << (23 - n))) & 0x7fffff;
r[129] = ((a[129] >> n) | (a[130] << (23 - n))) & 0x7fffff;
r[130] = ((a[130] >> n) | (a[131] << (23 - n))) & 0x7fffff;
r[131] = ((a[131] >> n) | (a[132] << (23 - n))) & 0x7fffff;
r[132] = ((a[132] >> n) | (a[133] << (23 - n))) & 0x7fffff;
#endif
r[133] = a[133] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_3072_div_word_134(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 23 bits from d1 and top 8 bits from d0. */
d = (d1 << 8) | (d0 >> 15);
r = d / dv;
d -= r * dv;
/* Up to 9 bits in r */
/* Next 8 bits from d0. */
r <<= 8;
d <<= 8;
d |= (d0 >> 7) & ((1 << 8) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 17 bits in r */
/* Remaining 7 bits from d0. */
r <<= 7;
d <<= 7;
d |= d0 & ((1 << 7) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_div_134(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[268 + 1], t2d[134 + 1], sdd[134 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 134 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
(void)m;
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 268 + 1;
sd = t2 + 134 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_3072_mul_d_134(sd, d, 1L << 10);
sp_3072_mul_d_268(t1, a, 1L << 10);
dv = sd[133];
for (i=134; i>=0; i--) {
t1[134 + i] += t1[134 + i - 1] >> 23;
t1[134 + i - 1] &= 0x7fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[134 + i];
d1 <<= 23;
d1 += t1[134 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_3072_div_word_134(t1[134 + i], t1[134 + i - 1], dv);
#endif
sp_3072_mul_d_134(t2, sd, r1);
(void)sp_3072_sub_134(&t1[i], &t1[i], t2);
t1[134 + i] -= t2[134];
t1[134 + i] += t1[134 + i - 1] >> 23;
t1[134 + i - 1] &= 0x7fffff;
r1 = (((-t1[134 + i]) << 23) - t1[134 + i - 1]) / dv;
r1 -= t1[134 + i];
sp_3072_mul_d_134(t2, sd, r1);
(void)sp_3072_add_134(&t1[i], &t1[i], t2);
t1[134 + i] += t1[134 + i - 1] >> 23;
t1[134 + i - 1] &= 0x7fffff;
}
t1[134 - 1] += t1[134 - 2] >> 23;
t1[134 - 2] &= 0x7fffff;
r1 = t1[134 - 1] / dv;
sp_3072_mul_d_134(t2, sd, r1);
sp_3072_sub_134(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 134U);
for (i=0; i<132; i++) {
r[i+1] += r[i] >> 23;
r[i] &= 0x7fffff;
}
sp_3072_cond_add_134(r, r, sd, 0 - ((r[133] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_3072_norm_134(r);
sp_3072_rshift_134(r, r, 10);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_3072_mod_134(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_3072_div_134(a, m, NULL, r);
}
#if (defined(WOLFSSL_HAVE_SP_RSA) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)) || \
defined(WOLFSSL_HAVE_SP_DH)
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_3072_mod_exp_134(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 134 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 134U * 2U);
norm = t[0] = td;
t[1] = &td[134 * 2];
t[2] = &td[2 * 134 * 2];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_134(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 134U);
}
}
if (err == MP_OKAY) {
sp_3072_mul_134(t[1], t[1], norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_134(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 134 * 2);
sp_3072_mont_sqr_134(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 134 * 2);
}
sp_3072_mont_reduce_134(t[0], m, mp);
n = sp_3072_cmp_134(t[0], m);
sp_3072_cond_sub_134(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 134 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][268];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 134 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[134 * 2];
t[2] = &td[2 * 134 * 2];
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_134(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_134(t[1], t[1], norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
else {
sp_3072_mul_134(t[1], a, norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 23;
c = bits % 23;
n = e[i--] << (23 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 23;
}
y = (n >> 22) & 1;
n <<= 1;
sp_3072_mont_mul_134(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_3072_mont_sqr_134(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_3072_mont_reduce_134(t[0], m, mp);
n = sp_3072_cmp_134(t[0], m);
sp_3072_cond_sub_134(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][268];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[268];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 268, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 268;
#endif
norm = t[0];
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
if (reduceA != 0) {
err = sp_3072_mod_134(t[1], a, m);
if (err == MP_OKAY) {
sp_3072_mul_134(t[1], t[1], norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
else {
sp_3072_mul_134(t[1], a, norm);
err = sp_3072_mod_134(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_3072_mont_sqr_134(t[ 2], t[ 1], m, mp);
sp_3072_mont_mul_134(t[ 3], t[ 2], t[ 1], m, mp);
sp_3072_mont_sqr_134(t[ 4], t[ 2], m, mp);
sp_3072_mont_mul_134(t[ 5], t[ 3], t[ 2], m, mp);
sp_3072_mont_sqr_134(t[ 6], t[ 3], m, mp);
sp_3072_mont_mul_134(t[ 7], t[ 4], t[ 3], m, mp);
sp_3072_mont_sqr_134(t[ 8], t[ 4], m, mp);
sp_3072_mont_mul_134(t[ 9], t[ 5], t[ 4], m, mp);
sp_3072_mont_sqr_134(t[10], t[ 5], m, mp);
sp_3072_mont_mul_134(t[11], t[ 6], t[ 5], m, mp);
sp_3072_mont_sqr_134(t[12], t[ 6], m, mp);
sp_3072_mont_mul_134(t[13], t[ 7], t[ 6], m, mp);
sp_3072_mont_sqr_134(t[14], t[ 7], m, mp);
sp_3072_mont_mul_134(t[15], t[ 8], t[ 7], m, mp);
sp_3072_mont_sqr_134(t[16], t[ 8], m, mp);
sp_3072_mont_mul_134(t[17], t[ 9], t[ 8], m, mp);
sp_3072_mont_sqr_134(t[18], t[ 9], m, mp);
sp_3072_mont_mul_134(t[19], t[10], t[ 9], m, mp);
sp_3072_mont_sqr_134(t[20], t[10], m, mp);
sp_3072_mont_mul_134(t[21], t[11], t[10], m, mp);
sp_3072_mont_sqr_134(t[22], t[11], m, mp);
sp_3072_mont_mul_134(t[23], t[12], t[11], m, mp);
sp_3072_mont_sqr_134(t[24], t[12], m, mp);
sp_3072_mont_mul_134(t[25], t[13], t[12], m, mp);
sp_3072_mont_sqr_134(t[26], t[13], m, mp);
sp_3072_mont_mul_134(t[27], t[14], t[13], m, mp);
sp_3072_mont_sqr_134(t[28], t[14], m, mp);
sp_3072_mont_mul_134(t[29], t[15], t[14], m, mp);
sp_3072_mont_sqr_134(t[30], t[15], m, mp);
sp_3072_mont_mul_134(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 134) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_sqr_134(rt, rt, m, mp);
sp_3072_mont_mul_134(rt, rt, t[y], m, mp);
}
sp_3072_mont_reduce_134(rt, m, mp);
n = sp_3072_cmp_134(rt, m);
sp_3072_cond_sub_134(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) || */
/* WOLFSSL_HAVE_SP_DH */
#ifdef WOLFSSL_HAVE_SP_RSA
/* RSA public key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* em Public exponent.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 384 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPublic_3072(const byte* in, word32 inLen, mp_int* em, mp_int* mm,
byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* d = NULL;
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit* norm;
sp_digit e[1] = {0};
sp_digit mp;
int i;
int err = MP_OKAY;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 134 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
a = d;
r = a + 134 * 2;
m = r + 134 * 2;
norm = r;
sp_3072_from_bin(a, 134, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_mp(m, 134, mm);
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
}
if (err == MP_OKAY) {
sp_3072_mul_134(a, a, norm);
err = sp_3072_mod_134(a, a, m);
}
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 134 * 2);
for (i--; i>=0; i--) {
sp_3072_mont_sqr_134(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_3072_mont_mul_134(r, r, a, m, mp);
}
}
sp_3072_mont_reduce_134(r, m, mp);
mp = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0)- 1);
sp_3072_to_bin(r, out);
*outLen = 384;
}
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit ad[268], md[134], rd[268];
#else
sp_digit* d = NULL;
#endif
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit e[1] = {0};
int err = MP_OKAY;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 23) {
err = MP_READ_E;
}
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 134 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d;
r = a + 134 * 2;
m = r + 134 * 2;
}
#else
a = ad;
m = md;
r = rd;
#endif
if (err == MP_OKAY) {
sp_3072_from_bin(a, 134, in, inLen);
#if DIGIT_BIT >= 23
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_mp(m, 134, mm);
if (e[0] == 0x3) {
sp_3072_sqr_134(r, a);
err = sp_3072_mod_134(r, r, m);
if (err == MP_OKAY) {
sp_3072_mul_134(r, a, r);
err = sp_3072_mod_134(r, r, m);
}
}
else {
sp_digit* norm = r;
int i;
sp_digit mp;
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
sp_3072_mul_134(a, a, norm);
err = sp_3072_mod_134(a, a, m);
if (err == MP_OKAY) {
for (i=22; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 268U);
for (i--; i>=0; i--) {
sp_3072_mont_sqr_134(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_3072_mont_mul_134(r, r, a, m, mp);
}
}
sp_3072_mont_reduce_134(r, m, mp);
mp = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
}
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
#endif
return err;
#endif /* WOLFSSL_SP_SMALL */
}
#ifndef WOLFSSL_RSA_PUBLIC_ONLY
#if !defined(SP_RSA_PRIVATE_EXP_D) && !defined(RSA_LOW_MEM)
#endif /* !SP_RSA_PRIVATE_EXP_D && !RSA_LOW_MEM */
/* RSA private key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* dm Private exponent.
* pm First prime.
* qm Second prime.
* dpm First prime's CRT exponent.
* dqm Second prime's CRT exponent.
* qim Inverse of second prime mod p.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 384 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPrivate_3072(const byte* in, word32 inLen, mp_int* dm,
mp_int* pm, mp_int* qm, mp_int* dpm, mp_int* dqm, mp_int* qim, mp_int* mm,
byte* out, word32* outLen)
{
#if defined(SP_RSA_PRIVATE_EXP_D) || defined(RSA_LOW_MEM)
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* a;
sp_digit* d = NULL;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 3072) {
err = MP_READ_E;
}
if (inLen > 384) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 134 * 4, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d + 134;
m = a + 268;
r = a;
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(d, 134, dm);
sp_3072_from_mp(m, 134, mm);
err = sp_3072_mod_exp_134(r, a, d, 3072, m, 0);
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
}
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 134);
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[268], d[134], m[134];
sp_digit* r = a;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 3072) {
err = MP_READ_E;
}
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(d, 134, dm);
sp_3072_from_mp(m, 134, mm);
err = sp_3072_mod_exp_134(r, a, d, 3072, m, 0);
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
}
XMEMSET(d, 0, sizeof(sp_digit) * 134);
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#else
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* t = NULL;
sp_digit* a;
sp_digit* p;
sp_digit* q;
sp_digit* dp;
sp_digit* dq;
sp_digit* qi;
sp_digit* tmpa;
sp_digit* tmpb;
sp_digit* r;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 384) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 67 * 11, NULL,
DYNAMIC_TYPE_RSA);
if (t == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = t;
p = a + 134 * 2;
q = p + 67;
qi = dq = dp = q + 67;
tmpa = qi + 67;
tmpb = tmpa + 134;
r = t + 134;
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(p, 67, pm);
sp_3072_from_mp(q, 67, qm);
sp_3072_from_mp(dp, 67, dpm);
err = sp_3072_mod_exp_67(tmpa, a, dp, 1536, p, 1);
}
if (err == MP_OKAY) {
sp_3072_from_mp(dq, 67, dqm);
err = sp_3072_mod_exp_67(tmpb, a, dq, 1536, q, 1);
}
if (err == MP_OKAY) {
(void)sp_3072_sub_67(tmpa, tmpa, tmpb);
sp_3072_cond_add_67(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[66] >> 31));
sp_3072_cond_add_67(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[66] >> 31));
sp_3072_from_mp(qi, 67, qim);
sp_3072_mul_67(tmpa, tmpa, qi);
err = sp_3072_mod_67(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_3072_mul_67(tmpa, q, tmpa);
(void)sp_3072_add_134(r, tmpb, tmpa);
sp_3072_norm_134(r);
sp_3072_to_bin(r, out);
*outLen = 384;
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_digit) * 67 * 11);
XFREE(t, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[134 * 2];
sp_digit p[67], q[67], dp[67], dq[67], qi[67];
sp_digit tmpa[134], tmpb[134];
sp_digit* r = a;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 384U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 384U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_3072_from_bin(a, 134, in, inLen);
sp_3072_from_mp(p, 67, pm);
sp_3072_from_mp(q, 67, qm);
sp_3072_from_mp(dp, 67, dpm);
sp_3072_from_mp(dq, 67, dqm);
sp_3072_from_mp(qi, 67, qim);
err = sp_3072_mod_exp_67(tmpa, a, dp, 1536, p, 1);
}
if (err == MP_OKAY) {
err = sp_3072_mod_exp_67(tmpb, a, dq, 1536, q, 1);
}
if (err == MP_OKAY) {
(void)sp_3072_sub_67(tmpa, tmpa, tmpb);
sp_3072_cond_add_67(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[66] >> 31));
sp_3072_cond_add_67(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[66] >> 31));
sp_3072_mul_67(tmpa, tmpa, qi);
err = sp_3072_mod_67(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_3072_mul_67(tmpa, tmpa, q);
(void)sp_3072_add_134(r, tmpb, tmpa);
sp_3072_norm_134(r);
sp_3072_to_bin(r, out);
*outLen = 384;
}
XMEMSET(tmpa, 0, sizeof(tmpa));
XMEMSET(tmpb, 0, sizeof(tmpb));
XMEMSET(p, 0, sizeof(p));
XMEMSET(q, 0, sizeof(q));
XMEMSET(dp, 0, sizeof(dp));
XMEMSET(dq, 0, sizeof(dq));
XMEMSET(qi, 0, sizeof(qi));
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#endif /* SP_RSA_PRIVATE_EXP_D || RSA_LOW_MEM */
}
#endif /* !WOLFSSL_RSA_PUBLIC_ONLY */
#endif /* WOLFSSL_HAVE_SP_RSA */
#if defined(WOLFSSL_HAVE_SP_DH) || (defined(WOLFSSL_HAVE_SP_RSA) && \
!defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_3072_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (3072 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 23
XMEMCPY(r->dp, a, sizeof(sp_digit) * 134);
r->used = 134;
mp_clamp(r);
#elif DIGIT_BIT < 23
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 134; i++) {
r->dp[j] |= (mp_digit)(a[i] << s);
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = (mp_digit)(a[i] >> s);
while (s + DIGIT_BIT <= 23) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = (mp_digit)(a[i] >> s);
}
}
s = 23 - s;
}
r->used = (3072 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 134; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 23 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 23 - s;
}
else {
s += 23;
}
}
r->used = (3072 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_3072(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
sp_3072_from_mp(b, 134, base);
sp_3072_from_mp(e, 134, exp);
sp_3072_from_mp(m, 134, mod);
err = sp_3072_mod_exp_134(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
err = sp_3072_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[268], ed[134], md[134];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_3072_from_mp(b, 134, base);
sp_3072_from_mp(e, 134, exp);
sp_3072_from_mp(m, 134, mod);
err = sp_3072_mod_exp_134(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
err = sp_3072_to_mp(r, res);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
#endif
return err;
#endif
}
#ifdef WOLFSSL_HAVE_SP_DH
#ifdef HAVE_FFDHE_3072
SP_NOINLINE static void sp_3072_lshift_134(sp_digit* r, sp_digit* a, byte n)
{
#ifdef WOLFSSL_SP_SMALL
int i;
r[134] = a[133] >> (23 - n);
for (i=133; i>0; i--) {
r[i] = ((a[i] << n) | (a[i-1] >> (23 - n))) & 0x7fffff;
}
#else
sp_int_digit s, t;
s = (sp_int_digit)a[133];
r[134] = s >> (23U - n);
s = (sp_int_digit)(a[133]); t = (sp_int_digit)(a[132]);
r[133] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[132]); t = (sp_int_digit)(a[131]);
r[132] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[131]); t = (sp_int_digit)(a[130]);
r[131] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[130]); t = (sp_int_digit)(a[129]);
r[130] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[129]); t = (sp_int_digit)(a[128]);
r[129] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[128]); t = (sp_int_digit)(a[127]);
r[128] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[127]); t = (sp_int_digit)(a[126]);
r[127] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[126]); t = (sp_int_digit)(a[125]);
r[126] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[125]); t = (sp_int_digit)(a[124]);
r[125] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[124]); t = (sp_int_digit)(a[123]);
r[124] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[123]); t = (sp_int_digit)(a[122]);
r[123] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[122]); t = (sp_int_digit)(a[121]);
r[122] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[121]); t = (sp_int_digit)(a[120]);
r[121] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[120]); t = (sp_int_digit)(a[119]);
r[120] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[119]); t = (sp_int_digit)(a[118]);
r[119] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[118]); t = (sp_int_digit)(a[117]);
r[118] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[117]); t = (sp_int_digit)(a[116]);
r[117] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[116]); t = (sp_int_digit)(a[115]);
r[116] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[115]); t = (sp_int_digit)(a[114]);
r[115] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[114]); t = (sp_int_digit)(a[113]);
r[114] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[113]); t = (sp_int_digit)(a[112]);
r[113] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[112]); t = (sp_int_digit)(a[111]);
r[112] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[111]); t = (sp_int_digit)(a[110]);
r[111] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[110]); t = (sp_int_digit)(a[109]);
r[110] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[109]); t = (sp_int_digit)(a[108]);
r[109] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[108]); t = (sp_int_digit)(a[107]);
r[108] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[107]); t = (sp_int_digit)(a[106]);
r[107] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[106]); t = (sp_int_digit)(a[105]);
r[106] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[105]); t = (sp_int_digit)(a[104]);
r[105] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[104]); t = (sp_int_digit)(a[103]);
r[104] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[103]); t = (sp_int_digit)(a[102]);
r[103] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[102]); t = (sp_int_digit)(a[101]);
r[102] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[101]); t = (sp_int_digit)(a[100]);
r[101] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[100]); t = (sp_int_digit)(a[99]);
r[100] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[99]); t = (sp_int_digit)(a[98]);
r[99] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[98]); t = (sp_int_digit)(a[97]);
r[98] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[97]); t = (sp_int_digit)(a[96]);
r[97] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[96]); t = (sp_int_digit)(a[95]);
r[96] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[95]); t = (sp_int_digit)(a[94]);
r[95] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[94]); t = (sp_int_digit)(a[93]);
r[94] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[93]); t = (sp_int_digit)(a[92]);
r[93] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[92]); t = (sp_int_digit)(a[91]);
r[92] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[91]); t = (sp_int_digit)(a[90]);
r[91] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[90]); t = (sp_int_digit)(a[89]);
r[90] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[89]); t = (sp_int_digit)(a[88]);
r[89] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[88]); t = (sp_int_digit)(a[87]);
r[88] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[87]); t = (sp_int_digit)(a[86]);
r[87] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[86]); t = (sp_int_digit)(a[85]);
r[86] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[85]); t = (sp_int_digit)(a[84]);
r[85] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[84]); t = (sp_int_digit)(a[83]);
r[84] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[83]); t = (sp_int_digit)(a[82]);
r[83] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[82]); t = (sp_int_digit)(a[81]);
r[82] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[81]); t = (sp_int_digit)(a[80]);
r[81] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[80]); t = (sp_int_digit)(a[79]);
r[80] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[79]); t = (sp_int_digit)(a[78]);
r[79] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[78]); t = (sp_int_digit)(a[77]);
r[78] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[77]); t = (sp_int_digit)(a[76]);
r[77] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[76]); t = (sp_int_digit)(a[75]);
r[76] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[75]); t = (sp_int_digit)(a[74]);
r[75] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[74]); t = (sp_int_digit)(a[73]);
r[74] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[73]); t = (sp_int_digit)(a[72]);
r[73] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[72]); t = (sp_int_digit)(a[71]);
r[72] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[71]); t = (sp_int_digit)(a[70]);
r[71] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[70]); t = (sp_int_digit)(a[69]);
r[70] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[69]); t = (sp_int_digit)(a[68]);
r[69] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[68]); t = (sp_int_digit)(a[67]);
r[68] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[67]); t = (sp_int_digit)(a[66]);
r[67] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[66]); t = (sp_int_digit)(a[65]);
r[66] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[65]); t = (sp_int_digit)(a[64]);
r[65] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[64]); t = (sp_int_digit)(a[63]);
r[64] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[63]); t = (sp_int_digit)(a[62]);
r[63] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[62]); t = (sp_int_digit)(a[61]);
r[62] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[61]); t = (sp_int_digit)(a[60]);
r[61] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[60]); t = (sp_int_digit)(a[59]);
r[60] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[59]); t = (sp_int_digit)(a[58]);
r[59] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[58]); t = (sp_int_digit)(a[57]);
r[58] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[57]); t = (sp_int_digit)(a[56]);
r[57] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[56]); t = (sp_int_digit)(a[55]);
r[56] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[55]); t = (sp_int_digit)(a[54]);
r[55] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[54]); t = (sp_int_digit)(a[53]);
r[54] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[53]); t = (sp_int_digit)(a[52]);
r[53] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[52]); t = (sp_int_digit)(a[51]);
r[52] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[51]); t = (sp_int_digit)(a[50]);
r[51] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[50]); t = (sp_int_digit)(a[49]);
r[50] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[49]); t = (sp_int_digit)(a[48]);
r[49] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[48]); t = (sp_int_digit)(a[47]);
r[48] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[47]); t = (sp_int_digit)(a[46]);
r[47] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[46]); t = (sp_int_digit)(a[45]);
r[46] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[45]); t = (sp_int_digit)(a[44]);
r[45] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[44]); t = (sp_int_digit)(a[43]);
r[44] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[43]); t = (sp_int_digit)(a[42]);
r[43] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[42]); t = (sp_int_digit)(a[41]);
r[42] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[41]); t = (sp_int_digit)(a[40]);
r[41] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[40]); t = (sp_int_digit)(a[39]);
r[40] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[39]); t = (sp_int_digit)(a[38]);
r[39] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[38]); t = (sp_int_digit)(a[37]);
r[38] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[37]); t = (sp_int_digit)(a[36]);
r[37] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[36]); t = (sp_int_digit)(a[35]);
r[36] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[35]); t = (sp_int_digit)(a[34]);
r[35] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[34]); t = (sp_int_digit)(a[33]);
r[34] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[33]); t = (sp_int_digit)(a[32]);
r[33] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[32]); t = (sp_int_digit)(a[31]);
r[32] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[31]); t = (sp_int_digit)(a[30]);
r[31] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[30]); t = (sp_int_digit)(a[29]);
r[30] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[29]); t = (sp_int_digit)(a[28]);
r[29] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[28]); t = (sp_int_digit)(a[27]);
r[28] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[27]); t = (sp_int_digit)(a[26]);
r[27] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[26]); t = (sp_int_digit)(a[25]);
r[26] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[25]); t = (sp_int_digit)(a[24]);
r[25] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[24]); t = (sp_int_digit)(a[23]);
r[24] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[23]); t = (sp_int_digit)(a[22]);
r[23] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[22]); t = (sp_int_digit)(a[21]);
r[22] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[21]); t = (sp_int_digit)(a[20]);
r[21] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[20]); t = (sp_int_digit)(a[19]);
r[20] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[19]); t = (sp_int_digit)(a[18]);
r[19] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[18]); t = (sp_int_digit)(a[17]);
r[18] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[17]); t = (sp_int_digit)(a[16]);
r[17] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[16]); t = (sp_int_digit)(a[15]);
r[16] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[15]); t = (sp_int_digit)(a[14]);
r[15] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[14]); t = (sp_int_digit)(a[13]);
r[14] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[13]); t = (sp_int_digit)(a[12]);
r[13] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[12]); t = (sp_int_digit)(a[11]);
r[12] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[11]); t = (sp_int_digit)(a[10]);
r[11] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[10]); t = (sp_int_digit)(a[9]);
r[10] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[9]); t = (sp_int_digit)(a[8]);
r[9] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[8]); t = (sp_int_digit)(a[7]);
r[8] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[7]); t = (sp_int_digit)(a[6]);
r[7] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[6]); t = (sp_int_digit)(a[5]);
r[6] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[5]); t = (sp_int_digit)(a[4]);
r[5] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[4]); t = (sp_int_digit)(a[3]);
r[4] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[3]); t = (sp_int_digit)(a[2]);
r[3] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[2]); t = (sp_int_digit)(a[1]);
r[2] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
s = (sp_int_digit)(a[1]); t = (sp_int_digit)(a[0]);
r[1] = ((s << n) | (t >> (23U - n))) & 0x7fffff;
#endif
r[0] = (a[0] << n) & 0x7fffff;
}
/* Modular exponentiate 2 to the e mod m. (r = 2^e mod m)
*
* r A single precision number that is the result of the operation.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_3072_mod_exp_2_134(sp_digit* r, const sp_digit* e, int bits, const sp_digit* m)
{
#ifndef WOLFSSL_SMALL_STACK
sp_digit nd[268];
sp_digit td[135];
#else
sp_digit* td;
#endif
sp_digit* norm;
sp_digit* tmp;
sp_digit mp = 1;
sp_digit n, o;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 403, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
norm = td;
tmp = td + 268;
XMEMSET(td, 0, sizeof(sp_digit) * 403);
#else
norm = nd;
tmp = td;
XMEMSET(td, 0, sizeof(td));
#endif
sp_3072_mont_setup(m, &mp);
sp_3072_mont_norm_134(norm, m);
bits = ((bits + 3) / 4) * 4;
i = ((bits + 22) / 23) - 1;
c = bits % 23;
if (c == 0) {
c = 23;
}
if (i < 134) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_3072_lshift_134(r, norm, y);
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= e[i--] << (9 - c);
c += 23;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_mont_sqr_134(r, r, m, mp);
sp_3072_lshift_134(r, r, y);
sp_3072_mul_d_134(tmp, norm, (r[134] << 10) + (r[133] >> 13));
r[134] = 0;
r[133] &= 0x1fffL;
(void)sp_3072_add_134(r, r, tmp);
sp_3072_norm_134(r);
o = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((o < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
sp_3072_mont_reduce_134(r, m, mp);
n = sp_3072_cmp_134(r, m);
sp_3072_cond_sub_134(r, r, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
#endif /* HAVE_FFDHE_3072 */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base.
* exp Array of bytes that is the exponent.
* expLen Length of data, in bytes, in exponent.
* mod Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 384 bytes long.
* outLen Length, in bytes, of exponentiation result.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_DhExp_3072(mp_int* base, const byte* exp, word32 expLen,
mp_int* mod, byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 384) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
sp_3072_from_mp(b, 134, base);
sp_3072_from_bin(e, 134, exp, expLen);
sp_3072_from_mp(m, 134, mod);
#ifdef HAVE_FFDHE_3072
if (base->used == 1 && base->dp[0] == 2 &&
((m[133] << 3) | (m[132] >> 20)) == 0xffffL) {
err = sp_3072_mod_exp_2_134(r, e, expLen * 8, m);
}
else
#endif
err = sp_3072_mod_exp_134(r, b, e, expLen * 8, m, 0);
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
for (i=0; i<384 && out[i] == 0; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[268], ed[134], md[134];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
int err = MP_OKAY;
if (mp_count_bits(base) > 3072) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 384U) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 3072) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 134 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 134 * 2;
m = e + 134;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_3072_from_mp(b, 134, base);
sp_3072_from_bin(e, 134, exp, expLen);
sp_3072_from_mp(m, 134, mod);
#ifdef HAVE_FFDHE_3072
if (base->used == 1 && base->dp[0] == 2U &&
((m[133] << 3) | (m[132] >> 20)) == 0xffffL) {
err = sp_3072_mod_exp_2_134(r, e, expLen * 8U, m);
}
else {
#endif
err = sp_3072_mod_exp_134(r, b, e, expLen * 8U, m, 0);
#ifdef HAVE_FFDHE_3072
}
#endif
}
if (err == MP_OKAY) {
sp_3072_to_bin(r, out);
*outLen = 384;
for (i=0; i<384U && out[i] == 0U; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 134U);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_1536(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1536) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1536) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1536) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 67 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 67 * 2;
m = e + 67;
r = b;
sp_3072_from_mp(b, 67, base);
sp_3072_from_mp(e, 67, exp);
sp_3072_from_mp(m, 67, mod);
err = sp_3072_mod_exp_67(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 67, 0, sizeof(*r) * 67U);
err = sp_3072_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 67U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[134], ed[67], md[67];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 1536) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 1536) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 1536) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 67 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 67 * 2;
m = e + 67;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_3072_from_mp(b, 67, base);
sp_3072_from_mp(e, 67, exp);
sp_3072_from_mp(m, 67, mod);
err = sp_3072_mod_exp_67(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
XMEMSET(r + 67, 0, sizeof(*r) * 67U);
err = sp_3072_to_mp(r, res);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 67U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 67U);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH || (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) */
#endif /* !WOLFSSL_SP_NO_3072 */
#ifdef WOLFSSL_SP_4096
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_4096_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 13U) {
r[j] &= 0x1fffff;
s = 21U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_4096_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 21
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 21
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x1fffff;
s = 21U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 21U) <= (word32)DIGIT_BIT) {
s += 21U;
r[j] &= 0x1fffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 21) {
r[j] &= 0x1fffff;
if (j + 1 >= size) {
break;
}
s = 21 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 512
*
* r A single precision integer.
* a Byte array.
*/
static void sp_4096_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<195; i++) {
r[i+1] += r[i] >> 21;
r[i] &= 0x1fffff;
}
j = 4096 / 8 - 1;
a[j] = 0;
for (i=0; i<196 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); /*lint !e9033*/
b += 8 - s;
if (j < 0) {
break;
}
while (b < 21) {
a[j--] = (byte)(r[i] >> b);
b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 21);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
#ifndef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_4096_mul_49(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j;
int64_t t[98];
XMEMSET(t, 0, sizeof(t));
for (i=0; i<49; i++) {
for (j=0; j<49; j++) {
t[i+j] += ((int64_t)a[i]) * b[j];
}
}
for (i=0; i<97; i++) {
r[i] = t[i] & 0x1fffff;
t[i+1] += t[i] >> 21;
}
r[97] = (sp_digit)t[97];
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_4096_sqr_49(sp_digit* r, const sp_digit* a)
{
int i, j;
int64_t t[98];
XMEMSET(t, 0, sizeof(t));
for (i=0; i<49; i++) {
for (j=0; j<i; j++) {
t[i+j] += (((int64_t)a[i]) * a[j]) * 2;
}
t[i+i] += ((int64_t)a[i]) * a[i];
}
for (i=0; i<97; i++) {
r[i] = t[i] & 0x1fffff;
t[i+1] += t[i] >> 21;
}
r[97] = (sp_digit)t[97];
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_49(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 48; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[48] = a[48] + b[48];
return 0;
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 96; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[96] = a[96] + b[96];
r[97] = a[97] + b[97];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_sub_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 96; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[96] = a[96] - b[96];
r[97] = a[97] - b[97];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_4096_mul_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit* z0 = r;
sp_digit z1[98];
sp_digit* a1 = z1;
sp_digit b1[49];
sp_digit* z2 = r + 98;
(void)sp_4096_add_49(a1, a, &a[49]);
(void)sp_4096_add_49(b1, b, &b[49]);
sp_4096_mul_49(z2, &a[49], &b[49]);
sp_4096_mul_49(z0, a, b);
sp_4096_mul_49(z1, a1, b1);
(void)sp_4096_sub_98(z1, z1, z2);
(void)sp_4096_sub_98(z1, z1, z0);
(void)sp_4096_add_98(r + 49, r + 49, z1);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_4096_sqr_98(sp_digit* r, const sp_digit* a)
{
sp_digit* z0 = r;
sp_digit z1[98];
sp_digit* a1 = z1;
sp_digit* z2 = r + 98;
(void)sp_4096_add_49(a1, a, &a[49]);
sp_4096_sqr_49(z2, &a[49]);
sp_4096_sqr_49(z0, a);
sp_4096_sqr_49(z1, a1);
(void)sp_4096_sub_98(z1, z1, z2);
(void)sp_4096_sub_98(z1, z1, z0);
(void)sp_4096_add_98(r + 49, r + 49, z1);
}
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 192; i += 8) {
r[i + 0] = a[i + 0] + b[i + 0];
r[i + 1] = a[i + 1] + b[i + 1];
r[i + 2] = a[i + 2] + b[i + 2];
r[i + 3] = a[i + 3] + b[i + 3];
r[i + 4] = a[i + 4] + b[i + 4];
r[i + 5] = a[i + 5] + b[i + 5];
r[i + 6] = a[i + 6] + b[i + 6];
r[i + 7] = a[i + 7] + b[i + 7];
}
r[192] = a[192] + b[192];
r[193] = a[193] + b[193];
r[194] = a[194] + b[194];
r[195] = a[195] + b[195];
return 0;
}
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_sub_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 192; i += 8) {
r[i + 0] = a[i + 0] - b[i + 0];
r[i + 1] = a[i + 1] - b[i + 1];
r[i + 2] = a[i + 2] - b[i + 2];
r[i + 3] = a[i + 3] - b[i + 3];
r[i + 4] = a[i + 4] - b[i + 4];
r[i + 5] = a[i + 5] - b[i + 5];
r[i + 6] = a[i + 6] - b[i + 6];
r[i + 7] = a[i + 7] - b[i + 7];
}
r[192] = a[192] - b[192];
r[193] = a[193] - b[193];
r[194] = a[194] - b[194];
r[195] = a[195] - b[195];
return 0;
}
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_4096_mul_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_digit* z0 = r;
sp_digit z1[196];
sp_digit* a1 = z1;
sp_digit b1[98];
sp_digit* z2 = r + 196;
(void)sp_4096_add_98(a1, a, &a[98]);
(void)sp_4096_add_98(b1, b, &b[98]);
sp_4096_mul_98(z2, &a[98], &b[98]);
sp_4096_mul_98(z0, a, b);
sp_4096_mul_98(z1, a1, b1);
(void)sp_4096_sub_196(z1, z1, z2);
(void)sp_4096_sub_196(z1, z1, z0);
(void)sp_4096_add_196(r + 98, r + 98, z1);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_4096_sqr_196(sp_digit* r, const sp_digit* a)
{
sp_digit* z0 = r;
sp_digit z1[196];
sp_digit* a1 = z1;
sp_digit* z2 = r + 196;
(void)sp_4096_add_98(a1, a, &a[98]);
sp_4096_sqr_98(z2, &a[98]);
sp_4096_sqr_98(z0, a);
sp_4096_sqr_98(z1, a1);
(void)sp_4096_sub_196(z1, z1, z2);
(void)sp_4096_sub_196(z1, z1, z0);
(void)sp_4096_add_196(r + 98, r + 98, z1);
}
#endif /* !WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 196; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_sub_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 196; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_4096_mul_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[195]) * b[195];
r[391] = (sp_digit)(c >> 21);
c = (c & 0x1fffff) << 21;
for (k = 389; k >= 0; k--) {
for (i = 195; i >= 0; i--) {
j = k - i;
if (j >= 196) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 42;
r[k + 1] = (c >> 21) & 0x1fffff;
c = (c & 0x1fffff) << 21;
}
r[0] = (sp_digit)(c >> 21);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_4096_sqr_196(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[195]) * a[195];
r[391] = (sp_digit)(c >> 21);
c = (c & 0x1fffff) << 21;
for (k = 389; k >= 0; k--) {
for (i = 195; i >= 0; i--) {
j = k - i;
if (j >= 196 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 42;
r[k + 1] = (c >> 21) & 0x1fffff;
c = (c & 0x1fffff) << 21;
}
r[0] = (sp_digit)(c >> 21);
}
#endif /* WOLFSSL_SP_SMALL */
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
#if defined(WOLFSSL_HAVE_SP_RSA) && !defined(SP_RSA_PRIVATE_EXP_D)
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 98; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_sub_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 98; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_4096_mul_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[97]) * b[97];
r[195] = (sp_digit)(c >> 21);
c = (c & 0x1fffff) << 21;
for (k = 193; k >= 0; k--) {
for (i = 97; i >= 0; i--) {
j = k - i;
if (j >= 98) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 42;
r[k + 1] = (c >> 21) & 0x1fffff;
c = (c & 0x1fffff) << 21;
}
r[0] = (sp_digit)(c >> 21);
}
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_4096_sqr_98(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[97]) * a[97];
r[195] = (sp_digit)(c >> 21);
c = (c & 0x1fffff) << 21;
for (k = 193; k >= 0; k--) {
for (i = 97; i >= 0; i--) {
j = k - i;
if (j >= 98 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 42;
r[k + 1] = (c >> 21) & 0x1fffff;
c = (c & 0x1fffff) << 21;
}
r[0] = (sp_digit)(c >> 21);
}
#endif /* WOLFSSL_SP_SMALL */
#endif /* WOLFSSL_HAVE_SP_RSA && !SP_RSA_PRIVATE_EXP_D */
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* Caclulate the bottom digit of -1/a mod 2^n.
*
* a A single precision number.
* rho Bottom word of inverse.
*/
static void sp_4096_mont_setup(const sp_digit* a, sp_digit* rho)
{
sp_digit x, b;
b = a[0];
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
x &= 0x1fffff;
/* rho = -1/m mod b */
*rho = (1L << 21) - x;
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_4096_mul_d_196(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 196; i++) {
t += tb * a[i];
r[i] = t & 0x1fffff;
t >>= 21;
}
r[196] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x1fffff;
for (i = 0; i < 192; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 21) + (t[1] & 0x1fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 21) + (t[2] & 0x1fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 21) + (t[3] & 0x1fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 21) + (t[4] & 0x1fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 21) + (t[5] & 0x1fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 21) + (t[6] & 0x1fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 21) + (t[7] & 0x1fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 21) + (t[0] & 0x1fffff);
}
t[1] = tb * a[193];
r[193] = (sp_digit)(t[0] >> 21) + (t[1] & 0x1fffff);
t[2] = tb * a[194];
r[194] = (sp_digit)(t[1] >> 21) + (t[2] & 0x1fffff);
t[3] = tb * a[195];
r[195] = (sp_digit)(t[2] >> 21) + (t[3] & 0x1fffff);
r[196] = (sp_digit)(t[3] >> 21);
#endif /* WOLFSSL_SP_SMALL */
}
#if (defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH)) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)
#if defined(WOLFSSL_HAVE_SP_RSA) && !defined(SP_RSA_PRIVATE_EXP_D)
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 4096 bits, just need to subtract.
*
* r A single precision number.
* m A single precision number.
*/
static void sp_4096_mont_norm_98(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<97; i++) {
r[i] = 0x1fffff;
}
#else
int i;
for (i = 0; i < 96; i += 8) {
r[i + 0] = 0x1fffff;
r[i + 1] = 0x1fffff;
r[i + 2] = 0x1fffff;
r[i + 3] = 0x1fffff;
r[i + 4] = 0x1fffff;
r[i + 5] = 0x1fffff;
r[i + 6] = 0x1fffff;
r[i + 7] = 0x1fffff;
}
r[96] = 0x1fffff;
#endif
r[97] = 0x7ffL;
/* r = (2^n - 1) mod n */
(void)sp_4096_sub_98(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_4096_cmp_98(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=97; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[97] - b[97]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[96] - b[96]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 88; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_4096_cond_sub_98(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 98; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 96; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[96] = a[96] - (b[96] & m);
r[97] = a[97] - (b[97] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_4096_mul_add_98(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 98; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x1fffff;
t >>= 21;
}
r[98] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += (sp_digit)(t[0] & 0x1fffff);
for (i = 0; i < 96; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (sp_digit)((t[0] >> 21) + (t[1] & 0x1fffff));
t[2] = tb * a[i+2];
r[i+2] += (sp_digit)((t[1] >> 21) + (t[2] & 0x1fffff));
t[3] = tb * a[i+3];
r[i+3] += (sp_digit)((t[2] >> 21) + (t[3] & 0x1fffff));
t[4] = tb * a[i+4];
r[i+4] += (sp_digit)((t[3] >> 21) + (t[4] & 0x1fffff));
t[5] = tb * a[i+5];
r[i+5] += (sp_digit)((t[4] >> 21) + (t[5] & 0x1fffff));
t[6] = tb * a[i+6];
r[i+6] += (sp_digit)((t[5] >> 21) + (t[6] & 0x1fffff));
t[7] = tb * a[i+7];
r[i+7] += (sp_digit)((t[6] >> 21) + (t[7] & 0x1fffff));
t[0] = tb * a[i+8];
r[i+8] += (sp_digit)((t[7] >> 21) + (t[0] & 0x1fffff));
}
t[1] = tb * a[97]; r[97] += (sp_digit)((t[0] >> 21) + (t[1] & 0x1fffff));
r[98] += (sp_digit)(t[1] >> 21);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 21.
*
* a Array of sp_digit to normalize.
*/
static void sp_4096_norm_98(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 97; i++) {
a[i+1] += a[i] >> 21;
a[i] &= 0x1fffff;
}
#else
int i;
for (i = 0; i < 96; i += 8) {
a[i+1] += a[i+0] >> 21; a[i+0] &= 0x1fffff;
a[i+2] += a[i+1] >> 21; a[i+1] &= 0x1fffff;
a[i+3] += a[i+2] >> 21; a[i+2] &= 0x1fffff;
a[i+4] += a[i+3] >> 21; a[i+3] &= 0x1fffff;
a[i+5] += a[i+4] >> 21; a[i+4] &= 0x1fffff;
a[i+6] += a[i+5] >> 21; a[i+5] &= 0x1fffff;
a[i+7] += a[i+6] >> 21; a[i+6] &= 0x1fffff;
a[i+8] += a[i+7] >> 21; a[i+7] &= 0x1fffff;
a[i+9] += a[i+8] >> 21; a[i+8] &= 0x1fffff;
}
a[96+1] += a[96] >> 21;
a[96] &= 0x1fffff;
#endif
}
/* Shift the result in the high 2048 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_4096_mont_shift_98(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[97] >> 11;
n += ((int64_t)a[98]) << 10;
for (i = 0; i < 97; i++) {
r[i] = n & 0x1fffff;
n >>= 21;
n += ((int64_t)a[99 + i]) << 10;
}
r[97] = (sp_digit)n;
#else
int i;
int64_t n = a[97] >> 11;
n += ((int64_t)a[98]) << 10;
for (i = 0; i < 96; i += 8) {
r[i + 0] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 99]) << 10;
r[i + 1] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 100]) << 10;
r[i + 2] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 101]) << 10;
r[i + 3] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 102]) << 10;
r[i + 4] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 103]) << 10;
r[i + 5] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 104]) << 10;
r[i + 6] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 105]) << 10;
r[i + 7] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 106]) << 10;
}
r[96] = n & 0x1fffff; n >>= 21; n += ((int64_t)a[195]) << 10;
r[97] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[98], 0, sizeof(*r) * 98U);
}
/* Reduce the number back to 4096 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_4096_mont_reduce_98(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_4096_norm_98(a + 98);
for (i=0; i<97; i++) {
mu = (a[i] * mp) & 0x1fffff;
sp_4096_mul_add_98(a+i, m, mu);
a[i+1] += a[i] >> 21;
}
mu = (a[i] * mp) & 0x7ffL;
sp_4096_mul_add_98(a+i, m, mu);
a[i+1] += a[i] >> 21;
a[i] &= 0x1fffff;
sp_4096_mont_shift_98(a, a);
sp_4096_cond_sub_98(a, a, m, 0 - (((a[97] >> 11) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_4096_norm_98(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_4096_mont_mul_98(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_4096_mul_98(r, a, b);
sp_4096_mont_reduce_98(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_4096_mont_sqr_98(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_4096_sqr_98(r, a);
sp_4096_mont_reduce_98(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_4096_mul_d_98(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 98; i++) {
t += tb * a[i];
r[i] = t & 0x1fffff;
t >>= 21;
}
r[98] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x1fffff;
for (i = 0; i < 96; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 21) + (t[1] & 0x1fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 21) + (t[2] & 0x1fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 21) + (t[3] & 0x1fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 21) + (t[4] & 0x1fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 21) + (t[5] & 0x1fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 21) + (t[6] & 0x1fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 21) + (t[7] & 0x1fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 21) + (t[0] & 0x1fffff);
}
t[1] = tb * a[97];
r[97] = (sp_digit)(t[0] >> 21) + (t[1] & 0x1fffff);
r[98] = (sp_digit)(t[1] >> 21);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_4096_cond_add_98(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 98; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 96; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[96] = a[96] + (b[96] & m);
r[97] = a[97] + (b[97] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_sub_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 98; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_98(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 98; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_4096_rshift_98(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<97; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (21 - n))) & 0x1fffff;
}
#else
for (i=0; i<96; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (21 - n))) & 0x1fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (21 - n))) & 0x1fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (21 - n))) & 0x1fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (21 - n))) & 0x1fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (21 - n))) & 0x1fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (21 - n))) & 0x1fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (21 - n))) & 0x1fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (21 - n))) & 0x1fffff;
}
r[96] = ((a[96] >> n) | (a[97] << (21 - n))) & 0x1fffff;
#endif
r[97] = a[97] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_4096_div_word_98(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 21 bits from d1 and top 10 bits from d0. */
d = (d1 << 10) | (d0 >> 11);
r = d / dv;
d -= r * dv;
/* Up to 11 bits in r */
/* Next 10 bits from d0. */
r <<= 10;
d <<= 10;
d |= (d0 >> 1) & ((1 << 10) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 21 bits in r */
/* Remaining 1 bits from d0. */
r <<= 1;
d <<= 1;
d |= d0 & ((1 << 1) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_4096_div_98(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[196 + 1], t2d[98 + 1], sdd[98 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 98 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
(void)m;
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 196 + 1;
sd = t2 + 98 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_4096_mul_d_98(sd, d, 1L << 10);
sp_4096_mul_d_196(t1, a, 1L << 10);
dv = sd[97];
for (i=98; i>=0; i--) {
t1[98 + i] += t1[98 + i - 1] >> 21;
t1[98 + i - 1] &= 0x1fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[98 + i];
d1 <<= 21;
d1 += t1[98 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_4096_div_word_98(t1[98 + i], t1[98 + i - 1], dv);
#endif
sp_4096_mul_d_98(t2, sd, r1);
(void)sp_4096_sub_98(&t1[i], &t1[i], t2);
t1[98 + i] -= t2[98];
t1[98 + i] += t1[98 + i - 1] >> 21;
t1[98 + i - 1] &= 0x1fffff;
r1 = (((-t1[98 + i]) << 21) - t1[98 + i - 1]) / dv;
r1 -= t1[98 + i];
sp_4096_mul_d_98(t2, sd, r1);
(void)sp_4096_add_98(&t1[i], &t1[i], t2);
t1[98 + i] += t1[98 + i - 1] >> 21;
t1[98 + i - 1] &= 0x1fffff;
}
t1[98 - 1] += t1[98 - 2] >> 21;
t1[98 - 2] &= 0x1fffff;
r1 = t1[98 - 1] / dv;
sp_4096_mul_d_98(t2, sd, r1);
sp_4096_sub_98(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 98U);
for (i=0; i<96; i++) {
r[i+1] += r[i] >> 21;
r[i] &= 0x1fffff;
}
sp_4096_cond_add_98(r, r, sd, 0 - ((r[97] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_4096_norm_98(r);
sp_4096_rshift_98(r, r, 10);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_4096_mod_98(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_4096_div_98(a, m, NULL, r);
}
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_4096_mod_exp_98(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 98 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 98U * 2U);
norm = t[0] = td;
t[1] = &td[98 * 2];
t[2] = &td[2 * 98 * 2];
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_98(norm, m);
if (reduceA != 0) {
err = sp_4096_mod_98(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 98U);
}
}
if (err == MP_OKAY) {
sp_4096_mul_98(t[1], t[1], norm);
err = sp_4096_mod_98(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 21;
c = bits % 21;
n = e[i--] << (21 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 21;
}
y = (n >> 20) & 1;
n <<= 1;
sp_4096_mont_mul_98(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 98 * 2);
sp_4096_mont_sqr_98(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 98 * 2);
}
sp_4096_mont_reduce_98(t[0], m, mp);
n = sp_4096_cmp_98(t[0], m);
sp_4096_cond_sub_98(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 98 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][196];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 98 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[98 * 2];
t[2] = &td[2 * 98 * 2];
#endif
norm = t[0];
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_98(norm, m);
if (reduceA != 0) {
err = sp_4096_mod_98(t[1], a, m);
if (err == MP_OKAY) {
sp_4096_mul_98(t[1], t[1], norm);
err = sp_4096_mod_98(t[1], t[1], m);
}
}
else {
sp_4096_mul_98(t[1], a, norm);
err = sp_4096_mod_98(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 21;
c = bits % 21;
n = e[i--] << (21 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 21;
}
y = (n >> 20) & 1;
n <<= 1;
sp_4096_mont_mul_98(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_4096_mont_sqr_98(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_4096_mont_reduce_98(t[0], m, mp);
n = sp_4096_cmp_98(t[0], m);
sp_4096_cond_sub_98(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][196];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[196];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 196, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 196;
#endif
norm = t[0];
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_98(norm, m);
if (reduceA != 0) {
err = sp_4096_mod_98(t[1], a, m);
if (err == MP_OKAY) {
sp_4096_mul_98(t[1], t[1], norm);
err = sp_4096_mod_98(t[1], t[1], m);
}
}
else {
sp_4096_mul_98(t[1], a, norm);
err = sp_4096_mod_98(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_4096_mont_sqr_98(t[ 2], t[ 1], m, mp);
sp_4096_mont_mul_98(t[ 3], t[ 2], t[ 1], m, mp);
sp_4096_mont_sqr_98(t[ 4], t[ 2], m, mp);
sp_4096_mont_mul_98(t[ 5], t[ 3], t[ 2], m, mp);
sp_4096_mont_sqr_98(t[ 6], t[ 3], m, mp);
sp_4096_mont_mul_98(t[ 7], t[ 4], t[ 3], m, mp);
sp_4096_mont_sqr_98(t[ 8], t[ 4], m, mp);
sp_4096_mont_mul_98(t[ 9], t[ 5], t[ 4], m, mp);
sp_4096_mont_sqr_98(t[10], t[ 5], m, mp);
sp_4096_mont_mul_98(t[11], t[ 6], t[ 5], m, mp);
sp_4096_mont_sqr_98(t[12], t[ 6], m, mp);
sp_4096_mont_mul_98(t[13], t[ 7], t[ 6], m, mp);
sp_4096_mont_sqr_98(t[14], t[ 7], m, mp);
sp_4096_mont_mul_98(t[15], t[ 8], t[ 7], m, mp);
sp_4096_mont_sqr_98(t[16], t[ 8], m, mp);
sp_4096_mont_mul_98(t[17], t[ 9], t[ 8], m, mp);
sp_4096_mont_sqr_98(t[18], t[ 9], m, mp);
sp_4096_mont_mul_98(t[19], t[10], t[ 9], m, mp);
sp_4096_mont_sqr_98(t[20], t[10], m, mp);
sp_4096_mont_mul_98(t[21], t[11], t[10], m, mp);
sp_4096_mont_sqr_98(t[22], t[11], m, mp);
sp_4096_mont_mul_98(t[23], t[12], t[11], m, mp);
sp_4096_mont_sqr_98(t[24], t[12], m, mp);
sp_4096_mont_mul_98(t[25], t[13], t[12], m, mp);
sp_4096_mont_sqr_98(t[26], t[13], m, mp);
sp_4096_mont_mul_98(t[27], t[14], t[13], m, mp);
sp_4096_mont_sqr_98(t[28], t[14], m, mp);
sp_4096_mont_mul_98(t[29], t[15], t[14], m, mp);
sp_4096_mont_sqr_98(t[30], t[15], m, mp);
sp_4096_mont_mul_98(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 20) / 21) - 1;
c = bits % 21;
if (c == 0) {
c = 21;
}
if (i < 98) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (11 - c);
c += 21;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (11 - c);
c += 21;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_4096_mont_sqr_98(rt, rt, m, mp);
sp_4096_mont_sqr_98(rt, rt, m, mp);
sp_4096_mont_sqr_98(rt, rt, m, mp);
sp_4096_mont_sqr_98(rt, rt, m, mp);
sp_4096_mont_sqr_98(rt, rt, m, mp);
sp_4096_mont_mul_98(rt, rt, t[y], m, mp);
}
sp_4096_mont_reduce_98(rt, m, mp);
n = sp_4096_cmp_98(rt, m);
sp_4096_cond_sub_98(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_RSA && !SP_RSA_PRIVATE_EXP_D */
#endif /* (WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH) && !WOLFSSL_RSA_PUBLIC_ONLY */
/* r = 2^n mod m where n is the number of bits to reduce by.
* Given m must be 4096 bits, just need to subtract.
*
* r A single precision number.
* m A single precision number.
*/
static void sp_4096_mont_norm_196(sp_digit* r, const sp_digit* m)
{
/* Set r = 2^n - 1. */
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<195; i++) {
r[i] = 0x1fffff;
}
#else
int i;
for (i = 0; i < 192; i += 8) {
r[i + 0] = 0x1fffff;
r[i + 1] = 0x1fffff;
r[i + 2] = 0x1fffff;
r[i + 3] = 0x1fffff;
r[i + 4] = 0x1fffff;
r[i + 5] = 0x1fffff;
r[i + 6] = 0x1fffff;
r[i + 7] = 0x1fffff;
}
r[192] = 0x1fffff;
r[193] = 0x1fffff;
r[194] = 0x1fffff;
#endif
r[195] = 0x1L;
/* r = (2^n - 1) mod n */
(void)sp_4096_sub_196(r, r, m);
/* Add one so r = 2^n mod m */
r[0] += 1;
}
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_4096_cmp_196(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=195; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
int i;
r |= (a[195] - b[195]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[194] - b[194]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[193] - b[193]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[192] - b[192]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
for (i = 184; i >= 0; i -= 8) {
r |= (a[i + 7] - b[i + 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 6] - b[i + 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 5] - b[i + 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 4] - b[i + 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 3] - b[i + 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 2] - b[i + 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 1] - b[i + 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[i + 0] - b[i + 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_4096_cond_sub_196(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 196; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
int i;
for (i = 0; i < 192; i += 8) {
r[i + 0] = a[i + 0] - (b[i + 0] & m);
r[i + 1] = a[i + 1] - (b[i + 1] & m);
r[i + 2] = a[i + 2] - (b[i + 2] & m);
r[i + 3] = a[i + 3] - (b[i + 3] & m);
r[i + 4] = a[i + 4] - (b[i + 4] & m);
r[i + 5] = a[i + 5] - (b[i + 5] & m);
r[i + 6] = a[i + 6] - (b[i + 6] & m);
r[i + 7] = a[i + 7] - (b[i + 7] & m);
}
r[192] = a[192] - (b[192] & m);
r[193] = a[193] - (b[193] & m);
r[194] = a[194] - (b[194] & m);
r[195] = a[195] - (b[195] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_4096_mul_add_196(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 196; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x1fffff;
t >>= 21;
}
r[196] += t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] += (sp_digit)(t[0] & 0x1fffff);
for (i = 0; i < 192; i += 8) {
t[1] = tb * a[i+1];
r[i+1] += (sp_digit)((t[0] >> 21) + (t[1] & 0x1fffff));
t[2] = tb * a[i+2];
r[i+2] += (sp_digit)((t[1] >> 21) + (t[2] & 0x1fffff));
t[3] = tb * a[i+3];
r[i+3] += (sp_digit)((t[2] >> 21) + (t[3] & 0x1fffff));
t[4] = tb * a[i+4];
r[i+4] += (sp_digit)((t[3] >> 21) + (t[4] & 0x1fffff));
t[5] = tb * a[i+5];
r[i+5] += (sp_digit)((t[4] >> 21) + (t[5] & 0x1fffff));
t[6] = tb * a[i+6];
r[i+6] += (sp_digit)((t[5] >> 21) + (t[6] & 0x1fffff));
t[7] = tb * a[i+7];
r[i+7] += (sp_digit)((t[6] >> 21) + (t[7] & 0x1fffff));
t[0] = tb * a[i+8];
r[i+8] += (sp_digit)((t[7] >> 21) + (t[0] & 0x1fffff));
}
t[1] = tb * a[193]; r[193] += (sp_digit)((t[0] >> 21) + (t[1] & 0x1fffff));
t[2] = tb * a[194]; r[194] += (sp_digit)((t[1] >> 21) + (t[2] & 0x1fffff));
t[3] = tb * a[195]; r[195] += (sp_digit)((t[2] >> 21) + (t[3] & 0x1fffff));
r[196] += (sp_digit)(t[3] >> 21);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 21.
*
* a Array of sp_digit to normalize.
*/
static void sp_4096_norm_196(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 195; i++) {
a[i+1] += a[i] >> 21;
a[i] &= 0x1fffff;
}
#else
int i;
for (i = 0; i < 192; i += 8) {
a[i+1] += a[i+0] >> 21; a[i+0] &= 0x1fffff;
a[i+2] += a[i+1] >> 21; a[i+1] &= 0x1fffff;
a[i+3] += a[i+2] >> 21; a[i+2] &= 0x1fffff;
a[i+4] += a[i+3] >> 21; a[i+3] &= 0x1fffff;
a[i+5] += a[i+4] >> 21; a[i+4] &= 0x1fffff;
a[i+6] += a[i+5] >> 21; a[i+5] &= 0x1fffff;
a[i+7] += a[i+6] >> 21; a[i+6] &= 0x1fffff;
a[i+8] += a[i+7] >> 21; a[i+7] &= 0x1fffff;
a[i+9] += a[i+8] >> 21; a[i+8] &= 0x1fffff;
}
a[192+1] += a[192] >> 21;
a[192] &= 0x1fffff;
a[193+1] += a[193] >> 21;
a[193] &= 0x1fffff;
a[194+1] += a[194] >> 21;
a[194] &= 0x1fffff;
#endif
}
/* Shift the result in the high 4096 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_4096_mont_shift_196(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[195] >> 1;
n += ((int64_t)a[196]) << 20;
for (i = 0; i < 195; i++) {
r[i] = n & 0x1fffff;
n >>= 21;
n += ((int64_t)a[197 + i]) << 20;
}
r[195] = (sp_digit)n;
#else
int i;
int64_t n = a[195] >> 1;
n += ((int64_t)a[196]) << 20;
for (i = 0; i < 192; i += 8) {
r[i + 0] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 197]) << 20;
r[i + 1] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 198]) << 20;
r[i + 2] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 199]) << 20;
r[i + 3] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 200]) << 20;
r[i + 4] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 201]) << 20;
r[i + 5] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 202]) << 20;
r[i + 6] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 203]) << 20;
r[i + 7] = n & 0x1fffff;
n >>= 21; n += ((int64_t)a[i + 204]) << 20;
}
r[192] = n & 0x1fffff; n >>= 21; n += ((int64_t)a[389]) << 20;
r[193] = n & 0x1fffff; n >>= 21; n += ((int64_t)a[390]) << 20;
r[194] = n & 0x1fffff; n >>= 21; n += ((int64_t)a[391]) << 20;
r[195] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[196], 0, sizeof(*r) * 196U);
}
/* Reduce the number back to 4096 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_4096_mont_reduce_196(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_4096_norm_196(a + 196);
#ifdef WOLFSSL_SP_DH
if (mp != 1) {
for (i=0; i<195; i++) {
mu = (a[i] * mp) & 0x1fffff;
sp_4096_mul_add_196(a+i, m, mu);
a[i+1] += a[i] >> 21;
}
mu = (a[i] * mp) & 0x1L;
sp_4096_mul_add_196(a+i, m, mu);
a[i+1] += a[i] >> 21;
a[i] &= 0x1fffff;
}
else {
for (i=0; i<195; i++) {
mu = a[i] & 0x1fffff;
sp_4096_mul_add_196(a+i, m, mu);
a[i+1] += a[i] >> 21;
}
mu = a[i] & 0x1L;
sp_4096_mul_add_196(a+i, m, mu);
a[i+1] += a[i] >> 21;
a[i] &= 0x1fffff;
}
#else
for (i=0; i<195; i++) {
mu = (a[i] * mp) & 0x1fffff;
sp_4096_mul_add_196(a+i, m, mu);
a[i+1] += a[i] >> 21;
}
mu = (a[i] * mp) & 0x1L;
sp_4096_mul_add_196(a+i, m, mu);
a[i+1] += a[i] >> 21;
a[i] &= 0x1fffff;
#endif
sp_4096_mont_shift_196(a, a);
sp_4096_cond_sub_196(a, a, m, 0 - (((a[195] >> 1) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_4096_norm_196(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_4096_mont_mul_196(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_4096_mul_196(r, a, b);
sp_4096_mont_reduce_196(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_4096_mont_sqr_196(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_4096_sqr_196(r, a);
sp_4096_mont_reduce_196(r, m, mp);
}
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_4096_mul_d_392(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 392; i++) {
t += tb * a[i];
r[i] = t & 0x1fffff;
t >>= 21;
}
r[392] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[8];
int i;
t[0] = tb * a[0]; r[0] = t[0] & 0x1fffff;
for (i = 0; i < 392; i += 8) {
t[1] = tb * a[i+1];
r[i+1] = (sp_digit)(t[0] >> 21) + (t[1] & 0x1fffff);
t[2] = tb * a[i+2];
r[i+2] = (sp_digit)(t[1] >> 21) + (t[2] & 0x1fffff);
t[3] = tb * a[i+3];
r[i+3] = (sp_digit)(t[2] >> 21) + (t[3] & 0x1fffff);
t[4] = tb * a[i+4];
r[i+4] = (sp_digit)(t[3] >> 21) + (t[4] & 0x1fffff);
t[5] = tb * a[i+5];
r[i+5] = (sp_digit)(t[4] >> 21) + (t[5] & 0x1fffff);
t[6] = tb * a[i+6];
r[i+6] = (sp_digit)(t[5] >> 21) + (t[6] & 0x1fffff);
t[7] = tb * a[i+7];
r[i+7] = (sp_digit)(t[6] >> 21) + (t[7] & 0x1fffff);
t[0] = tb * a[i+8];
r[i+8] = (sp_digit)(t[7] >> 21) + (t[0] & 0x1fffff);
}
r[392] = (sp_digit)(t[7] >> 21);
#endif /* WOLFSSL_SP_SMALL */
}
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_4096_cond_add_196(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 196; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
int i;
for (i = 0; i < 192; i += 8) {
r[i + 0] = a[i + 0] + (b[i + 0] & m);
r[i + 1] = a[i + 1] + (b[i + 1] & m);
r[i + 2] = a[i + 2] + (b[i + 2] & m);
r[i + 3] = a[i + 3] + (b[i + 3] & m);
r[i + 4] = a[i + 4] + (b[i + 4] & m);
r[i + 5] = a[i + 5] + (b[i + 5] & m);
r[i + 6] = a[i + 6] + (b[i + 6] & m);
r[i + 7] = a[i + 7] + (b[i + 7] & m);
}
r[192] = a[192] + (b[192] & m);
r[193] = a[193] + (b[193] & m);
r[194] = a[194] + (b[194] & m);
r[195] = a[195] + (b[195] & m);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_sub_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 196; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#endif
#ifdef WOLFSSL_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_4096_add_196(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 196; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#endif
SP_NOINLINE static void sp_4096_rshift_196(sp_digit* r, sp_digit* a, byte n)
{
int i;
#ifdef WOLFSSL_SP_SMALL
for (i=0; i<195; i++) {
r[i] = ((a[i] >> n) | (a[i + 1] << (21 - n))) & 0x1fffff;
}
#else
for (i=0; i<192; i += 8) {
r[i+0] = ((a[i+0] >> n) | (a[i+1] << (21 - n))) & 0x1fffff;
r[i+1] = ((a[i+1] >> n) | (a[i+2] << (21 - n))) & 0x1fffff;
r[i+2] = ((a[i+2] >> n) | (a[i+3] << (21 - n))) & 0x1fffff;
r[i+3] = ((a[i+3] >> n) | (a[i+4] << (21 - n))) & 0x1fffff;
r[i+4] = ((a[i+4] >> n) | (a[i+5] << (21 - n))) & 0x1fffff;
r[i+5] = ((a[i+5] >> n) | (a[i+6] << (21 - n))) & 0x1fffff;
r[i+6] = ((a[i+6] >> n) | (a[i+7] << (21 - n))) & 0x1fffff;
r[i+7] = ((a[i+7] >> n) | (a[i+8] << (21 - n))) & 0x1fffff;
}
r[192] = ((a[192] >> n) | (a[193] << (21 - n))) & 0x1fffff;
r[193] = ((a[193] >> n) | (a[194] << (21 - n))) & 0x1fffff;
r[194] = ((a[194] >> n) | (a[195] << (21 - n))) & 0x1fffff;
#endif
r[195] = a[195] >> n;
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_4096_div_word_196(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 21 bits from d1 and top 10 bits from d0. */
d = (d1 << 10) | (d0 >> 11);
r = d / dv;
d -= r * dv;
/* Up to 11 bits in r */
/* Next 10 bits from d0. */
r <<= 10;
d <<= 10;
d |= (d0 >> 1) & ((1 << 10) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 21 bits in r */
/* Remaining 1 bits from d0. */
r <<= 1;
d <<= 1;
d |= d0 & ((1 << 1) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Nmber to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_4096_div_196(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[392 + 1], t2d[196 + 1], sdd[196 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* sd;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (4 * 196 + 3), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
(void)m;
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 392 + 1;
sd = t2 + 196 + 1;
#else
t1 = t1d;
t2 = t2d;
sd = sdd;
#endif
sp_4096_mul_d_196(sd, d, 1L << 20);
sp_4096_mul_d_392(t1, a, 1L << 20);
dv = sd[195];
for (i=196; i>=0; i--) {
t1[196 + i] += t1[196 + i - 1] >> 21;
t1[196 + i - 1] &= 0x1fffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[196 + i];
d1 <<= 21;
d1 += t1[196 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_4096_div_word_196(t1[196 + i], t1[196 + i - 1], dv);
#endif
sp_4096_mul_d_196(t2, sd, r1);
(void)sp_4096_sub_196(&t1[i], &t1[i], t2);
t1[196 + i] -= t2[196];
t1[196 + i] += t1[196 + i - 1] >> 21;
t1[196 + i - 1] &= 0x1fffff;
r1 = (((-t1[196 + i]) << 21) - t1[196 + i - 1]) / dv;
r1 -= t1[196 + i];
sp_4096_mul_d_196(t2, sd, r1);
(void)sp_4096_add_196(&t1[i], &t1[i], t2);
t1[196 + i] += t1[196 + i - 1] >> 21;
t1[196 + i - 1] &= 0x1fffff;
}
t1[196 - 1] += t1[196 - 2] >> 21;
t1[196 - 2] &= 0x1fffff;
r1 = t1[196 - 1] / dv;
sp_4096_mul_d_196(t2, sd, r1);
sp_4096_sub_196(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 196U);
for (i=0; i<194; i++) {
r[i+1] += r[i] >> 21;
r[i] &= 0x1fffff;
}
sp_4096_cond_add_196(r, r, sd, 0 - ((r[195] < 0) ?
(sp_digit)1 : (sp_digit)0));
sp_4096_norm_196(r);
sp_4096_rshift_196(r, r, 20);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_4096_mod_196(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_4096_div_196(a, m, NULL, r);
}
#if (defined(WOLFSSL_HAVE_SP_RSA) && !defined(WOLFSSL_RSA_PUBLIC_ONLY)) || \
defined(WOLFSSL_HAVE_SP_DH)
/* Modular exponentiate a to the e mod m. (r = a^e mod m)
*
* r A single precision number that is the result of the operation.
* a A single precision number being exponentiated.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_4096_mod_exp_196(sp_digit* r, const sp_digit* a, const sp_digit* e, int bits,
const sp_digit* m, int reduceA)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* td;
sp_digit* t[3];
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 196 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
if (err == MP_OKAY) {
XMEMSET(td, 0, sizeof(*td) * 3U * 196U * 2U);
norm = t[0] = td;
t[1] = &td[196 * 2];
t[2] = &td[2 * 196 * 2];
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_196(norm, m);
if (reduceA != 0) {
err = sp_4096_mod_196(t[1], a, m);
}
else {
XMEMCPY(t[1], a, sizeof(sp_digit) * 196U);
}
}
if (err == MP_OKAY) {
sp_4096_mul_196(t[1], t[1], norm);
err = sp_4096_mod_196(t[1], t[1], m);
}
if (err == MP_OKAY) {
i = bits / 21;
c = bits % 21;
n = e[i--] << (21 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 21;
}
y = (n >> 20) & 1;
n <<= 1;
sp_4096_mont_mul_196(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])),
sizeof(*t[2]) * 196 * 2);
sp_4096_mont_sqr_196(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2],
sizeof(*t[2]) * 196 * 2);
}
sp_4096_mont_reduce_196(t[0], m, mp);
n = sp_4096_cmp_196(t[0], m);
sp_4096_cond_sub_196(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(*r) * 196 * 2);
}
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
return err;
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[3][392];
#else
sp_digit* td;
sp_digit* t[3];
#endif
sp_digit* norm;
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(*td) * 3 * 196 * 2, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
t[0] = td;
t[1] = &td[196 * 2];
t[2] = &td[2 * 196 * 2];
#endif
norm = t[0];
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_196(norm, m);
if (reduceA != 0) {
err = sp_4096_mod_196(t[1], a, m);
if (err == MP_OKAY) {
sp_4096_mul_196(t[1], t[1], norm);
err = sp_4096_mod_196(t[1], t[1], m);
}
}
else {
sp_4096_mul_196(t[1], a, norm);
err = sp_4096_mod_196(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
i = bits / 21;
c = bits % 21;
n = e[i--] << (21 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1) {
break;
}
n = e[i--];
c = 21;
}
y = (n >> 20) & 1;
n <<= 1;
sp_4096_mont_mul_196(t[y^1], t[0], t[1], m, mp);
XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), sizeof(t[2]));
sp_4096_mont_sqr_196(t[2], t[2], m, mp);
XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
((size_t)t[1] & addr_mask[y])), t[2], sizeof(t[2]));
}
sp_4096_mont_reduce_196(t[0], m, mp);
n = sp_4096_cmp_196(t[0], m);
sp_4096_cond_sub_196(t[0], t[0], m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, t[0], sizeof(t[0]));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit t[32][392];
#else
sp_digit* t[32];
sp_digit* td;
#endif
sp_digit* norm;
sp_digit rt[392];
sp_digit mp = 1;
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 32 * 392, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
for (i=0; i<32; i++)
t[i] = td + i * 392;
#endif
norm = t[0];
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_196(norm, m);
if (reduceA != 0) {
err = sp_4096_mod_196(t[1], a, m);
if (err == MP_OKAY) {
sp_4096_mul_196(t[1], t[1], norm);
err = sp_4096_mod_196(t[1], t[1], m);
}
}
else {
sp_4096_mul_196(t[1], a, norm);
err = sp_4096_mod_196(t[1], t[1], m);
}
}
if (err == MP_OKAY) {
sp_4096_mont_sqr_196(t[ 2], t[ 1], m, mp);
sp_4096_mont_mul_196(t[ 3], t[ 2], t[ 1], m, mp);
sp_4096_mont_sqr_196(t[ 4], t[ 2], m, mp);
sp_4096_mont_mul_196(t[ 5], t[ 3], t[ 2], m, mp);
sp_4096_mont_sqr_196(t[ 6], t[ 3], m, mp);
sp_4096_mont_mul_196(t[ 7], t[ 4], t[ 3], m, mp);
sp_4096_mont_sqr_196(t[ 8], t[ 4], m, mp);
sp_4096_mont_mul_196(t[ 9], t[ 5], t[ 4], m, mp);
sp_4096_mont_sqr_196(t[10], t[ 5], m, mp);
sp_4096_mont_mul_196(t[11], t[ 6], t[ 5], m, mp);
sp_4096_mont_sqr_196(t[12], t[ 6], m, mp);
sp_4096_mont_mul_196(t[13], t[ 7], t[ 6], m, mp);
sp_4096_mont_sqr_196(t[14], t[ 7], m, mp);
sp_4096_mont_mul_196(t[15], t[ 8], t[ 7], m, mp);
sp_4096_mont_sqr_196(t[16], t[ 8], m, mp);
sp_4096_mont_mul_196(t[17], t[ 9], t[ 8], m, mp);
sp_4096_mont_sqr_196(t[18], t[ 9], m, mp);
sp_4096_mont_mul_196(t[19], t[10], t[ 9], m, mp);
sp_4096_mont_sqr_196(t[20], t[10], m, mp);
sp_4096_mont_mul_196(t[21], t[11], t[10], m, mp);
sp_4096_mont_sqr_196(t[22], t[11], m, mp);
sp_4096_mont_mul_196(t[23], t[12], t[11], m, mp);
sp_4096_mont_sqr_196(t[24], t[12], m, mp);
sp_4096_mont_mul_196(t[25], t[13], t[12], m, mp);
sp_4096_mont_sqr_196(t[26], t[13], m, mp);
sp_4096_mont_mul_196(t[27], t[14], t[13], m, mp);
sp_4096_mont_sqr_196(t[28], t[14], m, mp);
sp_4096_mont_mul_196(t[29], t[15], t[14], m, mp);
sp_4096_mont_sqr_196(t[30], t[15], m, mp);
sp_4096_mont_mul_196(t[31], t[16], t[15], m, mp);
bits = ((bits + 4) / 5) * 5;
i = ((bits + 20) / 21) - 1;
c = bits % 21;
if (c == 0) {
c = 21;
}
if (i < 196) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 5) {
n |= e[i--] << (11 - c);
c += 21;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
XMEMCPY(rt, t[y], sizeof(rt));
for (; i>=0 || c>=5; ) {
if (c < 5) {
n |= e[i--] << (11 - c);
c += 21;
}
y = (n >> 27) & 0x1f;
n <<= 5;
c -= 5;
sp_4096_mont_sqr_196(rt, rt, m, mp);
sp_4096_mont_sqr_196(rt, rt, m, mp);
sp_4096_mont_sqr_196(rt, rt, m, mp);
sp_4096_mont_sqr_196(rt, rt, m, mp);
sp_4096_mont_sqr_196(rt, rt, m, mp);
sp_4096_mont_mul_196(rt, rt, t[y], m, mp);
}
sp_4096_mont_reduce_196(rt, m, mp);
n = sp_4096_cmp_196(rt, m);
sp_4096_cond_sub_196(rt, rt, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
XMEMCPY(r, rt, sizeof(rt));
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
#endif
}
#endif /* (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) || */
/* WOLFSSL_HAVE_SP_DH */
#ifdef WOLFSSL_HAVE_SP_RSA
/* RSA public key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* em Public exponent.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 512 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPublic_4096(const byte* in, word32 inLen, mp_int* em, mp_int* mm,
byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* d = NULL;
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit* norm;
sp_digit e[1] = {0};
sp_digit mp;
int i;
int err = MP_OKAY;
if (*outLen < 512U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 21) {
err = MP_READ_E;
}
if (inLen > 512U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 196 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
a = d;
r = a + 196 * 2;
m = r + 196 * 2;
norm = r;
sp_4096_from_bin(a, 196, in, inLen);
#if DIGIT_BIT >= 21
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_4096_from_mp(m, 196, mm);
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_196(norm, m);
}
if (err == MP_OKAY) {
sp_4096_mul_196(a, a, norm);
err = sp_4096_mod_196(a, a, m);
}
if (err == MP_OKAY) {
for (i=20; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 196 * 2);
for (i--; i>=0; i--) {
sp_4096_mont_sqr_196(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_4096_mont_mul_196(r, r, a, m, mp);
}
}
sp_4096_mont_reduce_196(r, m, mp);
mp = sp_4096_cmp_196(r, m);
sp_4096_cond_sub_196(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0)- 1);
sp_4096_to_bin(r, out);
*outLen = 512;
}
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit ad[392], md[196], rd[392];
#else
sp_digit* d = NULL;
#endif
sp_digit* a;
sp_digit* m;
sp_digit* r;
sp_digit e[1] = {0};
int err = MP_OKAY;
if (*outLen < 512U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(em) > 21) {
err = MP_READ_E;
}
if (inLen > 512U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 4096) {
err = MP_READ_E;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 196 * 5, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d;
r = a + 196 * 2;
m = r + 196 * 2;
}
#else
a = ad;
m = md;
r = rd;
#endif
if (err == MP_OKAY) {
sp_4096_from_bin(a, 196, in, inLen);
#if DIGIT_BIT >= 21
e[0] = (sp_digit)em->dp[0];
#else
e[0] = (sp_digit)em->dp[0];
if (em->used > 1) {
e[0] |= ((sp_digit)em->dp[1]) << DIGIT_BIT;
}
#endif
if (e[0] == 0) {
err = MP_EXPTMOD_E;
}
}
if (err == MP_OKAY) {
sp_4096_from_mp(m, 196, mm);
if (e[0] == 0x3) {
sp_4096_sqr_196(r, a);
err = sp_4096_mod_196(r, r, m);
if (err == MP_OKAY) {
sp_4096_mul_196(r, a, r);
err = sp_4096_mod_196(r, r, m);
}
}
else {
sp_digit* norm = r;
int i;
sp_digit mp;
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_196(norm, m);
sp_4096_mul_196(a, a, norm);
err = sp_4096_mod_196(a, a, m);
if (err == MP_OKAY) {
for (i=20; i>=0; i--) {
if ((e[0] >> i) != 0) {
break;
}
}
XMEMCPY(r, a, sizeof(sp_digit) * 392U);
for (i--; i>=0; i--) {
sp_4096_mont_sqr_196(r, r, m, mp);
if (((e[0] >> i) & 1) == 1) {
sp_4096_mont_mul_196(r, r, a, m, mp);
}
}
sp_4096_mont_reduce_196(r, m, mp);
mp = sp_4096_cmp_196(r, m);
sp_4096_cond_sub_196(r, r, m, ((mp < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
}
}
if (err == MP_OKAY) {
sp_4096_to_bin(r, out);
*outLen = 512;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
#endif
return err;
#endif /* WOLFSSL_SP_SMALL */
}
#ifndef WOLFSSL_RSA_PUBLIC_ONLY
#if !defined(SP_RSA_PRIVATE_EXP_D) && !defined(RSA_LOW_MEM)
#endif /* !SP_RSA_PRIVATE_EXP_D && !RSA_LOW_MEM */
/* RSA private key operation.
*
* in Array of bytes representing the number to exponentiate, base.
* inLen Number of bytes in base.
* dm Private exponent.
* pm First prime.
* qm Second prime.
* dpm First prime's CRT exponent.
* dqm Second prime's CRT exponent.
* qim Inverse of second prime mod p.
* mm Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 512 bytes long.
* outLen Number of bytes in result.
* returns 0 on success, MP_TO_E when the outLen is too small, MP_READ_E when
* an array is too long and MEMORY_E when dynamic memory allocation fails.
*/
int sp_RsaPrivate_4096(const byte* in, word32 inLen, mp_int* dm,
mp_int* pm, mp_int* qm, mp_int* dpm, mp_int* dqm, mp_int* qim, mp_int* mm,
byte* out, word32* outLen)
{
#if defined(SP_RSA_PRIVATE_EXP_D) || defined(RSA_LOW_MEM)
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* a;
sp_digit* d = NULL;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 512U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 4096) {
err = MP_READ_E;
}
if (inLen > 512) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 196 * 4, NULL,
DYNAMIC_TYPE_RSA);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = d + 196;
m = a + 392;
r = a;
sp_4096_from_bin(a, 196, in, inLen);
sp_4096_from_mp(d, 196, dm);
sp_4096_from_mp(m, 196, mm);
err = sp_4096_mod_exp_196(r, a, d, 4096, m, 0);
}
if (err == MP_OKAY) {
sp_4096_to_bin(r, out);
*outLen = 512;
}
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 196);
XFREE(d, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[392], d[196], m[196];
sp_digit* r = a;
int err = MP_OKAY;
(void)pm;
(void)qm;
(void)dpm;
(void)dqm;
(void)qim;
if (*outLen < 512U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (mp_count_bits(dm) > 4096) {
err = MP_READ_E;
}
if (inLen > 512U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_4096_from_bin(a, 196, in, inLen);
sp_4096_from_mp(d, 196, dm);
sp_4096_from_mp(m, 196, mm);
err = sp_4096_mod_exp_196(r, a, d, 4096, m, 0);
}
if (err == MP_OKAY) {
sp_4096_to_bin(r, out);
*outLen = 512;
}
XMEMSET(d, 0, sizeof(sp_digit) * 196);
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#else
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* t = NULL;
sp_digit* a;
sp_digit* p;
sp_digit* q;
sp_digit* dp;
sp_digit* dq;
sp_digit* qi;
sp_digit* tmpa;
sp_digit* tmpb;
sp_digit* r;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 512U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 512) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 98 * 11, NULL,
DYNAMIC_TYPE_RSA);
if (t == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
a = t;
p = a + 196 * 2;
q = p + 98;
qi = dq = dp = q + 98;
tmpa = qi + 98;
tmpb = tmpa + 196;
r = t + 196;
sp_4096_from_bin(a, 196, in, inLen);
sp_4096_from_mp(p, 98, pm);
sp_4096_from_mp(q, 98, qm);
sp_4096_from_mp(dp, 98, dpm);
err = sp_4096_mod_exp_98(tmpa, a, dp, 2048, p, 1);
}
if (err == MP_OKAY) {
sp_4096_from_mp(dq, 98, dqm);
err = sp_4096_mod_exp_98(tmpb, a, dq, 2048, q, 1);
}
if (err == MP_OKAY) {
(void)sp_4096_sub_98(tmpa, tmpa, tmpb);
sp_4096_cond_add_98(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[97] >> 31));
sp_4096_cond_add_98(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[97] >> 31));
sp_4096_from_mp(qi, 98, qim);
sp_4096_mul_98(tmpa, tmpa, qi);
err = sp_4096_mod_98(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_4096_mul_98(tmpa, q, tmpa);
(void)sp_4096_add_196(r, tmpb, tmpa);
sp_4096_norm_196(r);
sp_4096_to_bin(r, out);
*outLen = 512;
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_digit) * 98 * 11);
XFREE(t, NULL, DYNAMIC_TYPE_RSA);
}
return err;
#else
sp_digit a[196 * 2];
sp_digit p[98], q[98], dp[98], dq[98], qi[98];
sp_digit tmpa[196], tmpb[196];
sp_digit* r = a;
int err = MP_OKAY;
(void)dm;
(void)mm;
if (*outLen < 512U) {
err = MP_TO_E;
}
if (err == MP_OKAY) {
if (inLen > 512U) {
err = MP_READ_E;
}
if (mp_count_bits(mm) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
sp_4096_from_bin(a, 196, in, inLen);
sp_4096_from_mp(p, 98, pm);
sp_4096_from_mp(q, 98, qm);
sp_4096_from_mp(dp, 98, dpm);
sp_4096_from_mp(dq, 98, dqm);
sp_4096_from_mp(qi, 98, qim);
err = sp_4096_mod_exp_98(tmpa, a, dp, 2048, p, 1);
}
if (err == MP_OKAY) {
err = sp_4096_mod_exp_98(tmpb, a, dq, 2048, q, 1);
}
if (err == MP_OKAY) {
(void)sp_4096_sub_98(tmpa, tmpa, tmpb);
sp_4096_cond_add_98(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[97] >> 31));
sp_4096_cond_add_98(tmpa, tmpa, p, 0 - ((sp_int_digit)tmpa[97] >> 31));
sp_4096_mul_98(tmpa, tmpa, qi);
err = sp_4096_mod_98(tmpa, tmpa, p);
}
if (err == MP_OKAY) {
sp_4096_mul_98(tmpa, tmpa, q);
(void)sp_4096_add_196(r, tmpb, tmpa);
sp_4096_norm_196(r);
sp_4096_to_bin(r, out);
*outLen = 512;
}
XMEMSET(tmpa, 0, sizeof(tmpa));
XMEMSET(tmpb, 0, sizeof(tmpb));
XMEMSET(p, 0, sizeof(p));
XMEMSET(q, 0, sizeof(q));
XMEMSET(dp, 0, sizeof(dp));
XMEMSET(dq, 0, sizeof(dq));
XMEMSET(qi, 0, sizeof(qi));
return err;
#endif /* WOLFSSL_SP_SMALL || defined(WOLFSSL_SMALL_STACK) */
#endif /* SP_RSA_PRIVATE_EXP_D || RSA_LOW_MEM */
}
#endif /* !WOLFSSL_RSA_PUBLIC_ONLY */
#endif /* WOLFSSL_HAVE_SP_RSA */
#if defined(WOLFSSL_HAVE_SP_DH) || (defined(WOLFSSL_HAVE_SP_RSA) && \
!defined(WOLFSSL_RSA_PUBLIC_ONLY))
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_4096_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (4096 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 21
XMEMCPY(r->dp, a, sizeof(sp_digit) * 196);
r->used = 196;
mp_clamp(r);
#elif DIGIT_BIT < 21
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 196; i++) {
r->dp[j] |= (mp_digit)(a[i] << s);
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = (mp_digit)(a[i] >> s);
while (s + DIGIT_BIT <= 21) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = (mp_digit)(a[i] >> s);
}
}
s = 21 - s;
}
r->used = (4096 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 196; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 21 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 21 - s;
}
else {
s += 21;
}
}
r->used = (4096 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base. MP integer.
* exp Exponent. MP integer.
* mod Modulus. MP integer.
* res Result. MP integer.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_ModExp_4096(mp_int* base, mp_int* exp, mp_int* mod, mp_int* res)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 4096) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 196 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 196 * 2;
m = e + 196;
r = b;
sp_4096_from_mp(b, 196, base);
sp_4096_from_mp(e, 196, exp);
sp_4096_from_mp(m, 196, mod);
err = sp_4096_mod_exp_196(r, b, e, mp_count_bits(exp), m, 0);
}
if (err == MP_OKAY) {
err = sp_4096_to_mp(r, res);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 196U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[392], ed[196], md[196];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
int err = MP_OKAY;
int expBits = mp_count_bits(exp);
if (mp_count_bits(base) > 4096) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expBits > 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 4096) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 196 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 196 * 2;
m = e + 196;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_4096_from_mp(b, 196, base);
sp_4096_from_mp(e, 196, exp);
sp_4096_from_mp(m, 196, mod);
err = sp_4096_mod_exp_196(r, b, e, expBits, m, 0);
}
if (err == MP_OKAY) {
err = sp_4096_to_mp(r, res);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 196U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 196U);
#endif
return err;
#endif
}
#ifdef WOLFSSL_HAVE_SP_DH
#ifdef HAVE_FFDHE_4096
SP_NOINLINE static void sp_4096_lshift_196(sp_digit* r, sp_digit* a, byte n)
{
#ifdef WOLFSSL_SP_SMALL
int i;
r[196] = a[195] >> (21 - n);
for (i=195; i>0; i--) {
r[i] = ((a[i] << n) | (a[i-1] >> (21 - n))) & 0x1fffff;
}
#else
sp_int_digit s, t;
s = (sp_int_digit)a[195];
r[196] = s >> (21U - n);
s = (sp_int_digit)(a[195]); t = (sp_int_digit)(a[194]);
r[195] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[194]); t = (sp_int_digit)(a[193]);
r[194] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[193]); t = (sp_int_digit)(a[192]);
r[193] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[192]); t = (sp_int_digit)(a[191]);
r[192] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[191]); t = (sp_int_digit)(a[190]);
r[191] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[190]); t = (sp_int_digit)(a[189]);
r[190] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[189]); t = (sp_int_digit)(a[188]);
r[189] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[188]); t = (sp_int_digit)(a[187]);
r[188] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[187]); t = (sp_int_digit)(a[186]);
r[187] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[186]); t = (sp_int_digit)(a[185]);
r[186] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[185]); t = (sp_int_digit)(a[184]);
r[185] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[184]); t = (sp_int_digit)(a[183]);
r[184] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[183]); t = (sp_int_digit)(a[182]);
r[183] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[182]); t = (sp_int_digit)(a[181]);
r[182] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[181]); t = (sp_int_digit)(a[180]);
r[181] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[180]); t = (sp_int_digit)(a[179]);
r[180] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[179]); t = (sp_int_digit)(a[178]);
r[179] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[178]); t = (sp_int_digit)(a[177]);
r[178] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[177]); t = (sp_int_digit)(a[176]);
r[177] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[176]); t = (sp_int_digit)(a[175]);
r[176] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[175]); t = (sp_int_digit)(a[174]);
r[175] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[174]); t = (sp_int_digit)(a[173]);
r[174] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[173]); t = (sp_int_digit)(a[172]);
r[173] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[172]); t = (sp_int_digit)(a[171]);
r[172] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[171]); t = (sp_int_digit)(a[170]);
r[171] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[170]); t = (sp_int_digit)(a[169]);
r[170] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[169]); t = (sp_int_digit)(a[168]);
r[169] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[168]); t = (sp_int_digit)(a[167]);
r[168] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[167]); t = (sp_int_digit)(a[166]);
r[167] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[166]); t = (sp_int_digit)(a[165]);
r[166] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[165]); t = (sp_int_digit)(a[164]);
r[165] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[164]); t = (sp_int_digit)(a[163]);
r[164] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[163]); t = (sp_int_digit)(a[162]);
r[163] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[162]); t = (sp_int_digit)(a[161]);
r[162] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[161]); t = (sp_int_digit)(a[160]);
r[161] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[160]); t = (sp_int_digit)(a[159]);
r[160] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[159]); t = (sp_int_digit)(a[158]);
r[159] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[158]); t = (sp_int_digit)(a[157]);
r[158] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[157]); t = (sp_int_digit)(a[156]);
r[157] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[156]); t = (sp_int_digit)(a[155]);
r[156] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[155]); t = (sp_int_digit)(a[154]);
r[155] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[154]); t = (sp_int_digit)(a[153]);
r[154] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[153]); t = (sp_int_digit)(a[152]);
r[153] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[152]); t = (sp_int_digit)(a[151]);
r[152] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[151]); t = (sp_int_digit)(a[150]);
r[151] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[150]); t = (sp_int_digit)(a[149]);
r[150] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[149]); t = (sp_int_digit)(a[148]);
r[149] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[148]); t = (sp_int_digit)(a[147]);
r[148] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[147]); t = (sp_int_digit)(a[146]);
r[147] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[146]); t = (sp_int_digit)(a[145]);
r[146] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[145]); t = (sp_int_digit)(a[144]);
r[145] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[144]); t = (sp_int_digit)(a[143]);
r[144] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[143]); t = (sp_int_digit)(a[142]);
r[143] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[142]); t = (sp_int_digit)(a[141]);
r[142] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[141]); t = (sp_int_digit)(a[140]);
r[141] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[140]); t = (sp_int_digit)(a[139]);
r[140] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[139]); t = (sp_int_digit)(a[138]);
r[139] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[138]); t = (sp_int_digit)(a[137]);
r[138] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[137]); t = (sp_int_digit)(a[136]);
r[137] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[136]); t = (sp_int_digit)(a[135]);
r[136] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[135]); t = (sp_int_digit)(a[134]);
r[135] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[134]); t = (sp_int_digit)(a[133]);
r[134] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[133]); t = (sp_int_digit)(a[132]);
r[133] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[132]); t = (sp_int_digit)(a[131]);
r[132] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[131]); t = (sp_int_digit)(a[130]);
r[131] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[130]); t = (sp_int_digit)(a[129]);
r[130] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[129]); t = (sp_int_digit)(a[128]);
r[129] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[128]); t = (sp_int_digit)(a[127]);
r[128] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[127]); t = (sp_int_digit)(a[126]);
r[127] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[126]); t = (sp_int_digit)(a[125]);
r[126] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[125]); t = (sp_int_digit)(a[124]);
r[125] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[124]); t = (sp_int_digit)(a[123]);
r[124] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[123]); t = (sp_int_digit)(a[122]);
r[123] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[122]); t = (sp_int_digit)(a[121]);
r[122] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[121]); t = (sp_int_digit)(a[120]);
r[121] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[120]); t = (sp_int_digit)(a[119]);
r[120] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[119]); t = (sp_int_digit)(a[118]);
r[119] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[118]); t = (sp_int_digit)(a[117]);
r[118] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[117]); t = (sp_int_digit)(a[116]);
r[117] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[116]); t = (sp_int_digit)(a[115]);
r[116] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[115]); t = (sp_int_digit)(a[114]);
r[115] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[114]); t = (sp_int_digit)(a[113]);
r[114] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[113]); t = (sp_int_digit)(a[112]);
r[113] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[112]); t = (sp_int_digit)(a[111]);
r[112] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[111]); t = (sp_int_digit)(a[110]);
r[111] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[110]); t = (sp_int_digit)(a[109]);
r[110] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[109]); t = (sp_int_digit)(a[108]);
r[109] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[108]); t = (sp_int_digit)(a[107]);
r[108] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[107]); t = (sp_int_digit)(a[106]);
r[107] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[106]); t = (sp_int_digit)(a[105]);
r[106] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[105]); t = (sp_int_digit)(a[104]);
r[105] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[104]); t = (sp_int_digit)(a[103]);
r[104] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[103]); t = (sp_int_digit)(a[102]);
r[103] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[102]); t = (sp_int_digit)(a[101]);
r[102] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[101]); t = (sp_int_digit)(a[100]);
r[101] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[100]); t = (sp_int_digit)(a[99]);
r[100] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[99]); t = (sp_int_digit)(a[98]);
r[99] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[98]); t = (sp_int_digit)(a[97]);
r[98] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[97]); t = (sp_int_digit)(a[96]);
r[97] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[96]); t = (sp_int_digit)(a[95]);
r[96] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[95]); t = (sp_int_digit)(a[94]);
r[95] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[94]); t = (sp_int_digit)(a[93]);
r[94] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[93]); t = (sp_int_digit)(a[92]);
r[93] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[92]); t = (sp_int_digit)(a[91]);
r[92] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[91]); t = (sp_int_digit)(a[90]);
r[91] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[90]); t = (sp_int_digit)(a[89]);
r[90] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[89]); t = (sp_int_digit)(a[88]);
r[89] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[88]); t = (sp_int_digit)(a[87]);
r[88] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[87]); t = (sp_int_digit)(a[86]);
r[87] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[86]); t = (sp_int_digit)(a[85]);
r[86] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[85]); t = (sp_int_digit)(a[84]);
r[85] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[84]); t = (sp_int_digit)(a[83]);
r[84] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[83]); t = (sp_int_digit)(a[82]);
r[83] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[82]); t = (sp_int_digit)(a[81]);
r[82] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[81]); t = (sp_int_digit)(a[80]);
r[81] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[80]); t = (sp_int_digit)(a[79]);
r[80] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[79]); t = (sp_int_digit)(a[78]);
r[79] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[78]); t = (sp_int_digit)(a[77]);
r[78] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[77]); t = (sp_int_digit)(a[76]);
r[77] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[76]); t = (sp_int_digit)(a[75]);
r[76] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[75]); t = (sp_int_digit)(a[74]);
r[75] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[74]); t = (sp_int_digit)(a[73]);
r[74] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[73]); t = (sp_int_digit)(a[72]);
r[73] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[72]); t = (sp_int_digit)(a[71]);
r[72] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[71]); t = (sp_int_digit)(a[70]);
r[71] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[70]); t = (sp_int_digit)(a[69]);
r[70] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[69]); t = (sp_int_digit)(a[68]);
r[69] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[68]); t = (sp_int_digit)(a[67]);
r[68] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[67]); t = (sp_int_digit)(a[66]);
r[67] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[66]); t = (sp_int_digit)(a[65]);
r[66] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[65]); t = (sp_int_digit)(a[64]);
r[65] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[64]); t = (sp_int_digit)(a[63]);
r[64] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[63]); t = (sp_int_digit)(a[62]);
r[63] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[62]); t = (sp_int_digit)(a[61]);
r[62] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[61]); t = (sp_int_digit)(a[60]);
r[61] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[60]); t = (sp_int_digit)(a[59]);
r[60] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[59]); t = (sp_int_digit)(a[58]);
r[59] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[58]); t = (sp_int_digit)(a[57]);
r[58] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[57]); t = (sp_int_digit)(a[56]);
r[57] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[56]); t = (sp_int_digit)(a[55]);
r[56] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[55]); t = (sp_int_digit)(a[54]);
r[55] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[54]); t = (sp_int_digit)(a[53]);
r[54] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[53]); t = (sp_int_digit)(a[52]);
r[53] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[52]); t = (sp_int_digit)(a[51]);
r[52] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[51]); t = (sp_int_digit)(a[50]);
r[51] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[50]); t = (sp_int_digit)(a[49]);
r[50] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[49]); t = (sp_int_digit)(a[48]);
r[49] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[48]); t = (sp_int_digit)(a[47]);
r[48] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[47]); t = (sp_int_digit)(a[46]);
r[47] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[46]); t = (sp_int_digit)(a[45]);
r[46] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[45]); t = (sp_int_digit)(a[44]);
r[45] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[44]); t = (sp_int_digit)(a[43]);
r[44] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[43]); t = (sp_int_digit)(a[42]);
r[43] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[42]); t = (sp_int_digit)(a[41]);
r[42] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[41]); t = (sp_int_digit)(a[40]);
r[41] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[40]); t = (sp_int_digit)(a[39]);
r[40] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[39]); t = (sp_int_digit)(a[38]);
r[39] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[38]); t = (sp_int_digit)(a[37]);
r[38] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[37]); t = (sp_int_digit)(a[36]);
r[37] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[36]); t = (sp_int_digit)(a[35]);
r[36] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[35]); t = (sp_int_digit)(a[34]);
r[35] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[34]); t = (sp_int_digit)(a[33]);
r[34] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[33]); t = (sp_int_digit)(a[32]);
r[33] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[32]); t = (sp_int_digit)(a[31]);
r[32] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[31]); t = (sp_int_digit)(a[30]);
r[31] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[30]); t = (sp_int_digit)(a[29]);
r[30] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[29]); t = (sp_int_digit)(a[28]);
r[29] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[28]); t = (sp_int_digit)(a[27]);
r[28] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[27]); t = (sp_int_digit)(a[26]);
r[27] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[26]); t = (sp_int_digit)(a[25]);
r[26] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[25]); t = (sp_int_digit)(a[24]);
r[25] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[24]); t = (sp_int_digit)(a[23]);
r[24] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[23]); t = (sp_int_digit)(a[22]);
r[23] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[22]); t = (sp_int_digit)(a[21]);
r[22] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[21]); t = (sp_int_digit)(a[20]);
r[21] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[20]); t = (sp_int_digit)(a[19]);
r[20] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[19]); t = (sp_int_digit)(a[18]);
r[19] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[18]); t = (sp_int_digit)(a[17]);
r[18] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[17]); t = (sp_int_digit)(a[16]);
r[17] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[16]); t = (sp_int_digit)(a[15]);
r[16] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[15]); t = (sp_int_digit)(a[14]);
r[15] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[14]); t = (sp_int_digit)(a[13]);
r[14] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[13]); t = (sp_int_digit)(a[12]);
r[13] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[12]); t = (sp_int_digit)(a[11]);
r[12] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[11]); t = (sp_int_digit)(a[10]);
r[11] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[10]); t = (sp_int_digit)(a[9]);
r[10] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[9]); t = (sp_int_digit)(a[8]);
r[9] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[8]); t = (sp_int_digit)(a[7]);
r[8] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[7]); t = (sp_int_digit)(a[6]);
r[7] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[6]); t = (sp_int_digit)(a[5]);
r[6] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[5]); t = (sp_int_digit)(a[4]);
r[5] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[4]); t = (sp_int_digit)(a[3]);
r[4] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[3]); t = (sp_int_digit)(a[2]);
r[3] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[2]); t = (sp_int_digit)(a[1]);
r[2] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
s = (sp_int_digit)(a[1]); t = (sp_int_digit)(a[0]);
r[1] = ((s << n) | (t >> (21U - n))) & 0x1fffff;
#endif
r[0] = (a[0] << n) & 0x1fffff;
}
/* Modular exponentiate 2 to the e mod m. (r = 2^e mod m)
*
* r A single precision number that is the result of the operation.
* e A single precision number that is the exponent.
* bits The number of bits in the exponent.
* m A single precision number that is the modulus.
* returns 0 on success and MEMORY_E on dynamic memory allocation failure.
*/
static int sp_4096_mod_exp_2_196(sp_digit* r, const sp_digit* e, int bits, const sp_digit* m)
{
#ifndef WOLFSSL_SMALL_STACK
sp_digit nd[392];
sp_digit td[197];
#else
sp_digit* td;
#endif
sp_digit* norm;
sp_digit* tmp;
sp_digit mp = 1;
sp_digit n, o;
int i;
int c, y;
int err = MP_OKAY;
#ifdef WOLFSSL_SMALL_STACK
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * 589, NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
norm = td;
tmp = td + 392;
XMEMSET(td, 0, sizeof(sp_digit) * 589);
#else
norm = nd;
tmp = td;
XMEMSET(td, 0, sizeof(td));
#endif
sp_4096_mont_setup(m, &mp);
sp_4096_mont_norm_196(norm, m);
bits = ((bits + 3) / 4) * 4;
i = ((bits + 20) / 21) - 1;
c = bits % 21;
if (c == 0) {
c = 21;
}
if (i < 196) {
n = e[i--] << (32 - c);
}
else {
n = 0;
i--;
}
if (c < 4) {
n |= e[i--] << (11 - c);
c += 21;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_4096_lshift_196(r, norm, y);
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= e[i--] << (11 - c);
c += 21;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_4096_mont_sqr_196(r, r, m, mp);
sp_4096_mont_sqr_196(r, r, m, mp);
sp_4096_mont_sqr_196(r, r, m, mp);
sp_4096_mont_sqr_196(r, r, m, mp);
sp_4096_lshift_196(r, r, y);
sp_4096_mul_d_196(tmp, norm, (r[196] << 20) + (r[195] >> 1));
r[196] = 0;
r[195] &= 0x1L;
(void)sp_4096_add_196(r, r, tmp);
sp_4096_norm_196(r);
o = sp_4096_cmp_196(r, m);
sp_4096_cond_sub_196(r, r, m, ((o < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
sp_4096_mont_reduce_196(r, m, mp);
n = sp_4096_cmp_196(r, m);
sp_4096_cond_sub_196(r, r, m, ((n < 0) ?
(sp_digit)1 : (sp_digit)0) - 1);
}
#ifdef WOLFSSL_SMALL_STACK
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
#endif /* HAVE_FFDHE_4096 */
/* Perform the modular exponentiation for Diffie-Hellman.
*
* base Base.
* exp Array of bytes that is the exponent.
* expLen Length of data, in bytes, in exponent.
* mod Modulus.
* out Buffer to hold big-endian bytes of exponentiation result.
* Must be at least 512 bytes long.
* outLen Length, in bytes, of exponentiation result.
* returns 0 on success, MP_READ_E if there are too many bytes in an array
* and MEMORY_E if memory allocation fails.
*/
int sp_DhExp_4096(mp_int* base, const byte* exp, word32 expLen,
mp_int* mod, byte* out, word32* outLen)
{
#ifdef WOLFSSL_SP_SMALL
int err = MP_OKAY;
sp_digit* d = NULL;
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
if (mp_count_bits(base) > 4096) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 512) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 4096) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 196 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL) {
err = MEMORY_E;
}
}
if (err == MP_OKAY) {
b = d;
e = b + 196 * 2;
m = e + 196;
r = b;
sp_4096_from_mp(b, 196, base);
sp_4096_from_bin(e, 196, exp, expLen);
sp_4096_from_mp(m, 196, mod);
#ifdef HAVE_FFDHE_4096
if (base->used == 1 && base->dp[0] == 2 &&
((m[195] << 15) | (m[194] >> 6)) == 0xffffL) {
err = sp_4096_mod_exp_2_196(r, e, expLen * 8, m);
}
else
#endif
err = sp_4096_mod_exp_196(r, b, e, expLen * 8, m, 0);
}
if (err == MP_OKAY) {
sp_4096_to_bin(r, out);
*outLen = 512;
for (i=0; i<512 && out[i] == 0; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 196U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
return err;
#else
#ifndef WOLFSSL_SMALL_STACK
sp_digit bd[392], ed[196], md[196];
#else
sp_digit* d = NULL;
#endif
sp_digit* b;
sp_digit* e;
sp_digit* m;
sp_digit* r;
word32 i;
int err = MP_OKAY;
if (mp_count_bits(base) > 4096) {
err = MP_READ_E;
}
if (err == MP_OKAY) {
if (expLen > 512U) {
err = MP_READ_E;
}
}
if (err == MP_OKAY) {
if (mp_count_bits(mod) != 4096) {
err = MP_READ_E;
}
}
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(*d) * 196 * 4, NULL, DYNAMIC_TYPE_DH);
if (d == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
b = d;
e = b + 196 * 2;
m = e + 196;
r = b;
}
#else
r = b = bd;
e = ed;
m = md;
#endif
if (err == MP_OKAY) {
sp_4096_from_mp(b, 196, base);
sp_4096_from_bin(e, 196, exp, expLen);
sp_4096_from_mp(m, 196, mod);
#ifdef HAVE_FFDHE_4096
if (base->used == 1 && base->dp[0] == 2U &&
((m[195] << 15) | (m[194] >> 6)) == 0xffffL) {
err = sp_4096_mod_exp_2_196(r, e, expLen * 8U, m);
}
else {
#endif
err = sp_4096_mod_exp_196(r, b, e, expLen * 8U, m, 0);
#ifdef HAVE_FFDHE_4096
}
#endif
}
if (err == MP_OKAY) {
sp_4096_to_bin(r, out);
*outLen = 512;
for (i=0; i<512U && out[i] == 0U; i++) {
}
*outLen -= i;
XMEMMOVE(out, out + i, *outLen);
}
#ifdef WOLFSSL_SMALL_STACK
if (d != NULL) {
XMEMSET(e, 0, sizeof(sp_digit) * 196U);
XFREE(d, NULL, DYNAMIC_TYPE_DH);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 196U);
#endif
return err;
#endif
}
#endif /* WOLFSSL_HAVE_SP_DH */
#endif /* WOLFSSL_HAVE_SP_DH || (WOLFSSL_HAVE_SP_RSA && !WOLFSSL_RSA_PUBLIC_ONLY) */
#endif /* WOLFSSL_SP_4096 */
#endif /* WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH */
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
/* Point structure to use. */
typedef struct sp_point_256 {
sp_digit x[2 * 10];
sp_digit y[2 * 10];
sp_digit z[2 * 10];
int infinity;
} sp_point_256;
/* The modulus (prime) of the curve P256. */
static const sp_digit p256_mod[10] = {
0x3ffffff,0x3ffffff,0x3ffffff,0x003ffff,0x0000000,0x0000000,0x0000000,
0x0000400,0x3ff0000,0x03fffff
};
/* The Montogmery normalizer for modulus of the curve P256. */
static const sp_digit p256_norm_mod[10] = {
0x0000001,0x0000000,0x0000000,0x3fc0000,0x3ffffff,0x3ffffff,0x3ffffff,
0x3fffbff,0x000ffff,0x0000000
};
/* The Montogmery multiplier for modulus of the curve P256. */
static const sp_digit p256_mp_mod = 0x000001;
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* The order of the curve P256. */
static const sp_digit p256_order[10] = {
0x0632551,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,0x3ffffff,0x3ffffff,
0x00003ff,0x3ff0000,0x03fffff
};
#endif
/* The order of the curve P256 minus 2. */
static const sp_digit p256_order2[10] = {
0x063254f,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,0x3ffffff,0x3ffffff,
0x00003ff,0x3ff0000,0x03fffff
};
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* The Montogmery normalizer for order of the curve P256. */
static const sp_digit p256_norm_order[10] = {
0x39cdaaf,0x18d4f40,0x217b0c4,0x14963a1,0x0431905,0x0000000,0x0000000,
0x3fffc00,0x000ffff,0x0000000
};
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* The Montogmery multiplier for order of the curve P256. */
static const sp_digit p256_mp_order = 0x200bc4f;
#endif
/* The base point of curve P256. */
static const sp_point_256 p256_base = {
/* X ordinate */
{
0x098c296,0x04e5176,0x33a0f4a,0x204b7ac,0x277037d,0x0e9103c,0x3ce6e56,
0x1091fe2,0x1f2e12c,0x01ac5f4,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* Y ordinate */
{
0x3bf51f5,0x1901a0d,0x1ececbb,0x15dacc5,0x22bce33,0x303e785,0x27eb4a7,
0x1fe6e3b,0x2e2fe1a,0x013f8d0,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* Z ordinate */
{
0x0000001,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,
0x0000000,0x0000000,0x0000000,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* infinity */
0
};
#if defined(HAVE_ECC_CHECK_KEY) || defined(HAVE_COMP_KEY)
static const sp_digit p256_b[10] = {
0x3d2604b,0x38f0f89,0x30f63bc,0x2c3314e,0x0651d06,0x1a621af,0x2bbd557,
0x24f9ecf,0x1d8aa3a,0x016b18d
};
#endif
static int sp_256_point_new_ex_10(void* heap, sp_point_256* sp, sp_point_256** p)
{
int ret = MP_OKAY;
(void)heap;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
(void)sp;
*p = (sp_point_256*)XMALLOC(sizeof(sp_point_256), heap, DYNAMIC_TYPE_ECC);
#else
*p = sp;
#endif
if (*p == NULL) {
ret = MEMORY_E;
}
return ret;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
/* Allocate memory for point and return error. */
#define sp_256_point_new_10(heap, sp, p) sp_256_point_new_ex_10((heap), NULL, &(p))
#else
/* Set pointer to data and return no error. */
#define sp_256_point_new_10(heap, sp, p) sp_256_point_new_ex_10((heap), &(sp), &(p))
#endif
static void sp_256_point_free_10(sp_point_256* p, int clear, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
/* If valid pointer then clear point data if requested and free data. */
if (p != NULL) {
if (clear != 0) {
XMEMSET(p, 0, sizeof(*p));
}
XFREE(p, heap, DYNAMIC_TYPE_ECC);
}
#else
/* Clear point data if requested. */
if (clear != 0) {
XMEMSET(p, 0, sizeof(*p));
}
#endif
(void)heap;
}
/* Multiply a number by Montogmery normalizer mod modulus (prime).
*
* r The resulting Montgomery form number.
* a The number to convert.
* m The modulus (prime).
* returns MEMORY_E when memory allocation fails and MP_OKAY otherwise.
*/
static int sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
int64_t* td;
#else
int64_t td[8];
int64_t a32d[8];
#endif
int64_t* t;
int64_t* a32;
int64_t o;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (int64_t*)XMALLOC(sizeof(int64_t) * 2 * 8, NULL, DYNAMIC_TYPE_ECC);
if (td == NULL) {
return MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = td;
a32 = td + 8;
#else
t = td;
a32 = a32d;
#endif
a32[0] = a[0];
a32[0] |= a[1] << 26U;
a32[0] &= 0xffffffffL;
a32[1] = (sp_digit)(a[1] >> 6);
a32[1] |= a[2] << 20U;
a32[1] &= 0xffffffffL;
a32[2] = (sp_digit)(a[2] >> 12);
a32[2] |= a[3] << 14U;
a32[2] &= 0xffffffffL;
a32[3] = (sp_digit)(a[3] >> 18);
a32[3] |= a[4] << 8U;
a32[3] &= 0xffffffffL;
a32[4] = (sp_digit)(a[4] >> 24);
a32[4] |= a[5] << 2U;
a32[4] |= a[6] << 28U;
a32[4] &= 0xffffffffL;
a32[5] = (sp_digit)(a[6] >> 4);
a32[5] |= a[7] << 22U;
a32[5] &= 0xffffffffL;
a32[6] = (sp_digit)(a[7] >> 10);
a32[6] |= a[8] << 16U;
a32[6] &= 0xffffffffL;
a32[7] = (sp_digit)(a[8] >> 16);
a32[7] |= a[9] << 10U;
a32[7] &= 0xffffffffL;
/* 1 1 0 -1 -1 -1 -1 0 */
t[0] = 0 + a32[0] + a32[1] - a32[3] - a32[4] - a32[5] - a32[6];
/* 0 1 1 0 -1 -1 -1 -1 */
t[1] = 0 + a32[1] + a32[2] - a32[4] - a32[5] - a32[6] - a32[7];
/* 0 0 1 1 0 -1 -1 -1 */
t[2] = 0 + a32[2] + a32[3] - a32[5] - a32[6] - a32[7];
/* -1 -1 0 2 2 1 0 -1 */
t[3] = 0 - a32[0] - a32[1] + 2 * a32[3] + 2 * a32[4] + a32[5] - a32[7];
/* 0 -1 -1 0 2 2 1 0 */
t[4] = 0 - a32[1] - a32[2] + 2 * a32[4] + 2 * a32[5] + a32[6];
/* 0 0 -1 -1 0 2 2 1 */
t[5] = 0 - a32[2] - a32[3] + 2 * a32[5] + 2 * a32[6] + a32[7];
/* -1 -1 0 0 0 1 3 2 */
t[6] = 0 - a32[0] - a32[1] + a32[5] + 3 * a32[6] + 2 * a32[7];
/* 1 0 -1 -1 -1 -1 0 3 */
t[7] = 0 + a32[0] - a32[2] - a32[3] - a32[4] - a32[5] + 3 * a32[7];
t[1] += t[0] >> 32U; t[0] &= 0xffffffffL;
t[2] += t[1] >> 32U; t[1] &= 0xffffffffL;
t[3] += t[2] >> 32U; t[2] &= 0xffffffffL;
t[4] += t[3] >> 32U; t[3] &= 0xffffffffL;
t[5] += t[4] >> 32U; t[4] &= 0xffffffffL;
t[6] += t[5] >> 32U; t[5] &= 0xffffffffL;
t[7] += t[6] >> 32U; t[6] &= 0xffffffffL;
o = t[7] >> 32U; t[7] &= 0xffffffffL;
t[0] += o;
t[3] -= o;
t[6] -= o;
t[7] += o;
t[1] += t[0] >> 32U; t[0] &= 0xffffffffL;
t[2] += t[1] >> 32U; t[1] &= 0xffffffffL;
t[3] += t[2] >> 32U; t[2] &= 0xffffffffL;
t[4] += t[3] >> 32U; t[3] &= 0xffffffffL;
t[5] += t[4] >> 32U; t[4] &= 0xffffffffL;
t[6] += t[5] >> 32U; t[5] &= 0xffffffffL;
t[7] += t[6] >> 32U; t[6] &= 0xffffffffL;
r[0] = (sp_digit)(t[0]) & 0x3ffffffL;
r[1] = (sp_digit)(t[0] >> 26U);
r[1] |= t[1] << 6U;
r[1] &= 0x3ffffffL;
r[2] = (sp_digit)(t[1] >> 20U);
r[2] |= t[2] << 12U;
r[2] &= 0x3ffffffL;
r[3] = (sp_digit)(t[2] >> 14U);
r[3] |= t[3] << 18U;
r[3] &= 0x3ffffffL;
r[4] = (sp_digit)(t[3] >> 8U);
r[4] |= t[4] << 24U;
r[4] &= 0x3ffffffL;
r[5] = (sp_digit)(t[4] >> 2U) & 0x3ffffffL;
r[6] = (sp_digit)(t[4] >> 28U);
r[6] |= t[5] << 4U;
r[6] &= 0x3ffffffL;
r[7] = (sp_digit)(t[5] >> 22U);
r[7] |= t[6] << 10U;
r[7] &= 0x3ffffffL;
r[8] = (sp_digit)(t[6] >> 16U);
r[8] |= t[7] << 16U;
r[8] &= 0x3ffffffL;
r[9] = (sp_digit)(t[7] >> 10U);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_256_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 26
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 26
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x3ffffff;
s = 26U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 26U) <= (word32)DIGIT_BIT) {
s += 26U;
r[j] &= 0x3ffffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 26) {
r[j] &= 0x3ffffff;
if (j + 1 >= size) {
break;
}
s = 26 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Convert a point of type ecc_point to type sp_point_256.
*
* p Point of type sp_point_256 (result).
* pm Point of type ecc_point.
*/
static void sp_256_point_from_ecc_point_10(sp_point_256* p, const ecc_point* pm)
{
XMEMSET(p->x, 0, sizeof(p->x));
XMEMSET(p->y, 0, sizeof(p->y));
XMEMSET(p->z, 0, sizeof(p->z));
sp_256_from_mp(p->x, 10, pm->x);
sp_256_from_mp(p->y, 10, pm->y);
sp_256_from_mp(p->z, 10, pm->z);
p->infinity = 0;
}
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_256_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (256 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 26
XMEMCPY(r->dp, a, sizeof(sp_digit) * 10);
r->used = 10;
mp_clamp(r);
#elif DIGIT_BIT < 26
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 10; i++) {
r->dp[j] |= (mp_digit)(a[i] << s);
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = (mp_digit)(a[i] >> s);
while (s + DIGIT_BIT <= 26) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = (mp_digit)(a[i] >> s);
}
}
s = 26 - s;
}
r->used = (256 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 10; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 26 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 26 - s;
}
else {
s += 26;
}
}
r->used = (256 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Convert a point of type sp_point_256 to type ecc_point.
*
* p Point of type sp_point_256.
* pm Point of type ecc_point (result).
* returns MEMORY_E when allocation of memory in ecc_point fails otherwise
* MP_OKAY.
*/
static int sp_256_point_to_ecc_point_10(const sp_point_256* p, ecc_point* pm)
{
int err;
err = sp_256_to_mp(p->x, pm->x);
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, pm->y);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, pm->z);
}
return err;
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_256_mul_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[9]) * b[9];
r[19] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 17; k >= 0; k--) {
for (i = 9; i >= 0; i--) {
j = k - i;
if (j >= 10) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
#else
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_256_mul_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int64_t t0 = ((int64_t)a[ 0]) * b[ 0];
int64_t t1 = ((int64_t)a[ 0]) * b[ 1]
+ ((int64_t)a[ 1]) * b[ 0];
int64_t t2 = ((int64_t)a[ 0]) * b[ 2]
+ ((int64_t)a[ 1]) * b[ 1]
+ ((int64_t)a[ 2]) * b[ 0];
int64_t t3 = ((int64_t)a[ 0]) * b[ 3]
+ ((int64_t)a[ 1]) * b[ 2]
+ ((int64_t)a[ 2]) * b[ 1]
+ ((int64_t)a[ 3]) * b[ 0];
int64_t t4 = ((int64_t)a[ 0]) * b[ 4]
+ ((int64_t)a[ 1]) * b[ 3]
+ ((int64_t)a[ 2]) * b[ 2]
+ ((int64_t)a[ 3]) * b[ 1]
+ ((int64_t)a[ 4]) * b[ 0];
int64_t t5 = ((int64_t)a[ 0]) * b[ 5]
+ ((int64_t)a[ 1]) * b[ 4]
+ ((int64_t)a[ 2]) * b[ 3]
+ ((int64_t)a[ 3]) * b[ 2]
+ ((int64_t)a[ 4]) * b[ 1]
+ ((int64_t)a[ 5]) * b[ 0];
int64_t t6 = ((int64_t)a[ 0]) * b[ 6]
+ ((int64_t)a[ 1]) * b[ 5]
+ ((int64_t)a[ 2]) * b[ 4]
+ ((int64_t)a[ 3]) * b[ 3]
+ ((int64_t)a[ 4]) * b[ 2]
+ ((int64_t)a[ 5]) * b[ 1]
+ ((int64_t)a[ 6]) * b[ 0];
int64_t t7 = ((int64_t)a[ 0]) * b[ 7]
+ ((int64_t)a[ 1]) * b[ 6]
+ ((int64_t)a[ 2]) * b[ 5]
+ ((int64_t)a[ 3]) * b[ 4]
+ ((int64_t)a[ 4]) * b[ 3]
+ ((int64_t)a[ 5]) * b[ 2]
+ ((int64_t)a[ 6]) * b[ 1]
+ ((int64_t)a[ 7]) * b[ 0];
int64_t t8 = ((int64_t)a[ 0]) * b[ 8]
+ ((int64_t)a[ 1]) * b[ 7]
+ ((int64_t)a[ 2]) * b[ 6]
+ ((int64_t)a[ 3]) * b[ 5]
+ ((int64_t)a[ 4]) * b[ 4]
+ ((int64_t)a[ 5]) * b[ 3]
+ ((int64_t)a[ 6]) * b[ 2]
+ ((int64_t)a[ 7]) * b[ 1]
+ ((int64_t)a[ 8]) * b[ 0];
int64_t t9 = ((int64_t)a[ 0]) * b[ 9]
+ ((int64_t)a[ 1]) * b[ 8]
+ ((int64_t)a[ 2]) * b[ 7]
+ ((int64_t)a[ 3]) * b[ 6]
+ ((int64_t)a[ 4]) * b[ 5]
+ ((int64_t)a[ 5]) * b[ 4]
+ ((int64_t)a[ 6]) * b[ 3]
+ ((int64_t)a[ 7]) * b[ 2]
+ ((int64_t)a[ 8]) * b[ 1]
+ ((int64_t)a[ 9]) * b[ 0];
int64_t t10 = ((int64_t)a[ 1]) * b[ 9]
+ ((int64_t)a[ 2]) * b[ 8]
+ ((int64_t)a[ 3]) * b[ 7]
+ ((int64_t)a[ 4]) * b[ 6]
+ ((int64_t)a[ 5]) * b[ 5]
+ ((int64_t)a[ 6]) * b[ 4]
+ ((int64_t)a[ 7]) * b[ 3]
+ ((int64_t)a[ 8]) * b[ 2]
+ ((int64_t)a[ 9]) * b[ 1];
int64_t t11 = ((int64_t)a[ 2]) * b[ 9]
+ ((int64_t)a[ 3]) * b[ 8]
+ ((int64_t)a[ 4]) * b[ 7]
+ ((int64_t)a[ 5]) * b[ 6]
+ ((int64_t)a[ 6]) * b[ 5]
+ ((int64_t)a[ 7]) * b[ 4]
+ ((int64_t)a[ 8]) * b[ 3]
+ ((int64_t)a[ 9]) * b[ 2];
int64_t t12 = ((int64_t)a[ 3]) * b[ 9]
+ ((int64_t)a[ 4]) * b[ 8]
+ ((int64_t)a[ 5]) * b[ 7]
+ ((int64_t)a[ 6]) * b[ 6]
+ ((int64_t)a[ 7]) * b[ 5]
+ ((int64_t)a[ 8]) * b[ 4]
+ ((int64_t)a[ 9]) * b[ 3];
int64_t t13 = ((int64_t)a[ 4]) * b[ 9]
+ ((int64_t)a[ 5]) * b[ 8]
+ ((int64_t)a[ 6]) * b[ 7]
+ ((int64_t)a[ 7]) * b[ 6]
+ ((int64_t)a[ 8]) * b[ 5]
+ ((int64_t)a[ 9]) * b[ 4];
int64_t t14 = ((int64_t)a[ 5]) * b[ 9]
+ ((int64_t)a[ 6]) * b[ 8]
+ ((int64_t)a[ 7]) * b[ 7]
+ ((int64_t)a[ 8]) * b[ 6]
+ ((int64_t)a[ 9]) * b[ 5];
int64_t t15 = ((int64_t)a[ 6]) * b[ 9]
+ ((int64_t)a[ 7]) * b[ 8]
+ ((int64_t)a[ 8]) * b[ 7]
+ ((int64_t)a[ 9]) * b[ 6];
int64_t t16 = ((int64_t)a[ 7]) * b[ 9]
+ ((int64_t)a[ 8]) * b[ 8]
+ ((int64_t)a[ 9]) * b[ 7];
int64_t t17 = ((int64_t)a[ 8]) * b[ 9]
+ ((int64_t)a[ 9]) * b[ 8];
int64_t t18 = ((int64_t)a[ 9]) * b[ 9];
t1 += t0 >> 26; r[ 0] = t0 & 0x3ffffff;
t2 += t1 >> 26; r[ 1] = t1 & 0x3ffffff;
t3 += t2 >> 26; r[ 2] = t2 & 0x3ffffff;
t4 += t3 >> 26; r[ 3] = t3 & 0x3ffffff;
t5 += t4 >> 26; r[ 4] = t4 & 0x3ffffff;
t6 += t5 >> 26; r[ 5] = t5 & 0x3ffffff;
t7 += t6 >> 26; r[ 6] = t6 & 0x3ffffff;
t8 += t7 >> 26; r[ 7] = t7 & 0x3ffffff;
t9 += t8 >> 26; r[ 8] = t8 & 0x3ffffff;
t10 += t9 >> 26; r[ 9] = t9 & 0x3ffffff;
t11 += t10 >> 26; r[10] = t10 & 0x3ffffff;
t12 += t11 >> 26; r[11] = t11 & 0x3ffffff;
t13 += t12 >> 26; r[12] = t12 & 0x3ffffff;
t14 += t13 >> 26; r[13] = t13 & 0x3ffffff;
t15 += t14 >> 26; r[14] = t14 & 0x3ffffff;
t16 += t15 >> 26; r[15] = t15 & 0x3ffffff;
t17 += t16 >> 26; r[16] = t16 & 0x3ffffff;
t18 += t17 >> 26; r[17] = t17 & 0x3ffffff;
r[19] = (sp_digit)(t18 >> 26);
r[18] = t18 & 0x3ffffff;
}
#endif /* WOLFSSL_SP_SMALL */
#define sp_256_mont_reduce_order_10 sp_256_mont_reduce_10
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_256_cmp_10(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=9; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
r |= (a[ 9] - b[ 9]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 8] - b[ 8]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 7] - b[ 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 6] - b[ 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 5] - b[ 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 4] - b[ 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 3] - b[ 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 2] - b[ 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 1] - b[ 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 0] - b[ 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_256_cond_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
r[ 0] = a[ 0] - (b[ 0] & m);
r[ 1] = a[ 1] - (b[ 1] & m);
r[ 2] = a[ 2] - (b[ 2] & m);
r[ 3] = a[ 3] - (b[ 3] & m);
r[ 4] = a[ 4] - (b[ 4] & m);
r[ 5] = a[ 5] - (b[ 5] & m);
r[ 6] = a[ 6] - (b[ 6] & m);
r[ 7] = a[ 7] - (b[ 7] & m);
r[ 8] = a[ 8] - (b[ 8] & m);
r[ 9] = a[ 9] - (b[ 9] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 10; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[10] += t;
#else
int64_t tb = b;
int64_t t[10];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
t[ 5] = tb * a[ 5];
t[ 6] = tb * a[ 6];
t[ 7] = tb * a[ 7];
t[ 8] = tb * a[ 8];
t[ 9] = tb * a[ 9];
r[ 0] += (sp_digit) (t[ 0] & 0x3ffffff);
r[ 1] += (sp_digit)((t[ 0] >> 26) + (t[ 1] & 0x3ffffff));
r[ 2] += (sp_digit)((t[ 1] >> 26) + (t[ 2] & 0x3ffffff));
r[ 3] += (sp_digit)((t[ 2] >> 26) + (t[ 3] & 0x3ffffff));
r[ 4] += (sp_digit)((t[ 3] >> 26) + (t[ 4] & 0x3ffffff));
r[ 5] += (sp_digit)((t[ 4] >> 26) + (t[ 5] & 0x3ffffff));
r[ 6] += (sp_digit)((t[ 5] >> 26) + (t[ 6] & 0x3ffffff));
r[ 7] += (sp_digit)((t[ 6] >> 26) + (t[ 7] & 0x3ffffff));
r[ 8] += (sp_digit)((t[ 7] >> 26) + (t[ 8] & 0x3ffffff));
r[ 9] += (sp_digit)((t[ 8] >> 26) + (t[ 9] & 0x3ffffff));
r[10] += (sp_digit) (t[ 9] >> 26);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 26.
*
* a Array of sp_digit to normalize.
*/
static void sp_256_norm_10(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 9; i++) {
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
#else
a[1] += a[0] >> 26; a[0] &= 0x3ffffff;
a[2] += a[1] >> 26; a[1] &= 0x3ffffff;
a[3] += a[2] >> 26; a[2] &= 0x3ffffff;
a[4] += a[3] >> 26; a[3] &= 0x3ffffff;
a[5] += a[4] >> 26; a[4] &= 0x3ffffff;
a[6] += a[5] >> 26; a[5] &= 0x3ffffff;
a[7] += a[6] >> 26; a[6] &= 0x3ffffff;
a[8] += a[7] >> 26; a[7] &= 0x3ffffff;
a[9] += a[8] >> 26; a[8] &= 0x3ffffff;
#endif
}
/* Shift the result in the high 256 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_256_mont_shift_10(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
sp_digit n, s;
s = a[10];
n = a[9] >> 22;
for (i = 0; i < 9; i++) {
n += (s & 0x3ffffff) << 4;
r[i] = n & 0x3ffffff;
n >>= 26;
s = a[11 + i] + (s >> 26);
}
n += s << 4;
r[9] = n;
#else
sp_digit n, s;
s = a[10]; n = a[9] >> 22;
n += (s & 0x3ffffff) << 4; r[ 0] = n & 0x3ffffff;
n >>= 26; s = a[11] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 1] = n & 0x3ffffff;
n >>= 26; s = a[12] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 2] = n & 0x3ffffff;
n >>= 26; s = a[13] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 3] = n & 0x3ffffff;
n >>= 26; s = a[14] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 4] = n & 0x3ffffff;
n >>= 26; s = a[15] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 5] = n & 0x3ffffff;
n >>= 26; s = a[16] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 6] = n & 0x3ffffff;
n >>= 26; s = a[17] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 7] = n & 0x3ffffff;
n >>= 26; s = a[18] + (s >> 26);
n += (s & 0x3ffffff) << 4; r[ 8] = n & 0x3ffffff;
n >>= 26; s = a[19] + (s >> 26);
n += s << 4; r[ 9] = n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[10], 0, sizeof(*r) * 10U);
}
/* Reduce the number back to 256 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_256_mont_reduce_10(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
if (mp != 1) {
for (i=0; i<9; i++) {
mu = (a[i] * mp) & 0x3ffffff;
sp_256_mul_add_10(a+i, m, mu);
a[i+1] += a[i] >> 26;
}
mu = (a[i] * mp) & 0x3fffffL;
sp_256_mul_add_10(a+i, m, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
else {
for (i=0; i<9; i++) {
mu = a[i] & 0x3ffffff;
sp_256_mul_add_10(a+i, p256_mod, mu);
a[i+1] += a[i] >> 26;
}
mu = a[i] & 0x3fffffL;
sp_256_mul_add_10(a+i, p256_mod, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
sp_256_mont_shift_10(a, a);
sp_256_cond_sub_10(a, a, m, 0 - (((a[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_256_mul_10(r, a, b);
sp_256_mont_reduce_10(r, m, mp);
}
#ifdef WOLFSSL_SP_SMALL
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[9]) * a[9];
r[19] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 17; k >= 0; k--) {
for (i = 9; i >= 0; i--) {
j = k - i;
if (j >= 10 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
#else
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
{
int64_t t0 = ((int64_t)a[ 0]) * a[ 0];
int64_t t1 = (((int64_t)a[ 0]) * a[ 1]) * 2;
int64_t t2 = (((int64_t)a[ 0]) * a[ 2]) * 2
+ ((int64_t)a[ 1]) * a[ 1];
int64_t t3 = (((int64_t)a[ 0]) * a[ 3]
+ ((int64_t)a[ 1]) * a[ 2]) * 2;
int64_t t4 = (((int64_t)a[ 0]) * a[ 4]
+ ((int64_t)a[ 1]) * a[ 3]) * 2
+ ((int64_t)a[ 2]) * a[ 2];
int64_t t5 = (((int64_t)a[ 0]) * a[ 5]
+ ((int64_t)a[ 1]) * a[ 4]
+ ((int64_t)a[ 2]) * a[ 3]) * 2;
int64_t t6 = (((int64_t)a[ 0]) * a[ 6]
+ ((int64_t)a[ 1]) * a[ 5]
+ ((int64_t)a[ 2]) * a[ 4]) * 2
+ ((int64_t)a[ 3]) * a[ 3];
int64_t t7 = (((int64_t)a[ 0]) * a[ 7]
+ ((int64_t)a[ 1]) * a[ 6]
+ ((int64_t)a[ 2]) * a[ 5]
+ ((int64_t)a[ 3]) * a[ 4]) * 2;
int64_t t8 = (((int64_t)a[ 0]) * a[ 8]
+ ((int64_t)a[ 1]) * a[ 7]
+ ((int64_t)a[ 2]) * a[ 6]
+ ((int64_t)a[ 3]) * a[ 5]) * 2
+ ((int64_t)a[ 4]) * a[ 4];
int64_t t9 = (((int64_t)a[ 0]) * a[ 9]
+ ((int64_t)a[ 1]) * a[ 8]
+ ((int64_t)a[ 2]) * a[ 7]
+ ((int64_t)a[ 3]) * a[ 6]
+ ((int64_t)a[ 4]) * a[ 5]) * 2;
int64_t t10 = (((int64_t)a[ 1]) * a[ 9]
+ ((int64_t)a[ 2]) * a[ 8]
+ ((int64_t)a[ 3]) * a[ 7]
+ ((int64_t)a[ 4]) * a[ 6]) * 2
+ ((int64_t)a[ 5]) * a[ 5];
int64_t t11 = (((int64_t)a[ 2]) * a[ 9]
+ ((int64_t)a[ 3]) * a[ 8]
+ ((int64_t)a[ 4]) * a[ 7]
+ ((int64_t)a[ 5]) * a[ 6]) * 2;
int64_t t12 = (((int64_t)a[ 3]) * a[ 9]
+ ((int64_t)a[ 4]) * a[ 8]
+ ((int64_t)a[ 5]) * a[ 7]) * 2
+ ((int64_t)a[ 6]) * a[ 6];
int64_t t13 = (((int64_t)a[ 4]) * a[ 9]
+ ((int64_t)a[ 5]) * a[ 8]
+ ((int64_t)a[ 6]) * a[ 7]) * 2;
int64_t t14 = (((int64_t)a[ 5]) * a[ 9]
+ ((int64_t)a[ 6]) * a[ 8]) * 2
+ ((int64_t)a[ 7]) * a[ 7];
int64_t t15 = (((int64_t)a[ 6]) * a[ 9]
+ ((int64_t)a[ 7]) * a[ 8]) * 2;
int64_t t16 = (((int64_t)a[ 7]) * a[ 9]) * 2
+ ((int64_t)a[ 8]) * a[ 8];
int64_t t17 = (((int64_t)a[ 8]) * a[ 9]) * 2;
int64_t t18 = ((int64_t)a[ 9]) * a[ 9];
t1 += t0 >> 26; r[ 0] = t0 & 0x3ffffff;
t2 += t1 >> 26; r[ 1] = t1 & 0x3ffffff;
t3 += t2 >> 26; r[ 2] = t2 & 0x3ffffff;
t4 += t3 >> 26; r[ 3] = t3 & 0x3ffffff;
t5 += t4 >> 26; r[ 4] = t4 & 0x3ffffff;
t6 += t5 >> 26; r[ 5] = t5 & 0x3ffffff;
t7 += t6 >> 26; r[ 6] = t6 & 0x3ffffff;
t8 += t7 >> 26; r[ 7] = t7 & 0x3ffffff;
t9 += t8 >> 26; r[ 8] = t8 & 0x3ffffff;
t10 += t9 >> 26; r[ 9] = t9 & 0x3ffffff;
t11 += t10 >> 26; r[10] = t10 & 0x3ffffff;
t12 += t11 >> 26; r[11] = t11 & 0x3ffffff;
t13 += t12 >> 26; r[12] = t12 & 0x3ffffff;
t14 += t13 >> 26; r[13] = t13 & 0x3ffffff;
t15 += t14 >> 26; r[14] = t14 & 0x3ffffff;
t16 += t15 >> 26; r[15] = t15 & 0x3ffffff;
t17 += t16 >> 26; r[16] = t16 & 0x3ffffff;
t18 += t17 >> 26; r[17] = t17 & 0x3ffffff;
r[19] = (sp_digit)(t18 >> 26);
r[18] = t18 & 0x3ffffff;
}
#endif /* WOLFSSL_SP_SMALL */
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_sqr_10(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_256_sqr_10(r, a);
sp_256_mont_reduce_10(r, m, mp);
}
#if !defined(WOLFSSL_SP_SMALL) || defined(HAVE_COMP_KEY)
/* Square the Montgomery form number a number of times. (r = a ^ n mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* n Number of times to square.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_256_mont_sqr_n_10(sp_digit* r, const sp_digit* a, int n,
const sp_digit* m, sp_digit mp)
{
sp_256_mont_sqr_10(r, a, m, mp);
for (; n > 1; n--) {
sp_256_mont_sqr_10(r, r, m, mp);
}
}
#endif /* !WOLFSSL_SP_SMALL || HAVE_COMP_KEY */
#ifdef WOLFSSL_SP_SMALL
/* Mod-2 for the P256 curve. */
static const uint32_t p256_mod_minus_2[8] = {
0xfffffffdU,0xffffffffU,0xffffffffU,0x00000000U,0x00000000U,0x00000000U,
0x00000001U,0xffffffffU
};
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
* P256 curve. (r = 1 / a mod m)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_256_mont_inv_10(sp_digit* r, const sp_digit* a, sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 10);
for (i=254; i>=0; i--) {
sp_256_mont_sqr_10(t, t, p256_mod, p256_mp_mod);
if (p256_mod_minus_2[i / 32] & ((sp_digit)1 << (i % 32)))
sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
}
XMEMCPY(r, t, sizeof(sp_digit) * 10);
#else
sp_digit* t1 = td;
sp_digit* t2 = td + 2 * 10;
sp_digit* t3 = td + 4 * 10;
/* 0x2 */
sp_256_mont_sqr_10(t1, a, p256_mod, p256_mp_mod);
/* 0x3 */
sp_256_mont_mul_10(t2, t1, a, p256_mod, p256_mp_mod);
/* 0xc */
sp_256_mont_sqr_n_10(t1, t2, 2, p256_mod, p256_mp_mod);
/* 0xd */
sp_256_mont_mul_10(t3, t1, a, p256_mod, p256_mp_mod);
/* 0xf */
sp_256_mont_mul_10(t2, t2, t1, p256_mod, p256_mp_mod);
/* 0xf0 */
sp_256_mont_sqr_n_10(t1, t2, 4, p256_mod, p256_mp_mod);
/* 0xfd */
sp_256_mont_mul_10(t3, t3, t1, p256_mod, p256_mp_mod);
/* 0xff */
sp_256_mont_mul_10(t2, t2, t1, p256_mod, p256_mp_mod);
/* 0xff00 */
sp_256_mont_sqr_n_10(t1, t2, 8, p256_mod, p256_mp_mod);
/* 0xfffd */
sp_256_mont_mul_10(t3, t3, t1, p256_mod, p256_mp_mod);
/* 0xffff */
sp_256_mont_mul_10(t2, t2, t1, p256_mod, p256_mp_mod);
/* 0xffff0000 */
sp_256_mont_sqr_n_10(t1, t2, 16, p256_mod, p256_mp_mod);
/* 0xfffffffd */
sp_256_mont_mul_10(t3, t3, t1, p256_mod, p256_mp_mod);
/* 0xffffffff */
sp_256_mont_mul_10(t2, t2, t1, p256_mod, p256_mp_mod);
/* 0xffffffff00000000 */
sp_256_mont_sqr_n_10(t1, t2, 32, p256_mod, p256_mp_mod);
/* 0xffffffffffffffff */
sp_256_mont_mul_10(t2, t2, t1, p256_mod, p256_mp_mod);
/* 0xffffffff00000001 */
sp_256_mont_mul_10(r, t1, a, p256_mod, p256_mp_mod);
/* 0xffffffff000000010000000000000000000000000000000000000000 */
sp_256_mont_sqr_n_10(r, r, 160, p256_mod, p256_mp_mod);
/* 0xffffffff00000001000000000000000000000000ffffffffffffffff */
sp_256_mont_mul_10(r, r, t2, p256_mod, p256_mp_mod);
/* 0xffffffff00000001000000000000000000000000ffffffffffffffff00000000 */
sp_256_mont_sqr_n_10(r, r, 32, p256_mod, p256_mp_mod);
/* 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffd */
sp_256_mont_mul_10(r, r, t3, p256_mod, p256_mp_mod);
#endif /* WOLFSSL_SP_SMALL */
}
/* Map the Montgomery form projective coordinate point to an affine point.
*
* r Resulting affine coordinate point.
* p Montgomery form projective coordinate point.
* t Temporary ordinate data.
*/
static void sp_256_map_10(sp_point_256* r, const sp_point_256* p, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
int32_t n;
sp_256_mont_inv_10(t1, p->z, t + 2*10);
sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
/* x /= z^2 */
sp_256_mont_mul_10(r->x, p->x, t2, p256_mod, p256_mp_mod);
XMEMSET(r->x + 10, 0, sizeof(r->x) / 2U);
sp_256_mont_reduce_10(r->x, p256_mod, p256_mp_mod);
/* Reduce x to less than modulus */
n = sp_256_cmp_10(r->x, p256_mod);
sp_256_cond_sub_10(r->x, r->x, p256_mod, 0 - ((n >= 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r->x);
/* y /= z^3 */
sp_256_mont_mul_10(r->y, p->y, t1, p256_mod, p256_mp_mod);
XMEMSET(r->y + 10, 0, sizeof(r->y) / 2U);
sp_256_mont_reduce_10(r->y, p256_mod, p256_mp_mod);
/* Reduce y to less than modulus */
n = sp_256_cmp_10(r->y, p256_mod);
sp_256_cond_sub_10(r->y, r->y, p256_mod, 0 - ((n >= 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r->y);
XMEMSET(r->z, 0, sizeof(r->z));
r->z[0] = 1;
}
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#else
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] + b[ 0];
r[ 1] = a[ 1] + b[ 1];
r[ 2] = a[ 2] + b[ 2];
r[ 3] = a[ 3] + b[ 3];
r[ 4] = a[ 4] + b[ 4];
r[ 5] = a[ 5] + b[ 5];
r[ 6] = a[ 6] + b[ 6];
r[ 7] = a[ 7] + b[ 7];
r[ 8] = a[ 8] + b[ 8];
r[ 9] = a[ 9] + b[ 9];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Add two Montgomery form numbers (r = a + b % m).
*
* r Result of addition.
* a First number to add in Montogmery form.
* b Second number to add in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
(void)sp_256_add_10(r, a, b);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
}
/* Double a Montgomery form number (r = a + a % m).
*
* r Result of doubling.
* a Number to double in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_dbl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
(void)sp_256_add_10(r, a, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
}
/* Triple a Montgomery form number (r = a + a + a % m).
*
* r Result of Tripling.
* a Number to triple in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_tpl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
(void)sp_256_add_10(r, a, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
(void)sp_256_add_10(r, r, a);
sp_256_norm_10(r);
sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_10(r);
}
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_sub_10(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] - b[ 0];
r[ 1] = a[ 1] - b[ 1];
r[ 2] = a[ 2] - b[ 2];
r[ 3] = a[ 3] - b[ 3];
r[ 4] = a[ 4] - b[ 4];
r[ 5] = a[ 5] - b[ 5];
r[ 6] = a[ 6] - b[ 6];
r[ 7] = a[ 7] - b[ 7];
r[ 8] = a[ 8] - b[ 8];
r[ 9] = a[ 9] - b[ 9];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_256_cond_add_10(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 10; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
r[ 0] = a[ 0] + (b[ 0] & m);
r[ 1] = a[ 1] + (b[ 1] & m);
r[ 2] = a[ 2] + (b[ 2] & m);
r[ 3] = a[ 3] + (b[ 3] & m);
r[ 4] = a[ 4] + (b[ 4] & m);
r[ 5] = a[ 5] + (b[ 5] & m);
r[ 6] = a[ 6] + (b[ 6] & m);
r[ 7] = a[ 7] + (b[ 7] & m);
r[ 8] = a[ 8] + (b[ 8] & m);
r[ 9] = a[ 9] + (b[ 9] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Subtract two Montgomery form numbers (r = a - b % m).
*
* r Result of subtration.
* a Number to subtract from in Montogmery form.
* b Number to subtract with in Montogmery form.
* m Modulus (prime).
*/
static void sp_256_mont_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
(void)sp_256_sub_10(r, a, b);
sp_256_cond_add_10(r, r, m, r[9] >> 22);
sp_256_norm_10(r);
}
/* Shift number left one bit.
* Bottom bit is lost.
*
* r Result of shift.
* a Number to shift.
*/
SP_NOINLINE static void sp_256_rshift1_10(sp_digit* r, sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<9; i++) {
r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
}
#else
r[0] = ((a[0] >> 1) | (a[1] << 25)) & 0x3ffffff;
r[1] = ((a[1] >> 1) | (a[2] << 25)) & 0x3ffffff;
r[2] = ((a[2] >> 1) | (a[3] << 25)) & 0x3ffffff;
r[3] = ((a[3] >> 1) | (a[4] << 25)) & 0x3ffffff;
r[4] = ((a[4] >> 1) | (a[5] << 25)) & 0x3ffffff;
r[5] = ((a[5] >> 1) | (a[6] << 25)) & 0x3ffffff;
r[6] = ((a[6] >> 1) | (a[7] << 25)) & 0x3ffffff;
r[7] = ((a[7] >> 1) | (a[8] << 25)) & 0x3ffffff;
r[8] = ((a[8] >> 1) | (a[9] << 25)) & 0x3ffffff;
#endif
r[9] = a[9] >> 1;
}
/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m)
*
* r Result of division by 2.
* a Number to divide.
* m Modulus (prime).
*/
static void sp_256_div2_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
sp_256_cond_add_10(r, a, m, 0 - (a[0] & 1));
sp_256_norm_10(r);
sp_256_rshift1_10(r, r);
}
/* Double the Montgomery form projective point p.
*
* r Result of doubling point.
* p Point to double.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_dbl_10(sp_point_256* r, const sp_point_256* p, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
x = r->x;
y = r->y;
z = r->z;
/* Put infinity into result. */
if (r != p) {
r->infinity = p->infinity;
}
/* T1 = Z * Z */
sp_256_mont_sqr_10(t1, p->z, p256_mod, p256_mp_mod);
/* Z = Y * Z */
sp_256_mont_mul_10(z, p->y, p->z, p256_mod, p256_mp_mod);
/* Z = 2Z */
sp_256_mont_dbl_10(z, z, p256_mod);
/* T2 = X - T1 */
sp_256_mont_sub_10(t2, p->x, t1, p256_mod);
/* T1 = X + T1 */
sp_256_mont_add_10(t1, p->x, t1, p256_mod);
/* T2 = T1 * T2 */
sp_256_mont_mul_10(t2, t1, t2, p256_mod, p256_mp_mod);
/* T1 = 3T2 */
sp_256_mont_tpl_10(t1, t2, p256_mod);
/* Y = 2Y */
sp_256_mont_dbl_10(y, p->y, p256_mod);
/* Y = Y * Y */
sp_256_mont_sqr_10(y, y, p256_mod, p256_mp_mod);
/* T2 = Y * Y */
sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
/* T2 = T2/2 */
sp_256_div2_10(t2, t2, p256_mod);
/* Y = Y * X */
sp_256_mont_mul_10(y, y, p->x, p256_mod, p256_mp_mod);
/* X = T1 * T1 */
sp_256_mont_sqr_10(x, t1, p256_mod, p256_mp_mod);
/* X = X - Y */
sp_256_mont_sub_10(x, x, y, p256_mod);
/* X = X - Y */
sp_256_mont_sub_10(x, x, y, p256_mod);
/* Y = Y - X */
sp_256_mont_sub_10(y, y, x, p256_mod);
/* Y = Y * T1 */
sp_256_mont_mul_10(y, y, t1, p256_mod, p256_mp_mod);
/* Y = Y - T2 */
sp_256_mont_sub_10(y, y, t2, p256_mod);
}
/* Compare two numbers to determine if they are equal.
* Constant time implementation.
*
* a First number to compare.
* b Second number to compare.
* returns 1 when equal and 0 otherwise.
*/
static int sp_256_cmp_equal_10(const sp_digit* a, const sp_digit* b)
{
return ((a[0] ^ b[0]) | (a[1] ^ b[1]) | (a[2] ^ b[2]) | (a[3] ^ b[3]) |
(a[4] ^ b[4]) | (a[5] ^ b[5]) | (a[6] ^ b[6]) | (a[7] ^ b[7]) |
(a[8] ^ b[8]) | (a[9] ^ b[9])) == 0;
}
/* Add two Montgomery form projective points.
*
* r Result of addition.
* p First point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_add_10(sp_point_256* r, const sp_point_256* p, const sp_point_256* q,
sp_digit* t)
{
const sp_point_256* ap[2];
sp_point_256* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* t3 = t + 4*10;
sp_digit* t4 = t + 6*10;
sp_digit* t5 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Ensure only the first point is the same as the result. */
if (q == r) {
const sp_point_256* a = p;
p = q;
q = a;
}
/* Check double */
(void)sp_256_sub_10(t1, p256_mod, q->y);
sp_256_norm_10(t1);
if ((sp_256_cmp_equal_10(p->x, q->x) & sp_256_cmp_equal_10(p->z, q->z) &
(sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))) != 0) {
sp_256_proj_point_dbl_10(r, p, t);
}
else {
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point_256*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point_256));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<10; i++) {
r->x[i] = ap[p->infinity]->x[i];
}
for (i=0; i<10; i++) {
r->y[i] = ap[p->infinity]->y[i];
}
for (i=0; i<10; i++) {
r->z[i] = ap[p->infinity]->z[i];
}
r->infinity = ap[p->infinity]->infinity;
/* U1 = X1*Z2^2 */
sp_256_mont_sqr_10(t1, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t3, t1, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t1, x, p256_mod, p256_mp_mod);
/* U2 = X2*Z1^2 */
sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
/* S1 = Y1*Z2^3 */
sp_256_mont_mul_10(t3, t3, y, p256_mod, p256_mp_mod);
/* S2 = Y2*Z1^3 */
sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
/* H = U2 - U1 */
sp_256_mont_sub_10(t2, t2, t1, p256_mod);
/* R = S2 - S1 */
sp_256_mont_sub_10(t4, t4, t3, p256_mod);
/* Z3 = H*Z1*Z2 */
sp_256_mont_mul_10(z, z, q->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
/* X3 = R^2 - H^3 - 2*U1*H^2 */
sp_256_mont_sqr_10(x, t4, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(y, t1, t5, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(x, x, t5, p256_mod);
sp_256_mont_dbl_10(t1, y, p256_mod);
sp_256_mont_sub_10(x, x, t1, p256_mod);
/* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_mul_10(y, y, t4, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t3, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(y, y, t5, p256_mod);
}
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_10(sp_point_256* r, const sp_point_256* g, const sp_digit* k,
int map, void* heap)
{
#ifdef WOLFSSL_SP_NO_MALLOC
sp_point_256 t[3];
sp_digit tmp[2 * 10 * 5];
#else
sp_point_256* t;
sp_digit* tmp;
#endif
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
(void)heap;
#ifndef WOLFSSL_SP_NO_MALLOC
t = (sp_point_256*)XMALLOC(sizeof(sp_point_256) * 3, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#endif
if (err == MP_OKAY) {
XMEMSET(t, 0, sizeof(sp_point_256) * 3);
/* t[0] = {0, 0, 1} * norm */
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
err = sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
}
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
if (err == MP_OKAY) {
i = 9;
c = 22;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_256_proj_point_add_10(&t[y^1], &t[0], &t[1], tmp);
XMEMCPY(&t[2], (void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])),
sizeof(sp_point_256));
sp_256_proj_point_dbl_10(&t[2], &t[2], tmp);
XMEMCPY((void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), &t[2],
sizeof(sp_point_256));
}
if (map != 0) {
sp_256_map_10(r, &t[0], tmp);
}
else {
XMEMCPY(r, &t[0], sizeof(sp_point_256));
}
}
#ifndef WOLFSSL_SP_NO_MALLOC
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point_256) * 3);
XFREE(t, NULL, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmp, sizeof(tmp));
ForceZero(t, sizeof(t));
#endif
return err;
}
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_10(sp_point_256* r, const sp_point_256* g, const sp_digit* k,
int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 t[3];
sp_digit tmp[2 * 10 * 5];
#else
sp_point_256* t;
sp_digit* tmp;
#endif
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
(void)heap;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = (sp_point*)XMALLOC(sizeof(*t) * 3, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#endif
if (err == MP_OKAY) {
/* t[0] = {0, 0, 1} * norm */
XMEMSET(&t[0], 0, sizeof(t[0]));
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
t[1].infinity = 0;
err = sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
}
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
if (err == MP_OKAY)
err = sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
if (err == MP_OKAY) {
i = 9;
c = 22;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_256_proj_point_add_10(&t[y^1], &t[0], &t[1], tmp);
XMEMCPY(&t[2], (void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), sizeof(t[2]));
sp_256_proj_point_dbl_10(&t[2], &t[2], tmp);
XMEMCPY((void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), &t[2], sizeof(t[2]));
}
if (map != 0) {
sp_256_map_10(r, &t[0], tmp);
}
else {
XMEMCPY(r, &t[0], sizeof(sp_point_256));
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point_256) * 3);
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmp, sizeof(tmp));
ForceZero(t, sizeof(t));
#endif
return err;
}
#else
/* A table entry for pre-computed points. */
typedef struct sp_table_entry_256 {
sp_digit x[10];
sp_digit y[10];
} sp_table_entry_256;
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_fast_10(sp_point_256* r, const sp_point_256* g, const sp_digit* k,
int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 td[16];
sp_point_256 rtd;
sp_digit tmpd[2 * 10 * 5];
#endif
sp_point_256* t;
sp_point_256* rt;
sp_digit* tmp;
sp_digit n;
int i;
int c, y;
int err;
(void)heap;
err = sp_256_point_new_10(heap, rtd, rt);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = (sp_point_256*)XMALLOC(sizeof(sp_point_256) * 16, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#else
t = td;
tmp = tmpd;
#endif
if (err == MP_OKAY) {
/* t[0] = {0, 0, 1} * norm */
XMEMSET(&t[0], 0, sizeof(t[0]));
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
(void)sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
(void)sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
(void)sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
t[1].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 2], &t[ 1], tmp);
t[ 2].infinity = 0;
sp_256_proj_point_add_10(&t[ 3], &t[ 2], &t[ 1], tmp);
t[ 3].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 4], &t[ 2], tmp);
t[ 4].infinity = 0;
sp_256_proj_point_add_10(&t[ 5], &t[ 3], &t[ 2], tmp);
t[ 5].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 6], &t[ 3], tmp);
t[ 6].infinity = 0;
sp_256_proj_point_add_10(&t[ 7], &t[ 4], &t[ 3], tmp);
t[ 7].infinity = 0;
sp_256_proj_point_dbl_10(&t[ 8], &t[ 4], tmp);
t[ 8].infinity = 0;
sp_256_proj_point_add_10(&t[ 9], &t[ 5], &t[ 4], tmp);
t[ 9].infinity = 0;
sp_256_proj_point_dbl_10(&t[10], &t[ 5], tmp);
t[10].infinity = 0;
sp_256_proj_point_add_10(&t[11], &t[ 6], &t[ 5], tmp);
t[11].infinity = 0;
sp_256_proj_point_dbl_10(&t[12], &t[ 6], tmp);
t[12].infinity = 0;
sp_256_proj_point_add_10(&t[13], &t[ 7], &t[ 6], tmp);
t[13].infinity = 0;
sp_256_proj_point_dbl_10(&t[14], &t[ 7], tmp);
t[14].infinity = 0;
sp_256_proj_point_add_10(&t[15], &t[ 8], &t[ 7], tmp);
t[15].infinity = 0;
i = 8;
n = k[i+1] << 6;
c = 18;
y = n >> 24;
XMEMCPY(rt, &t[y], sizeof(sp_point_256));
n <<= 8;
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= k[i--] << (6 - c);
c += 26;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_dbl_10(rt, rt, tmp);
sp_256_proj_point_add_10(rt, rt, &t[y], tmp);
}
if (map != 0) {
sp_256_map_10(r, rt, tmp);
}
else {
XMEMCPY(r, rt, sizeof(sp_point_256));
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point_256) * 16);
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmpd, sizeof(tmpd));
ForceZero(td, sizeof(td));
#endif
sp_256_point_free_10(rt, 1, heap);
return err;
}
#ifdef FP_ECC
/* Double the Montgomery form projective point p a number of times.
*
* r Result of repeated doubling of point.
* p Point to double.
* n Number of times to double
* t Temporary ordinate data.
*/
static void sp_256_proj_point_dbl_n_10(sp_point_256* p, int n, sp_digit* t)
{
sp_digit* w = t;
sp_digit* a = t + 2*10;
sp_digit* b = t + 4*10;
sp_digit* t1 = t + 6*10;
sp_digit* t2 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
x = p->x;
y = p->y;
z = p->z;
/* Y = 2*Y */
sp_256_mont_dbl_10(y, y, p256_mod);
/* W = Z^4 */
sp_256_mont_sqr_10(w, z, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(w, w, p256_mod, p256_mp_mod);
#ifndef WOLFSSL_SP_SMALL
while (--n > 0)
#else
while (--n >= 0)
#endif
{
/* A = 3*(X^2 - W) */
sp_256_mont_sqr_10(t1, x, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(t1, t1, w, p256_mod);
sp_256_mont_tpl_10(a, t1, p256_mod);
/* B = X*Y^2 */
sp_256_mont_sqr_10(t1, y, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(b, t1, x, p256_mod, p256_mp_mod);
/* X = A^2 - 2B */
sp_256_mont_sqr_10(x, a, p256_mod, p256_mp_mod);
sp_256_mont_dbl_10(t2, b, p256_mod);
sp_256_mont_sub_10(x, x, t2, p256_mod);
/* Z = Z*Y */
sp_256_mont_mul_10(z, z, y, p256_mod, p256_mp_mod);
/* t2 = Y^4 */
sp_256_mont_sqr_10(t1, t1, p256_mod, p256_mp_mod);
#ifdef WOLFSSL_SP_SMALL
if (n != 0)
#endif
{
/* W = W*Y^4 */
sp_256_mont_mul_10(w, w, t1, p256_mod, p256_mp_mod);
}
/* y = 2*A*(B - X) - Y^4 */
sp_256_mont_sub_10(y, b, x, p256_mod);
sp_256_mont_mul_10(y, y, a, p256_mod, p256_mp_mod);
sp_256_mont_dbl_10(y, y, p256_mod);
sp_256_mont_sub_10(y, y, t1, p256_mod);
}
#ifndef WOLFSSL_SP_SMALL
/* A = 3*(X^2 - W) */
sp_256_mont_sqr_10(t1, x, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(t1, t1, w, p256_mod);
sp_256_mont_tpl_10(a, t1, p256_mod);
/* B = X*Y^2 */
sp_256_mont_sqr_10(t1, y, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(b, t1, x, p256_mod, p256_mp_mod);
/* X = A^2 - 2B */
sp_256_mont_sqr_10(x, a, p256_mod, p256_mp_mod);
sp_256_mont_dbl_10(t2, b, p256_mod);
sp_256_mont_sub_10(x, x, t2, p256_mod);
/* Z = Z*Y */
sp_256_mont_mul_10(z, z, y, p256_mod, p256_mp_mod);
/* t2 = Y^4 */
sp_256_mont_sqr_10(t1, t1, p256_mod, p256_mp_mod);
/* y = 2*A*(B - X) - Y^4 */
sp_256_mont_sub_10(y, b, x, p256_mod);
sp_256_mont_mul_10(y, y, a, p256_mod, p256_mp_mod);
sp_256_mont_dbl_10(y, y, p256_mod);
sp_256_mont_sub_10(y, y, t1, p256_mod);
#endif
/* Y = Y/2 */
sp_256_div2_10(y, y, p256_mod);
}
#endif /* FP_ECC */
/* Add two Montgomery form projective points. The second point has a q value of
* one.
* Only the first point can be the same pointer as the result point.
*
* r Result of addition.
* p First point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_256_proj_point_add_qz1_10(sp_point_256* r, const sp_point_256* p,
const sp_point_256* q, sp_digit* t)
{
const sp_point_256* ap[2];
sp_point_256* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*10;
sp_digit* t3 = t + 4*10;
sp_digit* t4 = t + 6*10;
sp_digit* t5 = t + 8*10;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Check double */
(void)sp_256_sub_10(t1, p256_mod, q->y);
sp_256_norm_10(t1);
if ((sp_256_cmp_equal_10(p->x, q->x) & sp_256_cmp_equal_10(p->z, q->z) &
(sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))) != 0) {
sp_256_proj_point_dbl_10(r, p, t);
}
else {
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point_256*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point_256));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<10; i++) {
r->x[i] = ap[p->infinity]->x[i];
}
for (i=0; i<10; i++) {
r->y[i] = ap[p->infinity]->y[i];
}
for (i=0; i<10; i++) {
r->z[i] = ap[p->infinity]->z[i];
}
r->infinity = ap[p->infinity]->infinity;
/* U2 = X2*Z1^2 */
sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
/* S2 = Y2*Z1^3 */
sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
/* H = U2 - X1 */
sp_256_mont_sub_10(t2, t2, x, p256_mod);
/* R = S2 - Y1 */
sp_256_mont_sub_10(t4, t4, y, p256_mod);
/* Z3 = H*Z1 */
sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
/* X3 = R^2 - H^3 - 2*X1*H^2 */
sp_256_mont_sqr_10(t1, t4, p256_mod, p256_mp_mod);
sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t3, x, t5, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(x, t1, t5, p256_mod);
sp_256_mont_dbl_10(t1, t3, p256_mod);
sp_256_mont_sub_10(x, x, t1, p256_mod);
/* Y3 = R*(X1*H^2 - X3) - Y1*H^3 */
sp_256_mont_sub_10(t3, t3, x, p256_mod);
sp_256_mont_mul_10(t3, t3, t4, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t5, t5, y, p256_mod, p256_mp_mod);
sp_256_mont_sub_10(y, t3, t5, p256_mod);
}
}
#ifdef FP_ECC
/* Convert the projective point to affine.
* Ordinates are in Montgomery form.
*
* a Point to convert.
* t Temporary data.
*/
static void sp_256_proj_to_affine_10(sp_point_256* a, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2 * 10;
sp_digit* tmp = t + 4 * 10;
sp_256_mont_inv_10(t1, a->z, tmp);
sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(a->x, a->x, t2, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(a->y, a->y, t1, p256_mod, p256_mp_mod);
XMEMCPY(a->z, p256_norm_mod, sizeof(p256_norm_mod));
}
/* Generate the pre-computed table of points for the base point.
*
* a The base point.
* table Place to store generated point data.
* tmp Temporary data.
* heap Heap to use for allocation.
*/
static int sp_256_gen_stripe_table_10(const sp_point_256* a,
sp_table_entry_256* table, sp_digit* tmp, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 td, s1d, s2d;
#endif
sp_point_256* t;
sp_point_256* s1 = NULL;
sp_point_256* s2 = NULL;
int i, j;
int err;
(void)heap;
err = sp_256_point_new_10(heap, td, t);
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, s1d, s1);
}
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, s2d, s2);
}
if (err == MP_OKAY) {
err = sp_256_mod_mul_norm_10(t->x, a->x, p256_mod);
}
if (err == MP_OKAY) {
err = sp_256_mod_mul_norm_10(t->y, a->y, p256_mod);
}
if (err == MP_OKAY) {
err = sp_256_mod_mul_norm_10(t->z, a->z, p256_mod);
}
if (err == MP_OKAY) {
t->infinity = 0;
sp_256_proj_to_affine_10(t, tmp);
XMEMCPY(s1->z, p256_norm_mod, sizeof(p256_norm_mod));
s1->infinity = 0;
XMEMCPY(s2->z, p256_norm_mod, sizeof(p256_norm_mod));
s2->infinity = 0;
/* table[0] = {0, 0, infinity} */
XMEMSET(&table[0], 0, sizeof(sp_table_entry_256));
/* table[1] = Affine version of 'a' in Montgomery form */
XMEMCPY(table[1].x, t->x, sizeof(table->x));
XMEMCPY(table[1].y, t->y, sizeof(table->y));
for (i=1; i<8; i++) {
sp_256_proj_point_dbl_n_10(t, 32, tmp);
sp_256_proj_to_affine_10(t, tmp);
XMEMCPY(table[1<<i].x, t->x, sizeof(table->x));
XMEMCPY(table[1<<i].y, t->y, sizeof(table->y));
}
for (i=1; i<8; i++) {
XMEMCPY(s1->x, table[1<<i].x, sizeof(table->x));
XMEMCPY(s1->y, table[1<<i].y, sizeof(table->y));
for (j=(1<<i)+1; j<(1<<(i+1)); j++) {
XMEMCPY(s2->x, table[j-(1<<i)].x, sizeof(table->x));
XMEMCPY(s2->y, table[j-(1<<i)].y, sizeof(table->y));
sp_256_proj_point_add_qz1_10(t, s1, s2, tmp);
sp_256_proj_to_affine_10(t, tmp);
XMEMCPY(table[j].x, t->x, sizeof(table->x));
XMEMCPY(table[j].y, t->y, sizeof(table->y));
}
}
}
sp_256_point_free_10(s2, 0, heap);
sp_256_point_free_10(s1, 0, heap);
sp_256_point_free_10( t, 0, heap);
return err;
}
#endif /* FP_ECC */
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_stripe_10(sp_point_256* r, const sp_point_256* g,
const sp_table_entry_256* table, const sp_digit* k, int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 rtd;
sp_point_256 pd;
sp_digit td[2 * 10 * 5];
#endif
sp_point_256* rt;
sp_point_256* p = NULL;
sp_digit* t;
int i, j;
int y, x;
int err;
(void)g;
(void)heap;
err = sp_256_point_new_10(heap, rtd, rt);
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, pd, p);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
DYNAMIC_TYPE_ECC);
if (t == NULL) {
err = MEMORY_E;
}
#else
t = td;
#endif
if (err == MP_OKAY) {
XMEMCPY(p->z, p256_norm_mod, sizeof(p256_norm_mod));
XMEMCPY(rt->z, p256_norm_mod, sizeof(p256_norm_mod));
y = 0;
for (j=0,x=31; j<8; j++,x+=32) {
y |= ((k[x / 26] >> (x % 26)) & 1) << j;
}
XMEMCPY(rt->x, table[y].x, sizeof(table[y].x));
XMEMCPY(rt->y, table[y].y, sizeof(table[y].y));
rt->infinity = !y;
for (i=30; i>=0; i--) {
y = 0;
for (j=0,x=i; j<8; j++,x+=32) {
y |= ((k[x / 26] >> (x % 26)) & 1) << j;
}
sp_256_proj_point_dbl_10(rt, rt, t);
XMEMCPY(p->x, table[y].x, sizeof(table[y].x));
XMEMCPY(p->y, table[y].y, sizeof(table[y].y));
p->infinity = !y;
sp_256_proj_point_add_qz1_10(rt, rt, p, t);
}
if (map != 0) {
sp_256_map_10(r, rt, t);
}
else {
XMEMCPY(r, rt, sizeof(sp_point_256));
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (t != NULL) {
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(p, 0, heap);
sp_256_point_free_10(rt, 0, heap);
return err;
}
#ifdef FP_ECC
#ifndef FP_ENTRIES
#define FP_ENTRIES 16
#endif
typedef struct sp_cache_256_t {
sp_digit x[10];
sp_digit y[10];
sp_table_entry_256 table[256];
uint32_t cnt;
int set;
} sp_cache_256_t;
static THREAD_LS_T sp_cache_256_t sp_cache_256[FP_ENTRIES];
static THREAD_LS_T int sp_cache_256_last = -1;
static THREAD_LS_T int sp_cache_256_inited = 0;
#ifndef HAVE_THREAD_LS
static volatile int initCacheMutex_256 = 0;
static wolfSSL_Mutex sp_cache_256_lock;
#endif
static void sp_ecc_get_cache_256(const sp_point_256* g, sp_cache_256_t** cache)
{
int i, j;
uint32_t least;
if (sp_cache_256_inited == 0) {
for (i=0; i<FP_ENTRIES; i++) {
sp_cache_256[i].set = 0;
}
sp_cache_256_inited = 1;
}
/* Compare point with those in cache. */
for (i=0; i<FP_ENTRIES; i++) {
if (!sp_cache_256[i].set)
continue;
if (sp_256_cmp_equal_10(g->x, sp_cache_256[i].x) &
sp_256_cmp_equal_10(g->y, sp_cache_256[i].y)) {
sp_cache_256[i].cnt++;
break;
}
}
/* No match. */
if (i == FP_ENTRIES) {
/* Find empty entry. */
i = (sp_cache_256_last + 1) % FP_ENTRIES;
for (; i != sp_cache_256_last; i=(i+1)%FP_ENTRIES) {
if (!sp_cache_256[i].set) {
break;
}
}
/* Evict least used. */
if (i == sp_cache_256_last) {
least = sp_cache_256[0].cnt;
for (j=1; j<FP_ENTRIES; j++) {
if (sp_cache_256[j].cnt < least) {
i = j;
least = sp_cache_256[i].cnt;
}
}
}
XMEMCPY(sp_cache_256[i].x, g->x, sizeof(sp_cache_256[i].x));
XMEMCPY(sp_cache_256[i].y, g->y, sizeof(sp_cache_256[i].y));
sp_cache_256[i].set = 1;
sp_cache_256[i].cnt = 1;
}
*cache = &sp_cache_256[i];
sp_cache_256_last = i;
}
#endif /* FP_ECC */
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_10(sp_point_256* r, const sp_point_256* g, const sp_digit* k,
int map, void* heap)
{
#ifndef FP_ECC
return sp_256_ecc_mulmod_fast_10(r, g, k, map, heap);
#else
sp_digit tmp[2 * 10 * 5];
sp_cache_256_t* cache;
int err = MP_OKAY;
#ifndef HAVE_THREAD_LS
if (initCacheMutex_256 == 0) {
wc_InitMutex(&sp_cache_256_lock);
initCacheMutex_256 = 1;
}
if (wc_LockMutex(&sp_cache_256_lock) != 0)
err = BAD_MUTEX_E;
#endif /* HAVE_THREAD_LS */
if (err == MP_OKAY) {
sp_ecc_get_cache_256(g, &cache);
if (cache->cnt == 2)
sp_256_gen_stripe_table_10(g, cache->table, tmp, heap);
#ifndef HAVE_THREAD_LS
wc_UnLockMutex(&sp_cache_256_lock);
#endif /* HAVE_THREAD_LS */
if (cache->cnt < 2) {
err = sp_256_ecc_mulmod_fast_10(r, g, k, map, heap);
}
else {
err = sp_256_ecc_mulmod_stripe_10(r, g, cache->table, k,
map, heap);
}
}
return err;
#endif
}
#endif
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* km Scalar to multiply by.
* p Point to multiply.
* r Resulting point.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_mulmod_256(mp_int* km, ecc_point* gm, ecc_point* r, int map,
void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 p;
sp_digit kd[10];
#endif
sp_point_256* point;
sp_digit* k = NULL;
int err = MP_OKAY;
err = sp_256_point_new_10(heap, p, point);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL)
err = MEMORY_E;
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(k, 10, km);
sp_256_point_from_ecc_point_10(point, gm);
err = sp_256_ecc_mulmod_10(point, point, k, map, heap);
}
if (err == MP_OKAY) {
err = sp_256_point_to_ecc_point_10(point, r);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(point, 0, heap);
return err;
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_base_10(sp_point_256* r, const sp_digit* k,
int map, void* heap)
{
/* No pre-computed values. */
return sp_256_ecc_mulmod_10(r, &p256_base, k, map, heap);
}
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_base_10(sp_point_256* r, const sp_digit* k,
int map, void* heap)
{
/* No pre-computed values. */
return sp_256_ecc_mulmod_10(r, &p256_base, k, map, heap);
}
#else
static const sp_table_entry_256 p256_table[256] = {
/* 0 */
{ { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
{ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
/* 1 */
{ { 0x0a9143c,0x1cc3506,0x360179e,0x3f17fb6,0x075ba95,0x1d88944,
0x3b732b7,0x15719e7,0x376a537,0x0062417 },
{ 0x295560a,0x094d5f3,0x245cddf,0x392e867,0x18b4ab8,0x3487cc9,
0x288688d,0x176174b,0x3182588,0x0215c7f } },
/* 2 */
{ { 0x147519a,0x2218090,0x32f0202,0x2b09acd,0x0d0981e,0x1e17af2,
0x14a7caa,0x163a6a7,0x10ddbdf,0x03654f1 },
{ 0x1590f8f,0x0d8733f,0x09179d6,0x1ad139b,0x372e962,0x0bad933,
0x1961102,0x223cdff,0x37e9eb2,0x0218fae } },
/* 3 */
{ { 0x0db6485,0x1ad88d7,0x2f97785,0x288bc28,0x3808f0e,0x3df8c02,
0x28d9544,0x20280f9,0x055b5ff,0x00001d8 },
{ 0x38d2010,0x13ae6e0,0x308a763,0x2ecc90d,0x254014f,0x10a9981,
0x247d398,0x0fb8383,0x3613437,0x020c21d } },
/* 4 */
{ { 0x2a0d2bb,0x08bf145,0x34994f9,0x1b06988,0x30d5cc1,0x1f18b22,
0x01cf3a5,0x199fe49,0x161fd1b,0x00bd79a },
{ 0x1a01797,0x171c2fd,0x21925c1,0x1358255,0x23d20b4,0x1c7f6d4,
0x111b370,0x03dec12,0x1168d6f,0x03d923e } },
/* 5 */
{ { 0x137bbbc,0x19a11f8,0x0bec9e5,0x27a29a8,0x3e43446,0x275cd18,
0x0427617,0x00056c7,0x285133d,0x016af80 },
{ 0x04c7dab,0x2a0df30,0x0c0792a,0x1310c98,0x3573d9f,0x239b30d,
0x1315627,0x1ce0c32,0x25b6b6f,0x0252edc } },
/* 6 */
{ { 0x20f141c,0x26d23dc,0x3c74bbf,0x334b7d6,0x06199b3,0x0441171,
0x3f61294,0x313bf70,0x3cb2f7d,0x03375ae },
{ 0x2f436fd,0x19c02fa,0x26becca,0x1b6e64c,0x26f647f,0x053c948,
0x0fa7920,0x397d830,0x2bd4bda,0x028d86f } },
/* 7 */
{ { 0x17c13c7,0x2895616,0x03e128a,0x17d42df,0x1c38d63,0x0f02747,
0x039aecf,0x0a4b01c,0x209c4b5,0x02e84b2 },
{ 0x1f91dfd,0x023e916,0x07fb9e4,0x19b3ba8,0x13af43b,0x35e02ca,
0x0eb0899,0x3bd2c7b,0x19d701f,0x014faee } },
/* 8 */
{ { 0x0e63d34,0x1fb8c6c,0x0fab4fe,0x1caa795,0x0f46005,0x179ed69,
0x093334d,0x120c701,0x39206d5,0x021627e },
{ 0x183553a,0x03d7319,0x09e5aa7,0x12b8959,0x2087909,0x0011194,
0x1045071,0x0713f32,0x16d0254,0x03aec1a } },
/* 9 */
{ { 0x01647c5,0x1b2856b,0x1799461,0x11f133d,0x0b8127d,0x1937eeb,
0x266aa37,0x1f68f71,0x0cbd1b2,0x03aca08 },
{ 0x287e008,0x1be361a,0x38f3940,0x276488d,0x2d87dfa,0x0333b2c,
0x2d2e428,0x368755b,0x09b55a7,0x007ca0a } },
/* 10 */
{ { 0x389da99,0x2a8300e,0x0022abb,0x27ae0a1,0x0a6f2d7,0x207017a,
0x047862b,0x1358c9e,0x35905e5,0x00cde92 },
{ 0x1f7794a,0x1d40348,0x3f613c6,0x2ddf5b5,0x0207005,0x133f5ba,
0x1a37810,0x3ef5829,0x0d5f4c2,0x0035978 } },
/* 11 */
{ { 0x1275d38,0x026efad,0x2358d9d,0x1142f82,0x14268a7,0x1cfac99,
0x362ff49,0x288cbc1,0x24252f4,0x0308f68 },
{ 0x394520c,0x06e13c2,0x178e5da,0x18ec16f,0x1096667,0x134a7a8,
0x0dcb869,0x33fc4e9,0x38cc790,0x006778e } },
/* 12 */
{ { 0x2c5fe04,0x29c5b09,0x1bdb183,0x02ceee8,0x03b28de,0x132dc4b,
0x32c586a,0x32ff5d0,0x3d491fc,0x038d372 },
{ 0x2a58403,0x2351aea,0x3a53b40,0x21a0ba5,0x39a6974,0x1aaaa2b,
0x3901273,0x03dfe78,0x3447b4e,0x039d907 } },
/* 13 */
{ { 0x364ba59,0x14e5077,0x02fc7d7,0x3b02c09,0x1d33f10,0x0560616,
0x06dfc6a,0x15efd3c,0x357052a,0x01284b7 },
{ 0x039dbd0,0x18ce3e5,0x3e1fbfa,0x352f794,0x0d3c24b,0x07c6cc5,
0x1e4ffa2,0x3a91bf5,0x293bb5b,0x01abd6a } },
/* 14 */
{ { 0x0c91999,0x02da644,0x0491da1,0x100a960,0x00a24b4,0x2330824,
0x0094b4b,0x1004cf8,0x35a66a4,0x017f8d1 },
{ 0x13e7b4b,0x232af7e,0x391ab0f,0x069f08f,0x3292b50,0x3479898,
0x2889aec,0x2a4590b,0x308ecfe,0x02d5138 } },
/* 15 */
{ { 0x2ddfdce,0x231ba45,0x39e6647,0x19be245,0x12c3291,0x35399f8,
0x0d6e764,0x3082d3a,0x2bda6b0,0x0382dac },
{ 0x37efb57,0x04b7cae,0x00070d3,0x379e431,0x01aac0d,0x1e6f251,
0x0336ad6,0x0ddd3e4,0x3de25a6,0x01c7008 } },
/* 16 */
{ { 0x3e20925,0x230912f,0x286762a,0x30e3f73,0x391c19a,0x34e1c18,
0x16a5d5d,0x093d96a,0x3d421d3,0x0187561 },
{ 0x37173ea,0x19ce8a8,0x0b65e87,0x0214dde,0x2238480,0x16ead0f,
0x38441e0,0x3bef843,0x2124621,0x03e847f } },
/* 17 */
{ { 0x0b19ffd,0x247cacb,0x3c231c8,0x16ec648,0x201ba8d,0x2b172a3,
0x103d678,0x2fb72db,0x04c1f13,0x0161bac },
{ 0x3e8ed09,0x171b949,0x2de20c3,0x0f06067,0x21e81a3,0x1b194be,
0x0fd6c05,0x13c449e,0x0087086,0x006756b } },
/* 18 */
{ { 0x09a4e1f,0x27d604c,0x00741e9,0x06fa49c,0x0ab7de7,0x3f4a348,
0x25ef0be,0x158fc9a,0x33f7f9c,0x039f001 },
{ 0x2f59f76,0x3598e83,0x30501f6,0x15083f2,0x0669b3b,0x29980b5,
0x0c1f7a7,0x0f02b02,0x0fec65b,0x0382141 } },
/* 19 */
{ { 0x031b3ca,0x23da368,0x2d66f09,0x27b9b69,0x06d1cab,0x13c91ba,
0x3d81fa9,0x25ad16f,0x0825b09,0x01e3c06 },
{ 0x225787f,0x3bf790e,0x2c9bb7e,0x0347732,0x28016f8,0x0d6ff0d,
0x2a4877b,0x1d1e833,0x3b87e94,0x010e9dc } },
/* 20 */
{ { 0x2b533d5,0x1ddcd34,0x1dc0625,0x3da86f7,0x3673b8a,0x1e7b0a4,
0x3e7c9aa,0x19ac55d,0x251c3b2,0x02edb79 },
{ 0x25259b3,0x24c0ead,0x3480e7e,0x34f40e9,0x3d6a0af,0x2cf3f09,
0x2c83d19,0x2e66f16,0x19a5d18,0x0182d18 } },
/* 21 */
{ { 0x2e5aa1c,0x28e3846,0x3658bd6,0x0ad279c,0x1b8b765,0x397e1fb,
0x130014e,0x3ff342c,0x3b2aeeb,0x02743c9 },
{ 0x2730a55,0x0918c5e,0x083aca9,0x0bf76ef,0x19c955b,0x300669c,
0x01dfe0a,0x312341f,0x26d356e,0x0091295 } },
/* 22 */
{ { 0x2cf1f96,0x00e52ba,0x271c6db,0x2a40930,0x19f2122,0x0b2f4ee,
0x26ac1b8,0x3bda498,0x0873581,0x0117963 },
{ 0x38f9dbc,0x3d1e768,0x2040d3f,0x11ba222,0x3a8aaf1,0x1b82fb5,
0x1adfb24,0x2de9251,0x21cc1e4,0x0301038 } },
/* 23 */
{ { 0x38117b6,0x2bc001b,0x1433847,0x3fdce8d,0x3651969,0x3651d7a,
0x2b35761,0x1bb1d20,0x097682c,0x00737d7 },
{ 0x1f04839,0x1dd6d04,0x16987db,0x3d12378,0x17dbeac,0x1c2cc86,
0x121dd1b,0x3fcf6ca,0x1f8a92d,0x00119d5 } },
/* 24 */
{ { 0x0e8ffcd,0x2b174af,0x1a82cc8,0x22cbf98,0x30d53c4,0x080b5b1,
0x3161727,0x297cfdb,0x2113b83,0x0011b97 },
{ 0x0007f01,0x23fd936,0x3183e7b,0x0496bd0,0x07fb1ef,0x178680f,
0x1c5ea63,0x0016c11,0x2c3303d,0x01b8041 } },
/* 25 */
{ { 0x0dd73b1,0x1cd6122,0x10d948c,0x23e657b,0x3767070,0x15a8aad,
0x385ea8c,0x33c7ce0,0x0ede901,0x0110965 },
{ 0x2d4b65b,0x2a8b244,0x0c37f8f,0x0ee5b24,0x394c234,0x3a5e347,
0x26e4a15,0x39a3b4c,0x2514c2e,0x029e5be } },
/* 26 */
{ { 0x23addd7,0x3ed8120,0x13b3359,0x20f959a,0x09e2a61,0x32fcf20,
0x05b78e3,0x19ba7e2,0x1a9c697,0x0392b4b },
{ 0x2048a61,0x3dfd0a3,0x19a0357,0x233024b,0x3082d19,0x00fb63b,
0x3a1af4c,0x1450ff0,0x046c37b,0x0317a50 } },
/* 27 */
{ { 0x3e75f9e,0x294e30a,0x3a78476,0x3a32c48,0x36fd1a9,0x0427012,
0x1e4df0b,0x11d1f61,0x1afdb46,0x018ca0f },
{ 0x2f2df15,0x0a33dee,0x27f4ce7,0x1542b66,0x3e592c4,0x20d2f30,
0x3226ade,0x2a4e3ea,0x1ab1981,0x01a2f46 } },
/* 28 */
{ { 0x087d659,0x3ab5446,0x305ac08,0x3d2cd64,0x33374d5,0x3f9d3f8,
0x186981c,0x37f5a5a,0x2f53c6f,0x01254a4 },
{ 0x2cec896,0x1e32786,0x04844a8,0x043b16d,0x3d964b2,0x1935829,
0x16f7e26,0x1a0dd9a,0x30d2603,0x003b1d4 } },
/* 29 */
{ { 0x12687bb,0x04e816b,0x21fa2da,0x1abccb8,0x3a1f83b,0x375181e,
0x0f5ef51,0x0fc2ce4,0x3a66486,0x003d881 },
{ 0x3138233,0x1f8eec3,0x2718bd6,0x1b09caa,0x2dd66b9,0x1bb222b,
0x1004072,0x1b73e3b,0x07208ed,0x03fc36c } },
/* 30 */
{ { 0x095d553,0x3e84053,0x0a8a749,0x3f575a0,0x3a44052,0x3ced59b,
0x3b4317f,0x03a8c60,0x13c8874,0x00c4ed4 },
{ 0x0d11549,0x0b8ab02,0x221cb40,0x02ed37b,0x2071ee1,0x1fc8c83,
0x3987dd4,0x27e049a,0x0f986f1,0x00b4eaf } },
/* 31 */
{ { 0x15581a2,0x2214060,0x11af4c2,0x1598c88,0x19a0a6d,0x32acba6,
0x3a7a0f0,0x2337c66,0x210ded9,0x0300dbe },
{ 0x1fbd009,0x3822eb0,0x181629a,0x2401b45,0x30b68b1,0x2e78363,
0x2b32779,0x006530b,0x2c4b6d4,0x029aca8 } },
/* 32 */
{ { 0x13549cf,0x0f943db,0x265ed43,0x1bfeb35,0x06f3369,0x3847f2d,
0x1bfdacc,0x26181a5,0x252af7c,0x02043b8 },
{ 0x159bb2c,0x143f85c,0x357b654,0x2f9d62c,0x2f7dfbe,0x1a7fa9c,
0x057e74d,0x05d14ac,0x17a9273,0x035215c } },
/* 33 */
{ { 0x0cb5a98,0x106a2bc,0x10bf117,0x24c7cc4,0x3d3da8f,0x2ce0ab7,
0x14e2cba,0x1813866,0x1a72f9a,0x01a9811 },
{ 0x2b2411d,0x3034fe8,0x16e0170,0x0f9443a,0x0be0eb8,0x2196cf3,
0x0c9f738,0x15e40ef,0x0faf9e1,0x034f917 } },
/* 34 */
{ { 0x03f7669,0x3da6efa,0x3d6bce1,0x209ca1d,0x109f8ae,0x09109e3,
0x08ae543,0x3067255,0x1dee3c2,0x0081dd5 },
{ 0x3ef1945,0x358765b,0x28c387b,0x3bec4b4,0x218813c,0x0b7d92a,
0x3cd1d67,0x2c0367e,0x2e57154,0x0123717 } },
/* 35 */
{ { 0x3e5a199,0x1e42ffd,0x0bb7123,0x33e6273,0x1e0efb8,0x294671e,
0x3a2bfe0,0x3d11709,0x2eddff6,0x03cbec2 },
{ 0x0b5025f,0x0255d7c,0x1f2241c,0x35d03ea,0x0550543,0x202fef4,
0x23c8ad3,0x354963e,0x015db28,0x0284fa4 } },
/* 36 */
{ { 0x2b65cbc,0x1e8d428,0x0226f9f,0x1c8a919,0x10b04b9,0x08fc1e8,
0x1ce241e,0x149bc99,0x2b01497,0x00afc35 },
{ 0x3216fb7,0x1374fd2,0x226ad3d,0x19fef76,0x0f7d7b8,0x1c21417,
0x37b83f6,0x3a27eba,0x25a162f,0x010aa52 } },
/* 37 */
{ { 0x2adf191,0x1ab42fa,0x28d7584,0x2409689,0x20f8a48,0x253707d,
0x2030504,0x378f7a1,0x169c65e,0x00b0b76 },
{ 0x3849c17,0x085c764,0x10dd6d0,0x2e87689,0x1460488,0x30e9521,
0x10c7063,0x1b6f120,0x21f42c5,0x03d0dfe } },
/* 38 */
{ { 0x20f7dab,0x035c512,0x29ac6aa,0x24c5ddb,0x20f0497,0x17ce5e1,
0x00a050f,0x1eaa14b,0x3335470,0x02abd16 },
{ 0x18d364a,0x0df0cf0,0x316585e,0x018f925,0x0d40b9b,0x17b1511,
0x1716811,0x1caf3d0,0x10df4f2,0x0337d8c } },
/* 39 */
{ { 0x2a8b7ef,0x0f188e3,0x2287747,0x06216f0,0x008e935,0x2f6a38d,
0x1567722,0x0bfc906,0x0bada9e,0x03c3402 },
{ 0x014d3b1,0x099c749,0x2a76291,0x216c067,0x3b37549,0x14ef2f6,
0x21b96d4,0x1ee2d71,0x2f5ca88,0x016f570 } },
/* 40 */
{ { 0x09a3154,0x3d1a7bd,0x2e9aef0,0x255b8ac,0x03e85a5,0x2a492a7,
0x2aec1ea,0x11c6516,0x3c8a09e,0x02a84b7 },
{ 0x1f69f1d,0x09c89d3,0x1e7326f,0x0b28bfd,0x0e0e4c8,0x1ea7751,
0x18ce73b,0x2a406e7,0x273e48c,0x01b00db } },
/* 41 */
{ { 0x36e3138,0x2b84a83,0x345a5cf,0x00096b4,0x16966ef,0x159caf1,
0x13c64b4,0x2f89226,0x25896af,0x00a4bfd },
{ 0x2213402,0x1435117,0x09fed52,0x09d0e4b,0x0f6580e,0x2871cba,
0x3b397fd,0x1c9d825,0x090311b,0x0191383 } },
/* 42 */
{ { 0x07153f0,0x1087869,0x18c9e1e,0x1e64810,0x2b86c3b,0x0175d9c,
0x3dce877,0x269de4e,0x393cab7,0x03c96b9 },
{ 0x1869d0c,0x06528db,0x02641f3,0x209261b,0x29d55c8,0x25ba517,
0x3b5ea30,0x028f927,0x25313db,0x00e6e39 } },
/* 43 */
{ { 0x2fd2e59,0x150802d,0x098f377,0x19a4957,0x135e2c0,0x38a95ce,
0x1ab21a0,0x36c1b67,0x32f0f19,0x00e448b },
{ 0x3cad53c,0x3387800,0x17e3cfb,0x03f9970,0x3225b2c,0x2a84e1d,
0x3af1d29,0x3fe35ca,0x2f8ce80,0x0237a02 } },
/* 44 */
{ { 0x07bbb76,0x3aa3648,0x2758afb,0x1f085e0,0x1921c7e,0x3010dac,
0x22b74b1,0x230137e,0x1062e36,0x021c652 },
{ 0x3993df5,0x24a2ee8,0x126ab5f,0x2d7cecf,0x0639d75,0x16d5414,
0x1aa78a8,0x3f78404,0x26a5b74,0x03f0c57 } },
/* 45 */
{ { 0x0d6ecfa,0x3f506ba,0x3f86561,0x3d86bb1,0x15f8c44,0x2491d07,
0x052a7b4,0x2422261,0x3adee38,0x039b529 },
{ 0x193c75d,0x14bb451,0x1162605,0x293749c,0x370a70d,0x2e8b1f6,
0x2ede937,0x2b95f4a,0x39a9be2,0x00d77eb } },
/* 46 */
{ { 0x2736636,0x15bf36a,0x2b7e6b9,0x25eb8b2,0x209f51d,0x3cd2659,
0x10bf410,0x034afec,0x3d71c83,0x0076971 },
{ 0x0ce6825,0x07920cf,0x3c3b5c4,0x23fe55c,0x015ad11,0x08c0dae,
0x0552c7f,0x2e75a8a,0x0fddbf4,0x01c1df0 } },
/* 47 */
{ { 0x2b9661c,0x0ffe351,0x3d71bf6,0x1ac34b3,0x3a1dfd3,0x211fe3d,
0x33e140a,0x3f9100d,0x32ee50e,0x014ea18 },
{ 0x16d8051,0x1bfda1a,0x068a097,0x2571d3d,0x1daec0c,0x39389af,
0x194dc35,0x3f3058a,0x36d34e1,0x000a329 } },
/* 48 */
{ { 0x09877ee,0x351f73f,0x0002d11,0x0420074,0x2c8b362,0x130982d,
0x02c1175,0x3c11b40,0x0d86962,0x001305f },
{ 0x0daddf5,0x2f4252c,0x15c06d9,0x1d49339,0x1bea235,0x0b680ed,
0x3356e67,0x1d1d198,0x1e9fed9,0x03dee93 } },
/* 49 */
{ { 0x3e1263f,0x2fe8d3a,0x3ce6d0d,0x0d5c6b9,0x3557637,0x0a9bd48,
0x0405538,0x0710749,0x2005213,0x038c7e5 },
{ 0x26b6ec6,0x2e485ba,0x3c44d1b,0x0b9cf0b,0x037a1d1,0x27428a5,
0x0e7eac8,0x351ef04,0x259ce34,0x02a8e98 } },
/* 50 */
{ { 0x2f3dcd3,0x3e77d4d,0x3360fbc,0x1434afd,0x36ceded,0x3d413d6,
0x1710fad,0x36bb924,0x1627e79,0x008e637 },
{ 0x109569e,0x1c168db,0x3769cf4,0x2ed4527,0x0ea0619,0x17d80d3,
0x1c03773,0x18843fe,0x1b21c04,0x015c5fd } },
/* 51 */
{ { 0x1dd895e,0x08a7248,0x04519fe,0x001030a,0x18e5185,0x358dfb3,
0x13d2391,0x0a37be8,0x0560e3c,0x019828b },
{ 0x27fcbd0,0x2a22bb5,0x30969cc,0x1e03aa7,0x1c84724,0x0ba4ad3,
0x32f4817,0x0914cca,0x14c4f52,0x01893b9 } },
/* 52 */
{ { 0x097eccc,0x1273936,0x00aa095,0x364fe62,0x04d49d1,0x10e9f08,
0x3c24230,0x3ef01c8,0x2fb92bd,0x013ce4a },
{ 0x1e44fd9,0x27e3e9f,0x2156696,0x3915ecc,0x0b66cfb,0x1a3af0f,
0x2fa8033,0x0e6736c,0x177ccdb,0x0228f9e } },
/* 53 */
{ { 0x2c4b125,0x06207c1,0x0a8cdde,0x003db8f,0x1ae34e3,0x31e84fa,
0x2999de5,0x11013bd,0x02370c2,0x00e2234 },
{ 0x0f91081,0x200d591,0x1504762,0x1857c05,0x23d9fcf,0x0cb34db,
0x27edc86,0x08cd860,0x2471810,0x029798b } },
/* 54 */
{ { 0x3acd6c8,0x097b8cb,0x3c661a8,0x15152f2,0x1699c63,0x237e64c,
0x23edf79,0x16b7033,0x0e6466a,0x00b11da },
{ 0x0a64bc9,0x1bfe324,0x1f5cb34,0x08391de,0x0630a60,0x3017a21,
0x09d064b,0x14a8365,0x041f9e6,0x01ed799 } },
/* 55 */
{ { 0x128444a,0x2508b07,0x2a39216,0x362f84d,0x2e996c5,0x2c31ff3,
0x07afe5f,0x1d1288e,0x3cb0c8d,0x02e2bdc },
{ 0x38b86fd,0x3a0ea8c,0x1cff5fd,0x1629629,0x3fee3f1,0x02b250c,
0x2e8f6f2,0x0225727,0x15f7f3f,0x0280d8e } },
/* 56 */
{ { 0x10f7770,0x0f1aee8,0x0e248c7,0x20684a8,0x3a6f16d,0x06f0ae7,
0x0df6825,0x2d4cc40,0x301875f,0x012f8da },
{ 0x3b56dbb,0x1821ba7,0x24f8922,0x22c1f9e,0x0306fef,0x1b54bc8,
0x2ccc056,0x00303ba,0x2871bdc,0x0232f26 } },
/* 57 */
{ { 0x0dac4ab,0x0625730,0x3112e13,0x101c4bf,0x3a874a4,0x2873b95,
0x32ae7c6,0x0d7e18c,0x13e0c08,0x01139d5 },
{ 0x334002d,0x00fffdd,0x025c6d5,0x22c2cd1,0x19d35cb,0x3a1ce2d,
0x3702760,0x3f06257,0x03a5eb8,0x011c29a } },
/* 58 */
{ { 0x0513482,0x1d87724,0x276a81b,0x0a807a4,0x3028720,0x339cc20,
0x2441ee0,0x31bbf36,0x290c63d,0x0059041 },
{ 0x106a2ed,0x0d2819b,0x100bf50,0x114626c,0x1dd4d77,0x2e08632,
0x14ae72a,0x2ed3f64,0x1fd7abc,0x035cd1e } },
/* 59 */
{ { 0x2d4c6e5,0x3bec596,0x104d7ed,0x23d6c1b,0x0262cf0,0x15d72c5,
0x2d5bb18,0x199ac4b,0x1e30771,0x020591a },
{ 0x21e291e,0x2e75e55,0x1661d7a,0x08b0778,0x3eb9daf,0x0d78144,
0x1827eb1,0x0fe73d2,0x123f0dd,0x0028db7 } },
/* 60 */
{ { 0x1d5533c,0x34cb1d0,0x228f098,0x27a1a11,0x17c5f5a,0x0d26f44,
0x2228ade,0x2c460e6,0x3d6fdba,0x038cc77 },
{ 0x3cc6ed8,0x02ada1a,0x260e510,0x2f7bde8,0x37160c3,0x33a1435,
0x23d9a7b,0x0ce2641,0x02a492e,0x034ed1e } },
/* 61 */
{ { 0x3821f90,0x26dba3c,0x3aada14,0x3b59bad,0x292edd9,0x2804c45,
0x3669531,0x296f42e,0x35a4c86,0x01ca049 },
{ 0x3ff47e5,0x2163df4,0x2441503,0x2f18405,0x15e1616,0x37f66ec,
0x30f11a7,0x141658a,0x27ece14,0x00b018b } },
/* 62 */
{ { 0x159ac2e,0x3e65bc0,0x2713a76,0x0db2f6c,0x3281e77,0x2391811,
0x16d2880,0x1fbc4ab,0x1f92c4e,0x00a0a8d },
{ 0x0ce5cd2,0x152c7b0,0x02299c3,0x3244de7,0x2cf99ef,0x3a0b047,
0x2caf383,0x0aaf664,0x113554d,0x031c735 } },
/* 63 */
{ { 0x1b578f4,0x177a702,0x3a7a488,0x1638ebf,0x31884e2,0x2460bc7,
0x36b1b75,0x3ce8e3d,0x340cf47,0x03143d9 },
{ 0x34b68ea,0x12b7ccd,0x1fe2a9c,0x08da659,0x0a406f3,0x1694c14,
0x06a2228,0x16370be,0x3a72129,0x02e7b2c } },
/* 64 */
{ { 0x0f8b16a,0x21043bd,0x266a56f,0x3fb11ec,0x197241a,0x36721f0,
0x006b8e6,0x2ac6c29,0x202cd42,0x0200fcf },
{ 0x0dbec69,0x0c26a01,0x105f7f0,0x3dceeeb,0x3a83b85,0x363865f,
0x097273a,0x2b70718,0x00e5067,0x03025d1 } },
/* 65 */
{ { 0x379ab34,0x295bcb0,0x38d1846,0x22e1077,0x3a8ee06,0x1db1a3b,
0x3144591,0x07cc080,0x2d5915f,0x03c6bcc },
{ 0x175bd50,0x0dd4c57,0x27bc99c,0x2ebdcbd,0x3837cff,0x235dc8f,
0x13a4184,0x0722c18,0x130e2d4,0x008f43c } },
/* 66 */
{ { 0x01500d9,0x2adbb7d,0x2da8857,0x397f2fa,0x10d890a,0x25c9654,
0x3e86488,0x3eb754b,0x1d6c0a3,0x02c0a23 },
{ 0x10bcb08,0x083cc19,0x2e16853,0x04da575,0x271af63,0x2626a9d,
0x3520a7b,0x32348c7,0x24ff408,0x03ff4dc } },
/* 67 */
{ { 0x058e6cb,0x1a3992d,0x1d28539,0x080c5e9,0x2992dad,0x2a9d7d5,
0x14ae0b7,0x09b7ce0,0x34ad78c,0x03d5643 },
{ 0x30ba55a,0x092f4f3,0x0bae0fc,0x12831de,0x20fc472,0x20ed9d2,
0x29864f6,0x1288073,0x254f6f7,0x00635b6 } },
/* 68 */
{ { 0x1be5a2b,0x0f88975,0x33c6ed9,0x20d64d3,0x06fe799,0x0989bff,
0x1409262,0x085a90c,0x0d97990,0x0142eed },
{ 0x17ec63e,0x06471b9,0x0db2378,0x1006077,0x265422c,0x08db83d,
0x28099b0,0x1270d06,0x11801fe,0x00ac400 } },
/* 69 */
{ { 0x3391593,0x22d7166,0x30fcfc6,0x2896609,0x3c385f5,0x066b72e,
0x04f3aad,0x2b831c5,0x19983fb,0x0375562 },
{ 0x0b82ff4,0x222e39d,0x34c993b,0x101c79c,0x2d2e03c,0x0f00c8a,
0x3a9eaf4,0x1810669,0x151149d,0x039b931 } },
/* 70 */
{ { 0x29af288,0x1956ec7,0x293155f,0x193deb6,0x1647e1a,0x2ca0839,
0x297e4bc,0x15bfd0d,0x1b107ed,0x0147803 },
{ 0x31c327e,0x05a6e1d,0x02ad43d,0x02d2a5b,0x129cdb2,0x37ad1de,
0x3d51f53,0x245df01,0x2414982,0x0388bd0 } },
/* 71 */
{ { 0x35f1abb,0x17a3d18,0x0874cd4,0x2d5a14e,0x17edc0c,0x16a00d3,
0x072c1fb,0x1232725,0x33d52dc,0x03dc24d },
{ 0x0af30d6,0x259aeea,0x369c401,0x12bc4de,0x295bf5f,0x0d8711f,
0x26162a9,0x16c44e5,0x288e727,0x02f54b4 } },
/* 72 */
{ { 0x05fa877,0x1571ea7,0x3d48ab1,0x1c9f4e8,0x017dad6,0x0f46276,
0x343f9e7,0x1de990f,0x0e4c8aa,0x028343e },
{ 0x094f92d,0x3abf633,0x1b3a0bb,0x2f83137,0x0d818c8,0x20bae85,
0x0c65f8b,0x1a8008b,0x0c7946d,0x0295b1e } },
/* 73 */
{ { 0x1d09529,0x08e46c3,0x1fcf296,0x298f6b7,0x1803e0e,0x2d6fd20,
0x37351f5,0x0d9e8b1,0x1f8731a,0x0362fbf },
{ 0x00157f4,0x06750bf,0x2650ab9,0x35ffb23,0x2f51cae,0x0b522c2,
0x39cb400,0x191e337,0x0a5ce9f,0x021529a } },
/* 74 */
{ { 0x3506ea5,0x17d9ed8,0x0d66dc3,0x22693f8,0x19286c4,0x3a57353,
0x101d3bf,0x1aa54fc,0x20b9884,0x0172b3a },
{ 0x0eac44d,0x37d8327,0x1c3aa90,0x3d0d534,0x23db29a,0x3576eaf,
0x1d3de8a,0x3bea423,0x11235e4,0x039260b } },
/* 75 */
{ { 0x34cd55e,0x01288b0,0x1132231,0x2cc9a03,0x358695b,0x3e87650,
0x345afa1,0x01267ec,0x3f616b2,0x02011ad },
{ 0x0e7d098,0x0d6078e,0x0b70b53,0x237d1bc,0x0d7f61e,0x132de31,
0x1ea9ea4,0x2bd54c3,0x27b9082,0x03ac5f2 } },
/* 76 */
{ { 0x2a145b9,0x06d661d,0x31ec175,0x03f06f1,0x3a5cf6b,0x249c56e,
0x2035653,0x384c74f,0x0bafab5,0x0025ec0 },
{ 0x25f69e1,0x1b23a55,0x1199aa6,0x16ad6f9,0x077e8f7,0x293f661,
0x33ba11d,0x3327980,0x07bafdb,0x03e571d } },
/* 77 */
{ { 0x2bae45e,0x3c074ef,0x2955558,0x3c312f1,0x2a8ebe9,0x2f193f1,
0x3705b1d,0x360deba,0x01e566e,0x00d4498 },
{ 0x21161cd,0x1bc787e,0x2f87933,0x3553197,0x1328ab8,0x093c879,
0x17eee27,0x2adad1d,0x1236068,0x003be5c } },
/* 78 */
{ { 0x0ca4226,0x2633dd5,0x2c8e025,0x0e3e190,0x05eede1,0x1a385e4,
0x163f744,0x2f25522,0x1333b4f,0x03f05b6 },
{ 0x3c800ca,0x1becc79,0x2daabe9,0x0c499e2,0x1138063,0x3fcfa2d,
0x2244976,0x1e85cf5,0x2f1b95d,0x0053292 } },
/* 79 */
{ { 0x12f81d5,0x1dc6eaf,0x11967a4,0x1a407df,0x31a5f9d,0x2b67241,
0x18bef7c,0x08c7762,0x063f59c,0x01015ec },
{ 0x1c05c0a,0x360bfa2,0x1f85bff,0x1bc7703,0x3e4911c,0x0d685b6,
0x2fccaea,0x02c4cef,0x164f133,0x0070ed7 } },
/* 80 */
{ { 0x0ec21fe,0x052ffa0,0x3e825fe,0x1ab0956,0x3f6ce11,0x3d29759,
0x3c5a072,0x18ebe62,0x148db7e,0x03eb49c },
{ 0x1ab05b3,0x02dab0a,0x1ae690c,0x0f13894,0x137a9a8,0x0aab79f,
0x3dc875c,0x06a1029,0x1e39f0e,0x01dce1f } },
/* 81 */
{ { 0x16c0dd7,0x3b31269,0x2c741e9,0x3611821,0x2a5cffc,0x1416bb3,
0x3a1408f,0x311fa3d,0x1c0bef0,0x02cdee1 },
{ 0x00e6a8f,0x1adb933,0x0f23359,0x2fdace2,0x2fd6d4b,0x0e73bd3,
0x2453fac,0x0a356ae,0x2c8f9f6,0x02704d6 } },
/* 82 */
{ { 0x0e35743,0x28c80a1,0x0def32a,0x2c6168f,0x1320d6a,0x37c6606,
0x21b1761,0x2147ee0,0x21fc433,0x015c84d },
{ 0x1fc9168,0x36cda9c,0x003c1f0,0x1cd7971,0x15f98ba,0x1ef363d,
0x0ca87e3,0x046f7d9,0x3c9e6bb,0x0372eb0 } },
/* 83 */
{ { 0x118cbe2,0x3665a11,0x304ef01,0x062727a,0x3d242fc,0x11ffbaf,
0x3663c7e,0x1a189c9,0x09e2d62,0x02e3072 },
{ 0x0e1d569,0x162f772,0x0cd051a,0x322df62,0x3563809,0x047cc7a,
0x027fd9f,0x08b509b,0x3da2f94,0x01748ee } },
/* 84 */
{ { 0x1c8f8be,0x31ca525,0x22bf0a1,0x200efcd,0x02961c4,0x3d8f52b,
0x018403d,0x3a40279,0x1cb91ec,0x030427e },
{ 0x0945705,0x0257416,0x05c0c2d,0x25b77ae,0x3b9083d,0x2901126,
0x292b8d7,0x07b8611,0x04f2eee,0x026f0cd } },
/* 85 */
{ { 0x2913074,0x2b8d590,0x02b10d5,0x09d2295,0x255491b,0x0c41cca,
0x1ca665b,0x133051a,0x1525f1a,0x00a5647 },
{ 0x04f983f,0x3d6daee,0x04e1e76,0x1067d7e,0x1be7eef,0x02ea862,
0x00d4968,0x0ccb048,0x11f18ef,0x018dd95 } },
/* 86 */
{ { 0x22976cc,0x17c5395,0x2c38bda,0x3983bc4,0x222bca3,0x332a614,
0x3a30646,0x261eaef,0x1c808e2,0x02f6de7 },
{ 0x306a772,0x32d7272,0x2dcefd2,0x2abf94d,0x038f475,0x30ad76e,
0x23e0227,0x3052b0a,0x001add3,0x023ba18 } },
/* 87 */
{ { 0x0ade873,0x25a6069,0x248ccbe,0x13713ee,0x17ee9aa,0x28152e9,
0x2e28995,0x2a92cb3,0x17a6f77,0x024b947 },
{ 0x190a34d,0x2ebea1c,0x1ed1948,0x16fdaf4,0x0d698f7,0x32bc451,
0x0ee6e30,0x2aaab40,0x06f0a56,0x01460be } },
/* 88 */
{ { 0x24cc99c,0x1884b1e,0x1ca1fba,0x1a0f9b6,0x2ff609b,0x2b26316,
0x3b27cb5,0x29bc976,0x35d4073,0x024772a },
{ 0x3575a70,0x1b30f57,0x07fa01b,0x0e5be36,0x20cb361,0x26605cd,
0x1d4e8c8,0x13cac59,0x2db9797,0x005e833 } },
/* 89 */
{ { 0x36c8d3a,0x1878a81,0x124b388,0x0e4843e,0x1701aad,0x0ea0d76,
0x10eae41,0x37d0653,0x36c7f4c,0x00ba338 },
{ 0x37a862b,0x1cf6ac0,0x08fa912,0x2dd8393,0x101ba9b,0x0eebcb7,
0x2453883,0x1a3cfe5,0x2cb34f6,0x03d3331 } },
/* 90 */
{ { 0x1f79687,0x3d4973c,0x281544e,0x2564bbe,0x17c5954,0x171e34a,
0x231741a,0x3cf2784,0x0889a0d,0x02b036d },
{ 0x301747f,0x3f1c477,0x1f1386b,0x163bc5f,0x1592b93,0x332daed,
0x080e4f5,0x1d28b96,0x26194c9,0x0256992 } },
/* 91 */
{ { 0x15a4c93,0x07bf6b0,0x114172c,0x1ce0961,0x140269b,0x1b2c2eb,
0x0dfb1c1,0x019ddaa,0x0ba2921,0x008c795 },
{ 0x2e6d2dc,0x37e45e2,0x2918a70,0x0fce444,0x34d6aa6,0x396dc88,
0x27726b5,0x0c787d8,0x032d8a7,0x02ac2f8 } },
/* 92 */
{ { 0x1131f2d,0x2b43a63,0x3101097,0x38cec13,0x0637f09,0x17a69d2,
0x086196d,0x299e46b,0x0802cf6,0x03c6f32 },
{ 0x0daacb4,0x1a4503a,0x100925c,0x15583d9,0x23c4e40,0x1de4de9,
0x1cc8fc4,0x2c9c564,0x0695aeb,0x02145a5 } },
/* 93 */
{ { 0x1dcf593,0x17050fc,0x3e3bde3,0x0a6c062,0x178202b,0x2f7674f,
0x0dadc29,0x15763a7,0x1d2daad,0x023d9f6 },
{ 0x081ea5f,0x045959d,0x190c841,0x3a78d31,0x0e7d2dd,0x1414fea,
0x1d43f40,0x22d77ff,0x2b9c072,0x03e115c } },
/* 94 */
{ { 0x3af71c9,0x29e9c65,0x25655e1,0x111e9cd,0x3a14494,0x3875418,
0x34ae070,0x0b06686,0x310616b,0x03b7b89 },
{ 0x1734121,0x00d3d44,0x29f0b2f,0x1552897,0x31cac6e,0x1030bb3,
0x0148f3a,0x35fd237,0x29b44eb,0x027f49f } },
/* 95 */
{ { 0x2e2cb16,0x1d962bd,0x19b63cc,0x0b3f964,0x3e3eb7d,0x1a35560,
0x0c58161,0x3ce1d6a,0x3b6958f,0x029030b },
{ 0x2dcc158,0x3b1583f,0x30568c9,0x31957c8,0x27ad804,0x28c1f84,
0x3967049,0x37b3f64,0x3b87dc6,0x0266f26 } },
/* 96 */
{ { 0x27dafc6,0x2548764,0x0d1984a,0x1a57027,0x252c1fb,0x24d9b77,
0x1581a0f,0x1f99276,0x10ba16d,0x026af88 },
{ 0x0915220,0x2be1292,0x16c6480,0x1a93760,0x2fa7317,0x1a07296,
0x1539871,0x112c31f,0x25787f3,0x01e2070 } },
/* 97 */
{ { 0x0bcf3ff,0x266d478,0x34f6933,0x31449fd,0x00d02cb,0x340765a,
0x3465a2d,0x225023e,0x319a30e,0x00579b8 },
{ 0x20e05f4,0x35b834f,0x0404646,0x3710d62,0x3fad7bd,0x13e1434,
0x21c7d1c,0x1cb3af9,0x2cf1911,0x003957e } },
/* 98 */
{ { 0x0787564,0x36601be,0x1ce67e9,0x084c7a1,0x21a3317,0x2067a35,
0x0158cab,0x195ddac,0x1766fe9,0x035cf42 },
{ 0x2b7206e,0x20d0947,0x3b42424,0x03f1862,0x0a51929,0x38c2948,
0x0bb8595,0x2942d77,0x3748f15,0x0249428 } },
/* 99 */
{ { 0x2577410,0x3c23e2f,0x28c6caf,0x00d41de,0x0fd408a,0x30298e9,
0x363289e,0x2302fc7,0x082c1cc,0x01dd050 },
{ 0x30991cd,0x103e9ba,0x029605a,0x19927f7,0x0c1ca08,0x0c93f50,
0x28a3c7b,0x082e4e9,0x34d12eb,0x0232c13 } },
/* 100 */
{ { 0x106171c,0x0b4155a,0x0c3fb1c,0x336c090,0x19073e9,0x2241a10,
0x0e6b4fd,0x0ed476e,0x1ef4712,0x039390a },
{ 0x0ec36f4,0x3754f0e,0x2a270b8,0x007fd2d,0x0f9d2dc,0x1e6a692,
0x066e078,0x1954974,0x2ff3c6e,0x00def28 } },
/* 101 */
{ { 0x3562470,0x0b8f1f7,0x0ac94cd,0x28b0259,0x244f272,0x031e4ef,
0x2d5df98,0x2c8a9f1,0x2dc3002,0x016644f },
{ 0x350592a,0x0e6a0d5,0x1e027a1,0x2039e0f,0x399e01d,0x2817593,
0x0c0375e,0x3889b3e,0x24ab013,0x010de1b } },
/* 102 */
{ { 0x256b5a6,0x0ac3b67,0x28f9ff3,0x29b67f1,0x30750d9,0x25e11a9,
0x15e8455,0x279ebb0,0x298b7e7,0x0218e32 },
{ 0x2fc24b2,0x2b82582,0x28f22f5,0x2bd36b3,0x305398e,0x3b2e9e3,
0x365dd0a,0x29bc0ed,0x36a7b3a,0x007b374 } },
/* 103 */
{ { 0x05ff2f3,0x2b3589b,0x29785d3,0x300a1ce,0x0a2d516,0x0844355,
0x14c9fad,0x3ccb6b6,0x385d459,0x0361743 },
{ 0x0b11da3,0x002e344,0x18c49f7,0x0c29e0c,0x1d2c22c,0x08237b3,
0x2988f49,0x0f18955,0x1c3b4ed,0x02813c6 } },
/* 104 */
{ { 0x17f93bd,0x249323b,0x11f6087,0x174e4bd,0x3cb64ac,0x086dc6b,
0x2e330a8,0x142c1f2,0x2ea5c09,0x024acbb },
{ 0x1b6e235,0x3132521,0x00f085a,0x2a4a4db,0x1ab2ca4,0x0142224,
0x3aa6b3e,0x09db203,0x2215834,0x007b9e0 } },
/* 105 */
{ { 0x23e79f7,0x28b8039,0x1906a60,0x2cbce67,0x1f590e7,0x181f027,
0x21054a6,0x3854240,0x2d857a6,0x03cfcb3 },
{ 0x10d9b55,0x1443cfc,0x2648200,0x2b36190,0x09d2fcf,0x22f439f,
0x231aa7e,0x3884395,0x0543da3,0x003d5a9 } },
/* 106 */
{ { 0x043e0df,0x06ffe84,0x3e6d5b2,0x3327001,0x26c74b6,0x12a145e,
0x256ec0d,0x3898c69,0x3411969,0x02f63c5 },
{ 0x2b7494a,0x2eee1af,0x38388a9,0x1bd17ce,0x21567d4,0x13969e6,
0x3a12a7a,0x3e8277d,0x03530cc,0x00b4687 } },
/* 107 */
{ { 0x06508da,0x38e04d4,0x15a7192,0x312875e,0x3336180,0x2a6512c,
0x1b59497,0x2e91b37,0x25eb91f,0x02841e9 },
{ 0x394d639,0x0747143,0x37d7e6d,0x1d62962,0x08b4af3,0x34df287,
0x3c5584b,0x26bc869,0x20af87a,0x0060f5d } },
/* 108 */
{ { 0x1de59a4,0x1a5c443,0x2f8729d,0x01c3a2f,0x0f1ad8d,0x3cbaf9e,
0x1b49634,0x35d508a,0x39dc269,0x0075105 },
{ 0x390d30e,0x37033e0,0x110cb32,0x14c37a0,0x20a3b27,0x2f00ce6,
0x2f1dc52,0x34988c6,0x0c29606,0x01dc7e7 } },
/* 109 */
{ { 0x1040739,0x24f9de1,0x2939999,0x2e6009a,0x244539d,0x17e3f09,
0x00f6f2f,0x1c63b3d,0x2310362,0x019109e },
{ 0x1428aa8,0x3cb61e1,0x09a84f4,0x0ffafed,0x07b7adc,0x08f406b,
0x1b2c6df,0x035b480,0x3496ae9,0x012766d } },
/* 110 */
{ { 0x35d1099,0x2362f10,0x1a08cc7,0x13a3a34,0x12adbcd,0x32da290,
0x02e2a02,0x151140b,0x01b3f60,0x0240df6 },
{ 0x34c7b61,0x2eb09c1,0x172e7cd,0x2ad5eff,0x2fe2031,0x25b54d4,
0x0cec965,0x18e7187,0x26a7cc0,0x00230f7 } },
/* 111 */
{ { 0x2d552ab,0x374083d,0x01f120f,0x2601736,0x156baff,0x04d44a4,
0x3b7c3e9,0x1acbc1b,0x0424579,0x031a425 },
{ 0x1231bd1,0x0eba710,0x020517b,0x21d7316,0x21eac6e,0x275a848,
0x0837abf,0x0eb0082,0x302cafe,0x00fe8f6 } },
/* 112 */
{ { 0x1058880,0x28f9941,0x03f2d75,0x3bd90e5,0x17da365,0x2ac9249,
0x07861cf,0x023fd05,0x1b0fdb8,0x031712f },
{ 0x272b56b,0x04f8d2c,0x043a735,0x25446e4,0x1c8327e,0x221125a,
0x0ce37df,0x2dad7f6,0x39446c2,0x00b55b6 } },
/* 113 */
{ { 0x346ac6b,0x05e0bff,0x2425246,0x0981e8b,0x1d19f79,0x2692378,
0x3ea3c40,0x2e90beb,0x19de503,0x003d5af },
{ 0x05cda49,0x353b44d,0x299d137,0x3f205bc,0x2821158,0x3ad0d00,
0x06a54aa,0x2d7c79f,0x39d1173,0x01000ee } },
/* 114 */
{ { 0x0803387,0x3a06268,0x14043b8,0x3d4e72f,0x1ece115,0x0a1dfc8,
0x17208dd,0x0be790a,0x122a07f,0x014dd95 },
{ 0x0a4182d,0x202886a,0x1f79a49,0x1e8c867,0x0a2bbd0,0x28668b5,
0x0d0a2e1,0x115259d,0x3586c5d,0x01e815b } },
/* 115 */
{ { 0x18a2a47,0x2c95627,0x2773646,0x1230f7c,0x15b5829,0x2fc354e,
0x2c000ea,0x099d547,0x2f17a1a,0x01df520 },
{ 0x3853948,0x06f6561,0x3feeb8a,0x2f5b3ef,0x3a6f817,0x01a0791,
0x2ec0578,0x2c392ad,0x12b2b38,0x0104540 } },
/* 116 */
{ { 0x1e28ced,0x0fc3d1b,0x2c473c7,0x1826c4f,0x21d5da7,0x39718e4,
0x38ce9e6,0x0251986,0x172fbea,0x0337c11 },
{ 0x053c3b0,0x0f162db,0x043c1cb,0x04111ee,0x297fe3c,0x32e5e03,
0x2b8ae12,0x0c427ec,0x1da9738,0x03b9c0f } },
/* 117 */
{ { 0x357e43a,0x054503f,0x11b8345,0x34ec6e0,0x2d44660,0x3d0ae61,
0x3b5dff8,0x33884ac,0x09da162,0x00a82b6 },
{ 0x3c277ba,0x129a51a,0x027664e,0x1530507,0x0c788c9,0x2afd89d,
0x1aa64cc,0x1196450,0x367ac2b,0x0358b42 } },
/* 118 */
{ { 0x0054ac4,0x1761ecb,0x378839c,0x167c9f7,0x2570058,0x0604a35,
0x37cbf3b,0x0909bb7,0x3f2991c,0x02ce688 },
{ 0x0b16ae5,0x212857c,0x351b952,0x2c684db,0x30c6a05,0x09c01e0,
0x23c137f,0x1331475,0x092c067,0x0013b40 } },
/* 119 */
{ { 0x2e90393,0x0617466,0x24e61f4,0x0a528f5,0x03047b4,0x2153f05,
0x0001a69,0x30e1eb8,0x3c10177,0x0282a47 },
{ 0x22c831e,0x28fc06b,0x3e16ff0,0x208adc9,0x0bb76ae,0x28c1d6d,
0x12c8a15,0x031063c,0x1889ed2,0x002133e } },
/* 120 */
{ { 0x0a6becf,0x14277bf,0x3328d98,0x201f7fe,0x12fceae,0x1de3a2e,
0x0a15c44,0x3ddf976,0x1b273ab,0x0355e55 },
{ 0x1b5d4f1,0x369e78c,0x3a1c210,0x12cf3e9,0x3aa52f0,0x309f082,
0x112089d,0x107c753,0x24202d1,0x023853a } },
/* 121 */
{ { 0x2897042,0x140d17c,0x2c4aeed,0x07d0d00,0x18d0533,0x22f7ec8,
0x19c194c,0x3456323,0x2372aa4,0x0165f86 },
{ 0x30bd68c,0x1fb06b3,0x0945032,0x372ac09,0x06d4be0,0x27f8fa1,
0x1c8d7ac,0x137a96e,0x236199b,0x0328fc0 } },
/* 122 */
{ { 0x170bd20,0x2842d58,0x1de7592,0x3c5b4fd,0x20ea897,0x12cab78,
0x363ff14,0x01f928c,0x17e309c,0x02f79ff },
{ 0x0f5432c,0x2edb4ae,0x044b516,0x32f810d,0x2210dc1,0x23e56d6,
0x301e6ff,0x34660f6,0x10e0a7d,0x02d88eb } },
/* 123 */
{ { 0x0c7b65b,0x2f59d58,0x2289a75,0x2408e92,0x1ab8c55,0x1ec99e5,
0x220fd0d,0x04defe0,0x24658ec,0x035aa8b },
{ 0x138bb85,0x2f002d4,0x295c10a,0x08760ce,0x28c31d1,0x1c0a8cb,
0x0ff00b1,0x144eac9,0x2e02dcc,0x0044598 } },
/* 124 */
{ { 0x3b42b87,0x050057b,0x0dff781,0x1c06db1,0x1bd9f5d,0x1f5f04a,
0x2cccd7a,0x143e19b,0x1cb94b7,0x036cfb8 },
{ 0x34837cf,0x3cf6c3c,0x0d4fb26,0x22ee55e,0x1e7eed1,0x315995f,
0x2cdf937,0x1a96574,0x0425220,0x0221a99 } },
/* 125 */
{ { 0x1b569ea,0x0d33ed9,0x19c13c2,0x107dc84,0x2200111,0x0569867,
0x2dc85da,0x05ef22e,0x0eb018a,0x029c33d },
{ 0x04a6a65,0x3e5eba3,0x378f224,0x09c04d0,0x036e5cf,0x3df8258,
0x3a609e4,0x1eddef8,0x2abd174,0x02a91dc } },
/* 126 */
{ { 0x2a60cc0,0x1d84c5e,0x115f676,0x1840da0,0x2c79163,0x2f06ed6,
0x198bb4b,0x3e5d37b,0x1dc30fa,0x018469b },
{ 0x15ee47a,0x1e32f30,0x16a530e,0x2093836,0x02e8962,0x3767b62,
0x335adf3,0x27220db,0x2f81642,0x0173ffe } },
/* 127 */
{ { 0x37a99cd,0x1533fe6,0x05a1c0d,0x27610f1,0x17bf3b9,0x0b1ce78,
0x0a908f6,0x265300e,0x3237dc1,0x01b969a },
{ 0x3a5db77,0x2d15382,0x0d63ef8,0x1feb3d8,0x0b7b880,0x19820de,
0x11c0c67,0x2af3396,0x38d242d,0x0120688 } },
/* 128 */
{ { 0x1d0b34a,0x05ef00d,0x00a7e34,0x1ae0c9f,0x1440b38,0x300d8b4,
0x37262da,0x3e50e3e,0x14ce0cd,0x00b1044 },
{ 0x195a0b1,0x173bc6b,0x03622ba,0x2a19f55,0x1c09b37,0x07921b2,
0x16cdd20,0x24a5c9b,0x2bf42ff,0x00811de } },
/* 129 */
{ { 0x0d65dbf,0x145cf06,0x1ad82f7,0x038ce7b,0x077bf94,0x33c4007,
0x22d26bd,0x25ad9c0,0x09ac773,0x02b1990 },
{ 0x2261cc3,0x2ecdbf1,0x3e908b0,0x3246439,0x0213f7b,0x1179b04,
0x01cebaa,0x0be1595,0x175cc12,0x033a39a } },
/* 130 */
{ { 0x00a67d2,0x086d06f,0x248a0f1,0x0291134,0x362d476,0x166d1cd,
0x044f1d6,0x2d2a038,0x365250b,0x0023f78 },
{ 0x08bf287,0x3b0f6a1,0x1d6eace,0x20b4cda,0x2c2a621,0x0912520,
0x02dfdc9,0x1b35cd6,0x3d2565d,0x00bdf8b } },
/* 131 */
{ { 0x3770fa7,0x2e4b6f0,0x03f9ae4,0x170de41,0x1095e8d,0x1dd845c,
0x334e9d1,0x00ab953,0x12e9077,0x03196fa },
{ 0x2fd0a40,0x228c0fd,0x384b275,0x38ef339,0x3e7d822,0x3e5d9ef,
0x24f5854,0x0ece9eb,0x247d119,0x012ffe3 } },
/* 132 */
{ { 0x0ff1480,0x07487c0,0x1b16cd4,0x1f41d53,0x22ab8fb,0x2f83cfa,
0x01d2efb,0x259f6b2,0x2e65772,0x00f9392 },
{ 0x05303e6,0x23cdb4f,0x23977e1,0x12e4898,0x03bd999,0x0c930f0,
0x170e261,0x180a27b,0x2fd58ec,0x014e22b } },
/* 133 */
{ { 0x25d7713,0x0c5fad7,0x09daad1,0x3b9d779,0x109b985,0x1d3ec98,
0x35bc4fc,0x2f838cb,0x0d14f75,0x0173e42 },
{ 0x2657b12,0x10d4423,0x19e6760,0x296e5bb,0x2bfd421,0x25c3330,
0x29f51f8,0x0338838,0x24060f0,0x029a62e } },
/* 134 */
{ { 0x3748fec,0x2c5a1bb,0x2cf973d,0x289fa74,0x3e6e755,0x38997bf,
0x0b6544c,0x2b6358c,0x38a7aeb,0x02c50bb },
{ 0x3d5770a,0x06be7c5,0x012fad3,0x19cb2cd,0x266af3b,0x3ccd677,
0x160d1bd,0x141d5af,0x2965851,0x034625a } },
/* 135 */
{ { 0x3c41c08,0x255eacc,0x22e1ec5,0x2b151a3,0x087de94,0x311cbdb,
0x016b73a,0x368e462,0x20b7981,0x0099ec3 },
{ 0x262b988,0x1539763,0x21e76e5,0x15445b4,0x1d8ddc7,0x34a9be6,
0x10faf03,0x24e4d18,0x07aa111,0x02d538a } },
/* 136 */
{ { 0x38a876b,0x048ad45,0x04b40a0,0x3fc2144,0x251ff96,0x13ca7dd,
0x0b31ab1,0x3539814,0x28b5f87,0x0212aec },
{ 0x270790a,0x350e7e0,0x346bd5e,0x276178f,0x22d6cb5,0x3078884,
0x355c1b6,0x15901d7,0x3671765,0x03950db } },
/* 137 */
{ { 0x286e8d5,0x2409788,0x13be53f,0x2d21911,0x0353c95,0x10238e8,
0x32f5bde,0x3a67b60,0x28b5b9c,0x001013d },
{ 0x381e8e5,0x0cef7a9,0x2f5bcad,0x06058f0,0x33cdf50,0x04672a8,
0x1769600,0x31c055d,0x3df0ac1,0x00e9098 } },
/* 138 */
{ { 0x2eb596d,0x197b326,0x12b4c29,0x39c08f2,0x101ea03,0x3804e58,
0x04b4b62,0x28d9d1c,0x13f905e,0x0032a3f },
{ 0x11b2b61,0x08e9095,0x0d06925,0x270e43f,0x21eb7a8,0x0e4a98f,
0x31d2be0,0x030cf9f,0x2644ddb,0x025b728 } },
/* 139 */
{ { 0x07510af,0x2ed0e8e,0x2a01203,0x2a2a68d,0x0846fea,0x3e540de,
0x3a57702,0x1677348,0x2123aad,0x010d8f8 },
{ 0x0246a47,0x0e871d0,0x124dca4,0x34b9577,0x2b362b8,0x363ebe5,
0x3086045,0x26313e6,0x15cd8bb,0x0210384 } },
/* 140 */
{ { 0x023e8a7,0x0817884,0x3a0bf12,0x3376371,0x3c808a8,0x18e9777,
0x12a2721,0x35b538a,0x2bd30de,0x017835a },
{ 0x0fc0f64,0x1c8709f,0x2d8807a,0x0743957,0x242eec0,0x347e76c,
0x27bef91,0x289689a,0x0f42945,0x01f7a92 } },
/* 141 */
{ { 0x1060a81,0x3dbc739,0x1615abd,0x1cbe3e5,0x3e79f9c,0x1ab09a2,
0x136c540,0x05b473f,0x2beebfd,0x02af0a8 },
{ 0x3e2eac7,0x19be474,0x04668ac,0x18f4b74,0x36f10ba,0x0a0b4c6,
0x10e3770,0x3bf059e,0x3946c7e,0x013a8d4 } },
/* 142 */
{ { 0x266309d,0x28be354,0x1a3eed8,0x3020651,0x10a51c6,0x1e31770,
0x0af45a5,0x3ff0f3b,0x2891c94,0x00e9db9 },
{ 0x17b0d0f,0x33a291f,0x0a5f9aa,0x25a3d61,0x2963ace,0x39a5fef,
0x230c724,0x1919146,0x10a465e,0x02084a8 } },
/* 143 */
{ { 0x3ab8caa,0x31870f3,0x2390ef7,0x2103850,0x218eb8e,0x3a5ccf2,
0x1dff677,0x2c59334,0x371599c,0x02a9f2a },
{ 0x0837bd1,0x3249cef,0x35d702f,0x3430dab,0x1c06407,0x108f692,
0x221292f,0x05f0c5d,0x073fe06,0x01038e0 } },
/* 144 */
{ { 0x3bf9b7c,0x2020929,0x30d0f4f,0x080fef8,0x3365d23,0x1f3e738,
0x3e53209,0x1549afe,0x300b305,0x038d811 },
{ 0x0c6c2c7,0x2e6445b,0x3ee64dc,0x022e932,0x0726837,0x0deb67b,
0x1ed4346,0x3857f73,0x277a3de,0x01950b5 } },
/* 145 */
{ { 0x36c377a,0x0adb41e,0x08be3f3,0x11e40d1,0x36cb038,0x036a2bd,
0x3dd3a82,0x1bc875b,0x2ee09bb,0x02994d2 },
{ 0x035facf,0x05e0344,0x07e630a,0x0ce772d,0x335e55a,0x111fce4,
0x250fe1c,0x3bc89ba,0x32fdc9a,0x03cf2d9 } },
/* 146 */
{ { 0x355fd83,0x1c67f8e,0x1d10eb3,0x1b21d77,0x0e0d7a4,0x173a9e1,
0x2c9fa90,0x1c39cce,0x22eaae8,0x01f2bea },
{ 0x153b338,0x0534107,0x26c69b8,0x283be1f,0x3e0acc0,0x059cac3,
0x13d1081,0x148bbee,0x3c1b9bd,0x002aac4 } },
/* 147 */
{ { 0x2681297,0x3389e34,0x146addc,0x2c6d425,0x2cb350e,0x1986abc,
0x0431737,0x04ba4b7,0x2028470,0x012e469 },
{ 0x2f8ddcf,0x3c4255c,0x1af4dcf,0x07a6a44,0x208ebf6,0x0dc90c3,
0x34360ac,0x072ad23,0x0537232,0x01254d3 } },
/* 148 */
{ { 0x07b7e9d,0x3df5c7c,0x116f83d,0x28c4f35,0x3a478ef,0x3011fb8,
0x2f264b6,0x317b9e3,0x04fd65a,0x032bd1b },
{ 0x2aa8266,0x3431de4,0x04bba04,0x19a44da,0x0edf454,0x392c5ac,
0x265168a,0x1dc3d5b,0x25704c6,0x00533a7 } },
/* 149 */
{ { 0x25e8f91,0x1178fa5,0x2492994,0x2eb2c3c,0x0d3aca1,0x0322828,
0x1cc70f9,0x269c74c,0x0a53e4c,0x006edc2 },
{ 0x18bdd7a,0x2a79a55,0x26b1d5c,0x0200628,0x0734a05,0x3273c7b,
0x13aa714,0x0040ac2,0x2f2da30,0x03e7449 } },
/* 150 */
{ { 0x3f9563e,0x2f29eab,0x14a0749,0x3fad264,0x1dd077a,0x3d7c59c,
0x3a0311b,0x331a789,0x0b9729e,0x0201ebf },
{ 0x1b08b77,0x2a4cdf2,0x3e387f8,0x21510f1,0x286c3a7,0x1dbf62e,
0x3afa594,0x3363217,0x0d16568,0x01d46b7 } },
/* 151 */
{ { 0x0715c0d,0x28e2d04,0x17f78ae,0x1c63dda,0x1d113ea,0x0fefc1b,
0x1eab149,0x1d0fd99,0x0682537,0x00a7b11 },
{ 0x10bebbc,0x11c672d,0x14223d9,0x2ff9141,0x1399ee5,0x34b7b6c,
0x0d5b3a8,0x01df643,0x0e392a4,0x03fe4dc } },
/* 152 */
{ { 0x2b75b65,0x0b5a6f1,0x11c559a,0x3549999,0x24188f8,0x37a75f4,
0x29f33e3,0x34068a2,0x38ba2a9,0x025dd91 },
{ 0x29af2c7,0x0988b64,0x0923885,0x1b539a4,0x1334f5d,0x226947a,
0x2cc7e5a,0x20beb39,0x13fac2f,0x01d298c } },
/* 153 */
{ { 0x35f079c,0x137f76d,0x2fbbb2f,0x254638d,0x185b07c,0x1f34db7,
0x2cfcf0e,0x218f46d,0x2150ff4,0x02add6f },
{ 0x33fc9b7,0x0d9f005,0x0fd081b,0x0834965,0x2b90a74,0x102448d,
0x3dbf03c,0x167d857,0x02e0b44,0x013afab } },
/* 154 */
{ { 0x09f2c53,0x317f9d7,0x1411eb6,0x0463aba,0x0d25220,0x256b176,
0x087633f,0x2bff322,0x07b2c1b,0x037e662 },
{ 0x10aaecb,0x23bb4a1,0x2272bb7,0x06c075a,0x09d4918,0x0736f2b,
0x0dd511b,0x101625e,0x0a7779f,0x009ec10 } },
/* 155 */
{ { 0x33b2eb2,0x0176dfd,0x2118904,0x022386c,0x2e0df85,0x2588c9f,
0x1b71525,0x28fd540,0x137e4cf,0x02ce4f7 },
{ 0x3d75165,0x0c39ecf,0x3554a12,0x30af34c,0x2d66344,0x3ded408,
0x36f1be0,0x0d065b0,0x012d046,0x0025623 } },
/* 156 */
{ { 0x2601c3b,0x1824fc0,0x335fe08,0x3e33d70,0x0fb0252,0x252bfca,
0x1cf2808,0x1922e55,0x1a9db9f,0x020721e },
{ 0x2f56c51,0x39a1f31,0x218c040,0x1a4fc5d,0x3fed471,0x0164d4e,
0x388a419,0x06f1113,0x0f55fc1,0x03e8352 } },
/* 157 */
{ { 0x1608e4d,0x3872778,0x022cbc6,0x044d60a,0x3010dda,0x15fb0b5,
0x37ddc11,0x19f5bda,0x156b6a3,0x023a838 },
{ 0x383b3b4,0x1380bc8,0x353ca35,0x250fc07,0x169966b,0x3780f29,
0x36632b2,0x2d6b13f,0x124fa00,0x00fd6ae } },
/* 158 */
{ { 0x1739efb,0x2ec3656,0x2c0d337,0x3d39faf,0x1c751b0,0x04699f4,
0x252dd64,0x095b8b6,0x0872b74,0x022f1da },
{ 0x2d3d253,0x38edca0,0x379fa5b,0x287d635,0x3a9f679,0x059d9ee,
0x0ac168e,0x3cd3e87,0x19060fc,0x02ce1bc } },
/* 159 */
{ { 0x3edcfc2,0x0f04d4b,0x2f0d31f,0x1898be2,0x25396bf,0x15ca230,
0x02b4eae,0x2713668,0x0f71b06,0x0132d18 },
{ 0x38095ea,0x1ed34d6,0x3603ae6,0x165bf01,0x192bbf8,0x1852859,
0x075f66b,0x1488f85,0x10895ef,0x014b035 } },
/* 160 */
{ { 0x1339848,0x3084385,0x0c8d231,0x3a1c1de,0x0e87a28,0x255b85c,
0x1de6616,0x2702e74,0x1382bb0,0x012b0f2 },
{ 0x198987d,0x381545a,0x34d619b,0x312b827,0x18b2376,0x28fe4cf,
0x20b7651,0x017d077,0x0c7e397,0x00e0365 } },
/* 161 */
{ { 0x1542e75,0x0d56aa0,0x39b701a,0x287b806,0x396c724,0x0935c21,
0x3a29776,0x0debdac,0x171de26,0x00b38f8 },
{ 0x1d5bc1a,0x3fad27d,0x22b5cfe,0x1f89ddf,0x0a65560,0x144dd5b,
0x2aac2f9,0x139353f,0x0520b62,0x00b9b36 } },
/* 162 */
{ { 0x031c31d,0x16552e3,0x1a0c368,0x0016fc8,0x168533d,0x171e7b2,
0x17626e7,0x275502f,0x14742c6,0x03285dd },
{ 0x2d2dbb2,0x3b6bffd,0x1d18cc6,0x2f45d2a,0x0fd0d8c,0x2915e3a,
0x1e8793a,0x0b39a1d,0x3139cab,0x02a5da9 } },
/* 163 */
{ { 0x3fb353d,0x147c6e4,0x3a720a6,0x22d5ff3,0x1d75cab,0x06c54a0,
0x08cfa73,0x12666aa,0x3170a1f,0x021c829 },
{ 0x13e1b90,0x3a34dda,0x1fc38c3,0x02c5bdb,0x2d345dc,0x14aa1d0,
0x28d00ab,0x224f23a,0x329c769,0x025c67b } },
/* 164 */
{ { 0x0e35909,0x3bb6356,0x0116820,0x370cf77,0x29366d8,0x3881409,
0x3999d06,0x013075f,0x176e157,0x02941ca },
{ 0x0e70b2e,0x28dfab1,0x2a8a002,0x15da242,0x084dcf6,0x116ca97,
0x31bf186,0x1dc9735,0x09df7b7,0x0264e27 } },
/* 165 */
{ { 0x2da7a4b,0x3023c9e,0x1366238,0x00ff4e2,0x03abe9d,0x19bd44b,
0x272e897,0x20b91ad,0x2aa202c,0x02a2201 },
{ 0x380184e,0x08112b4,0x0b85660,0x31049aa,0x3a8cb78,0x36113c5,
0x1670c0a,0x373f9e7,0x3fb4738,0x00010ef } },
/* 166 */
{ { 0x2d5192e,0x26d770d,0x32af8d5,0x34d1642,0x1acf885,0x05805e0,
0x166d0a1,0x1219a0d,0x301ba6c,0x014bcfb },
{ 0x2dcb64d,0x19cca83,0x379f398,0x08e01a0,0x10a482c,0x0103cc2,
0x0be5fa7,0x1f9d45b,0x1899ef2,0x00ca5af } },
/* 167 */
{ { 0x14d81d7,0x2aea251,0x1b3c476,0x3bd47ae,0x29eade7,0x0715e61,
0x1a21cd8,0x1c7a586,0x2bfaee5,0x00ee43f },
{ 0x096f7cb,0x0c08f95,0x1bc4939,0x361fed4,0x255be41,0x26fad73,
0x31dd489,0x02c600f,0x29d9f81,0x01ba201 } },
/* 168 */
{ { 0x03ea1db,0x1eac46d,0x1292ce3,0x2a54967,0x20a7ff1,0x3e13c61,
0x1b02218,0x2b44e14,0x3eadefa,0x029c88a },
{ 0x30a9144,0x31e3b0a,0x19c5a2a,0x147cbe9,0x05a0240,0x051f38e,
0x11eca56,0x31a4247,0x123bc2a,0x02fa535 } },
/* 169 */
{ { 0x3226ce7,0x1251782,0x0b7072f,0x11e59fa,0x2b8afd7,0x169b18f,
0x2a46f18,0x31d9bb7,0x2fe9be8,0x01de0b7 },
{ 0x1b38626,0x34aa90f,0x3ad1760,0x21ddbd9,0x3460ae7,0x1126736,
0x1b86fc5,0x0b92cd0,0x167a289,0x000e0e1 } },
/* 170 */
{ { 0x1ec1a0f,0x36bbf5e,0x1c972d8,0x3f73ace,0x13bbcd6,0x23d86a5,
0x175ffc5,0x2d083d5,0x2c4adf7,0x036f661 },
{ 0x1f39eb7,0x2a20505,0x176c81a,0x3d6e636,0x16ee2fc,0x3cbdc5f,
0x25475dc,0x2ef4151,0x3c46860,0x0238934 } },
/* 171 */
{ { 0x2587390,0x3639526,0x0588749,0x13c32fb,0x212bb19,0x09660f1,
0x207da4b,0x2bf211b,0x1c4407b,0x01506a6 },
{ 0x24c8842,0x105a498,0x05ffdb2,0x0ab61b0,0x26044c1,0x3dff3d8,
0x1d14b44,0x0d74716,0x049f57d,0x030024b } },
/* 172 */
{ { 0x32e61ef,0x31d70f7,0x35cad3c,0x320b86c,0x07e8841,0x027ca7d,
0x2d30d19,0x2513718,0x2347286,0x01d7901 },
{ 0x3c237d0,0x107f16e,0x01c9e7d,0x3c3b13c,0x0c9537b,0x20af54d,
0x051a162,0x2161a47,0x258c784,0x016df2d } },
/* 173 */
{ { 0x228ead1,0x29c2122,0x07f6964,0x023f4ed,0x1802dc5,0x19f96ce,
0x24bfd17,0x25e866b,0x2ba8df0,0x01eb84f },
{ 0x2dd384e,0x05bbe3a,0x3f06fd2,0x366dacb,0x30361a2,0x2f36d7c,
0x0b98784,0x38ff481,0x074e2a8,0x01e1f60 } },
/* 174 */
{ { 0x17fbb1c,0x0975add,0x1debc5e,0x2cb2880,0x3e47bdd,0x3488cff,
0x15e9a36,0x2121129,0x0199ef2,0x017088a },
{ 0x0315250,0x352a162,0x17c1773,0x0ae09c2,0x321b21a,0x3bd74cf,
0x3c4ea1d,0x3cac2ad,0x3abbaf0,0x039174d } },
/* 175 */
{ { 0x0511c8a,0x3c78d0a,0x2cd3d2d,0x322f729,0x3ebb229,0x09f0e69,
0x0a71a76,0x2e74d5e,0x12284df,0x03b5ef0 },
{ 0x3dea561,0x0a9b7e4,0x0ed1cf2,0x237523c,0x05443f1,0x2eb48fa,
0x3861405,0x1b49f62,0x0c945ca,0x02ab25f } },
/* 176 */
{ { 0x16bd00a,0x13a9d28,0x3cc1eb5,0x2b7d702,0x2d839e9,0x3e6ff01,
0x2bb7f11,0x3713824,0x3b31163,0x00c63e5 },
{ 0x30d7138,0x0316fb0,0x0220ecc,0x08eaf0c,0x244e8df,0x0088d81,
0x37972fb,0x3fd34ae,0x2a19a84,0x03e907e } },
/* 177 */
{ { 0x2642269,0x0b65d29,0x03bd440,0x33a6ede,0x3c81814,0x2507982,
0x0d38e47,0x3a788e6,0x32c1d26,0x00e2eda },
{ 0x2577f87,0x392895a,0x3e1cc64,0x14f7047,0x08b52d2,0x08a01ca,
0x336abf6,0x00697fc,0x105ce76,0x0253742 } },
/* 178 */
{ { 0x293f92a,0x33df737,0x3315156,0x32e26d7,0x0a01333,0x26579d4,
0x004df9c,0x0aba409,0x067d25c,0x02481de },
{ 0x3f39d44,0x1c78042,0x13d7e24,0x0825aed,0x35f2c90,0x3270f63,
0x04b7b35,0x3ad4531,0x28bd29b,0x0207a10 } },
/* 179 */
{ { 0x077199f,0x270aeb1,0x0dd96dd,0x3b9ad7b,0x28cb8ee,0x3903f43,
0x37db3fe,0x292c62b,0x362dbbf,0x006e52a },
{ 0x247f143,0x0362cf3,0x216344f,0x3f18fd1,0x351e623,0x31664e0,
0x0f270fc,0x243bbc6,0x2280555,0x001a8e3 } },
/* 180 */
{ { 0x3355b49,0x2c04e6c,0x399b2e5,0x182d3af,0x020e265,0x09a7cf7,
0x0ffa6bd,0x353e302,0x02083d9,0x029ecdb },
{ 0x33e8830,0x0570e86,0x1c0b64d,0x386a27e,0x0d5fcea,0x0b45a4c,
0x2ee4a2e,0x0a8833f,0x2b4a282,0x02f9531 } },
/* 181 */
{ { 0x191167c,0x36cf7e3,0x225ed6c,0x1e79e99,0x0517c3f,0x11ab1fd,
0x05648f3,0x08aedc4,0x1abeae0,0x02fcc29 },
{ 0x3828a68,0x1e16fa4,0x30368e7,0x0c9fcfb,0x25161c3,0x24851ac,
0x1b5feb5,0x344eb84,0x0de2732,0x0347208 } },
/* 182 */
{ { 0x038b363,0x384d1e4,0x2519043,0x151ac17,0x158c11f,0x009b2b4,
0x257abe6,0x2368d3f,0x3ed68a1,0x02df45e },
{ 0x29c2559,0x2962478,0x3d8444c,0x1d96fff,0x04f7a03,0x1391a52,
0x0de4af7,0x3319126,0x15e6412,0x00e65ff } },
/* 183 */
{ { 0x3d61507,0x1d1a0a2,0x0d2af20,0x354d299,0x329e132,0x2a28578,
0x2ddfb08,0x04fa3ff,0x1293c6c,0x003bae2 },
{ 0x3e259f8,0x1a68fa9,0x3e67e9b,0x39b44f9,0x1ce1db7,0x347e9a1,
0x3318f6a,0x2dbbc9d,0x2f8c922,0x008a245 } },
/* 184 */
{ { 0x212ab5b,0x2b896c2,0x0136959,0x07e55ef,0x0cc1117,0x05b8ac3,
0x18429ed,0x025fa01,0x11d6e93,0x03b016b },
{ 0x03f3708,0x2e96fab,0x1d77157,0x0d4c2d6,0x131baf9,0x0608d39,
0x3552371,0x06cdd1e,0x1567ff1,0x01f4c50 } },
/* 185 */
{ { 0x2dfefab,0x270173d,0x37077bd,0x1a372cd,0x1be2f22,0x28e2ee5,
0x3ead973,0x35e8f94,0x2fc9bc1,0x03a7399 },
{ 0x36a02a1,0x2855d9b,0x00ed75a,0x37d8398,0x138c087,0x233706e,
0x147f346,0x01947e2,0x3017228,0x0365942 } },
/* 186 */
{ { 0x2057e60,0x2d31296,0x25e4504,0x2fa37bc,0x1cbccc3,0x1f0732f,
0x3532081,0x2de8a98,0x19a804e,0x005359a },
{ 0x31f411a,0x2a10576,0x369c2c8,0x02fe035,0x109fbaf,0x30bddeb,
0x1eef901,0x1662ad3,0x0410d43,0x01bd31a } },
/* 187 */
{ { 0x2c24a96,0x1b7d3a5,0x19a3872,0x217f2f6,0x2534dbc,0x2cab8c2,
0x066ef28,0x26aecf1,0x0fd6118,0x01310d4 },
{ 0x055b8da,0x1fdc5be,0x38a1296,0x25118f0,0x341a423,0x2ba4cd0,
0x3e1413e,0x062d70d,0x2425a31,0x029c9b4 } },
/* 188 */
{ { 0x08c1086,0x1acfba5,0x22e1dae,0x0f72f4e,0x3f1de50,0x0f408bc,
0x35ed3f0,0x3ce48fc,0x282cc6c,0x004d8e7 },
{ 0x1afaa86,0x24e3ef3,0x22589ac,0x3ec9952,0x1f45bc5,0x14144ca,
0x23b26e4,0x0d68c65,0x1e1c1a3,0x032a4d9 } },
/* 189 */
{ { 0x03b2d20,0x16b1d53,0x241b361,0x05e4138,0x1742a54,0x32741c7,
0x0521c4c,0x1ca96c2,0x034970b,0x02738a7 },
{ 0x13e0ad6,0x207dcdb,0x034c8cc,0x27bcbe1,0x18060da,0x33a18b6,
0x2d1d1a6,0x2be60d7,0x3d7ab42,0x012312a } },
/* 190 */
{ { 0x0c7485a,0x06c3310,0x0dbfd22,0x2ef949d,0x0ead455,0x098f4ba,
0x3c76989,0x0cf2d24,0x032f67b,0x01e005f },
{ 0x30cb5ee,0x0d5da64,0x0ed2b9d,0x2503102,0x1c0d14e,0x1cbc693,
0x37bf552,0x07013e2,0x054de5c,0x014f341 } },
/* 191 */
{ { 0x128ccac,0x1617e97,0x346ebcd,0x158016d,0x25f823e,0x34048ea,
0x39f0a1c,0x3ea3df1,0x1c1d3d7,0x03ba919 },
{ 0x151803b,0x01967c1,0x2f70781,0x27df39a,0x06c0b59,0x24a239c,
0x15a7702,0x2464d06,0x2a47ae6,0x006db90 } },
/* 192 */
{ { 0x27d04c3,0x024df3d,0x38112e8,0x38a27ba,0x01e312b,0x0965358,
0x35d8879,0x2f4f55a,0x214187f,0x0008936 },
{ 0x05fe36f,0x2ee18c3,0x1f5f87a,0x1813bd4,0x0580f3c,0x0ed0a7b,
0x0fb1bfb,0x3fcce59,0x2f042bf,0x01820e3 } },
/* 193 */
{ { 0x20bbe99,0x32cbc9f,0x39ee432,0x3cc12a8,0x37bda44,0x3ea4e40,
0x097c7a9,0x0590d7d,0x2022d33,0x018dbac },
{ 0x3ae00aa,0x3439864,0x2d2ffcf,0x3f8c6b9,0x0875a00,0x3e4e407,
0x3658a29,0x22eb3d0,0x2b63921,0x022113b } },
/* 194 */
{ { 0x33bae58,0x05c749a,0x1f3e114,0x1c45f8e,0x27db3df,0x06a3ab6,
0x37bc7f8,0x1e27b34,0x3dc51fb,0x009eea0 },
{ 0x3f54de5,0x3d0e7fe,0x1a71a7d,0x02ed7f8,0x0727703,0x2ca5e92,
0x2e8e35d,0x292ad0b,0x13487f3,0x02b6d8b } },
/* 195 */
{ { 0x175df2a,0x05a28a8,0x32e99b1,0x13d8630,0x2082aa0,0x11ac245,
0x24f2e71,0x322cb27,0x17675e7,0x02e643f },
{ 0x1f37313,0x2765ad3,0x0789082,0x1e742d0,0x11c2055,0x2021dc4,
0x09ae4a7,0x346359b,0x2f94d10,0x0205c1f } },
/* 196 */
{ { 0x3d6ff96,0x1f2ac80,0x336097d,0x3f03610,0x35b851b,0x010b6d2,
0x0823c4d,0x2a9709a,0x2ead5a8,0x00de4b6 },
{ 0x01afa0b,0x0621965,0x3671528,0x1050b60,0x3f3e9e7,0x2f93829,
0x0825275,0x006e85f,0x35e94b0,0x016af58 } },
/* 197 */
{ { 0x2c4927c,0x3ea1382,0x0f23727,0x0d69f23,0x3e38860,0x2b72837,
0x3cd5ea4,0x2d84292,0x321846a,0x016656f },
{ 0x29dfa33,0x3e182e0,0x018be90,0x2ba563f,0x2caafe2,0x218c0d9,
0x3baf447,0x1047a6c,0x0a2d483,0x01130cb } },
/* 198 */
{ { 0x00ed80c,0x2a5fc79,0x0a82a74,0x2c4c74b,0x15f938c,0x30b5ab6,
0x32124b7,0x295314f,0x2fb8082,0x007c858 },
{ 0x20b173e,0x19f315c,0x12f97e4,0x198217c,0x040e8a6,0x3275977,
0x2bc20e4,0x01f2633,0x02bc3e9,0x023c750 } },
/* 199 */
{ { 0x3c4058a,0x24be73e,0x16704f5,0x2d8a4bd,0x3b15e14,0x3076315,
0x1cfe37b,0x36fe715,0x343926e,0x02c6603 },
{ 0x2c76b09,0x0cf824c,0x3f7898c,0x274cec1,0x11df527,0x18eed18,
0x08ead48,0x23915bc,0x19b3744,0x00a0a2b } },
/* 200 */
{ { 0x0cf4ac5,0x1c8b131,0x0afb696,0x0ff7799,0x2f5ac1a,0x022420c,
0x11baa2e,0x2ce4015,0x1275a14,0x0125cfc },
{ 0x22eac5d,0x360cd4c,0x3568e59,0x3d42f66,0x35e07ee,0x09620e4,
0x36720fa,0x22b1eac,0x2d0db16,0x01b6b23 } },
/* 201 */
{ { 0x1a835ef,0x1516bbb,0x2d51f7b,0x3487443,0x14aa113,0x0dd06c2,
0x1a65e01,0x379300d,0x35920b9,0x012c8fb },
{ 0x04c7341,0x2eda00f,0x3c37e82,0x1b4fd62,0x0d45770,0x1478fba,
0x127863a,0x26939cd,0x134ddf4,0x01375c5 } },
/* 202 */
{ { 0x1476cd9,0x1119ca5,0x325bbf9,0x0bf8c69,0x0648d07,0x312d9f8,
0x01c8b8f,0x136ec51,0x0002f4a,0x03f4c5c },
{ 0x195d0e1,0x10ffd22,0x29aa1cb,0x3443bdc,0x276e695,0x05e6260,
0x15f9764,0x3cd9783,0x18c9569,0x0053eb1 } },
/* 203 */
{ { 0x312ae18,0x280197c,0x3fc9ad9,0x303f324,0x251958d,0x29f4a11,
0x2142408,0x3694366,0x25136ab,0x03b5f1d },
{ 0x1d4abbc,0x1c3c689,0x13ea462,0x3cfc684,0x39b5dd8,0x2d4654b,
0x09b0755,0x27d4f18,0x3f74d2e,0x03fbf2d } },
/* 204 */
{ { 0x2119185,0x2525eae,0x1ba4bd0,0x0c2ab11,0x1d54e8c,0x294845e,
0x2479dea,0x3602d24,0x17e87e0,0x0060069 },
{ 0x0afffb0,0x34fe37f,0x1240073,0x02eb895,0x06cf33c,0x2d7f7ef,
0x1d763b5,0x04191e0,0x11e1ead,0x027e3f0 } },
/* 205 */
{ { 0x269544c,0x0e85c57,0x3813158,0x19fc12d,0x20eaf85,0x1e2930c,
0x22a8fd2,0x1a6a478,0x09d3d3a,0x02a74e0 },
{ 0x1a2da3b,0x30b0b16,0x0847936,0x3d86257,0x138ccbc,0x0f5421a,
0x25244e6,0x23bdd79,0x1aee117,0x00c01ae } },
/* 206 */
{ { 0x1eead28,0x07cac32,0x1fbc0bb,0x17627d3,0x17eef63,0x0b3a24e,
0x0757fdb,0x3dd841d,0x3d745f8,0x002ae17 },
{ 0x25b4549,0x29f24cf,0x2f21ecd,0x1725e48,0x04be2bb,0x10ee010,
0x1a1274b,0x10b0898,0x27511e9,0x02c48b5 } },
/* 207 */
{ { 0x2a5ae7a,0x181ef99,0x0be33be,0x3e9dab7,0x101e703,0x3adb971,
0x1043014,0x2ebb2be,0x1c1097d,0x027d667 },
{ 0x3f250ed,0x16dc603,0x20dc6d7,0x1d0d268,0x38eb915,0x02c89e8,
0x1605a41,0x12de109,0x0e08a29,0x01f554a } },
/* 208 */
{ { 0x0c26def,0x163d988,0x2d1ef0f,0x3a960ac,0x1025585,0x0738e20,
0x27d79b0,0x05cc3ef,0x201303f,0x00a333a },
{ 0x1644ba5,0x2af345e,0x30b8d1d,0x3a01bff,0x31fc643,0x1acf85e,
0x0a76fc6,0x04efe98,0x348a1d0,0x03062eb } },
/* 209 */
{ { 0x1c4216d,0x18e3217,0x02ac34e,0x19c8185,0x200c010,0x17d4192,
0x13a1719,0x165af51,0x09db7a9,0x0277be0 },
{ 0x3ab8d2c,0x2190b99,0x22b641e,0x0cd88de,0x3b42404,0x1310862,
0x106a6d6,0x23395f5,0x0b06880,0x000d5fe } },
/* 210 */
{ { 0x0d2cc88,0x36f9913,0x339d8e9,0x237c2e3,0x0cc61c2,0x34c2832,
0x309874c,0x2621d28,0x2dd1b48,0x0392806 },
{ 0x17cd8f9,0x07bab3d,0x0c482ed,0x0faf565,0x31b767d,0x2f4bde1,
0x295c717,0x330c29c,0x179ce10,0x0119b5f } },
/* 211 */
{ { 0x1ada2c7,0x0c624a7,0x227d47d,0x30e3e6a,0x14fa0a6,0x0829678,
0x24fd288,0x2b46a43,0x122451e,0x0319ca9 },
{ 0x186b655,0x01f3217,0x0af1306,0x0efe6b5,0x2f0235d,0x1c45ca9,
0x2086805,0x1d44e66,0x0faf2a6,0x0178f59 } },
/* 212 */
{ { 0x33b4416,0x10431e6,0x2d99aa6,0x217aac9,0x0cd8fcf,0x2d95a9d,
0x3ff74ad,0x10bf17a,0x295eb8e,0x01b229e },
{ 0x02a63bd,0x182e9ec,0x004710c,0x00e2e3c,0x06b2f23,0x04b642c,
0x2c37383,0x32a4631,0x022ad82,0x00d22b9 } },
/* 213 */
{ { 0x0cda2fb,0x1d198d7,0x26d27f4,0x286381c,0x022acca,0x24ac7c8,
0x2df7824,0x0b4ba16,0x1e0d9ef,0x03041d3 },
{ 0x29a65b3,0x0f3912b,0x151bfcf,0x2b0175c,0x0fd71e4,0x39aa5e2,
0x311f50c,0x13ff351,0x3dbc9e5,0x03eeb7e } },
/* 214 */
{ { 0x0a99363,0x0fc7348,0x2775171,0x23db3c8,0x2b91565,0x134d66c,
0x0175cd2,0x1bf365a,0x2b48371,0x02dfe5d },
{ 0x16dbf74,0x2389357,0x2f36575,0x3f5c70e,0x38d23ba,0x090f7f8,
0x3477600,0x3201523,0x32ecafc,0x03d3506 } },
/* 215 */
{ { 0x1abd48d,0x073ca3f,0x38a451f,0x0d8cb01,0x1ce81be,0x05c51ba,
0x0e29741,0x03c41ab,0x0eae016,0x0060209 },
{ 0x2e58358,0x1da62d9,0x2358038,0x14b39b2,0x1635687,0x39079b1,
0x380e345,0x1b49608,0x23983cf,0x019f97d } },
/* 216 */
{ { 0x34899ef,0x332e373,0x04c0f89,0x3c27aed,0x1949015,0x09663b2,
0x2f9276b,0x07f1951,0x09a04c1,0x027fbde },
{ 0x3d2a071,0x19fb3d4,0x1b096d3,0x1fe9146,0x3b10e1a,0x0478bbb,
0x2b3fb06,0x1388329,0x181a99c,0x02f2030 } },
/* 217 */
{ { 0x1eb82e6,0x14dbe39,0x3920972,0x31fd5b2,0x21a484f,0x02d7697,
0x0e21715,0x37c431e,0x2629f8c,0x01249c3 },
{ 0x26b50ad,0x26deefa,0x0ffc1a3,0x30688e2,0x39a0284,0x041c65e,
0x03eb178,0x0bdfd50,0x2f96137,0x034bb94 } },
/* 218 */
{ { 0x0e0362a,0x334a162,0x194dd37,0x29e3e97,0x2442fa8,0x10d2949,
0x3836e5a,0x2dccebf,0x0bee5ab,0x037ed1e },
{ 0x33eede6,0x3c739d9,0x2f04a91,0x350ad6c,0x3a5390a,0x14c368b,
0x26f7bf5,0x11ce979,0x0b408df,0x0366850 } },
/* 219 */
{ { 0x28ea498,0x0886d5b,0x2e090e0,0x0a4d58f,0x2623478,0x0d74ab7,
0x2b83913,0x12c6b81,0x18d623f,0x01d8301 },
{ 0x198aa79,0x26d6330,0x3a7f0b8,0x34bc1ea,0x2f74890,0x378955a,
0x204110f,0x0102538,0x02d8f19,0x01c5066 } },
/* 220 */
{ { 0x14b0f45,0x2838cd3,0x14e16f0,0x0e0e4aa,0x2d9280b,0x0f18757,
0x3324c6b,0x1391ceb,0x1ce89d5,0x00ebe74 },
{ 0x0930371,0x3de6048,0x3097fd8,0x1308705,0x3eda266,0x3108c26,
0x1545dcd,0x1f7583a,0x1c37395,0x02c7e05 } },
/* 221 */
{ { 0x1fec44a,0x2a9e3a2,0x0caf84f,0x11cf2a9,0x0c8c2ae,0x06da989,
0x1c807dc,0x3c149a4,0x1141543,0x02906bb },
{ 0x15ffe04,0x0d4e65f,0x2e20424,0x37d896d,0x18bacb2,0x1e05ddd,
0x1660be8,0x183be17,0x1dd86fb,0x035ba70 } },
/* 222 */
{ { 0x2853264,0x0ba5fb1,0x0a0b3aa,0x2df88c1,0x2771533,0x23aba6f,
0x112bb7b,0x3e3086e,0x210ae9b,0x027271b },
{ 0x030b74c,0x0269678,0x1e90a23,0x135a98c,0x24ed749,0x126de7c,
0x344b23a,0x186da27,0x19640fa,0x0159af5 } },
/* 223 */
{ { 0x18061f3,0x3004630,0x3c70066,0x34df20f,0x1190b25,0x1c9cc91,
0x1fc8e02,0x0d17bc1,0x390f525,0x033cb1c },
{ 0x0eb30cf,0x2f3ad04,0x303aa09,0x2e835dd,0x1cfd2eb,0x143fc95,
0x02c43a1,0x025e7a1,0x3558aa2,0x000bd45 } },
/* 224 */
{ { 0x1db7d07,0x3bde52b,0x1500396,0x1089115,0x20b4fc7,0x1e2a8f3,
0x3f8eacc,0x365f7eb,0x1a5e8d4,0x0053a6b },
{ 0x37079e2,0x120284b,0x000edaa,0x33792c2,0x145baa3,0x20e055f,
0x365e2d7,0x26ba005,0x3ab8e9d,0x0282b53 } },
/* 225 */
{ { 0x2653618,0x2dd8852,0x2a5f0bf,0x0f0c7aa,0x2187281,0x1252757,
0x13e7374,0x3b47855,0x0b86e56,0x02f354c },
{ 0x2e9c47b,0x2fa14cc,0x19ab169,0x3fad401,0x0dc2776,0x24afeed,
0x3a97611,0x0d07736,0x3cf6979,0x02424a0 } },
/* 226 */
{ { 0x2e81a13,0x000c91d,0x123967b,0x265885c,0x29bee1a,0x0cb8675,
0x2d361bd,0x1526823,0x3c9ace1,0x00d7bad },
{ 0x24e5bdc,0x02b969f,0x2c6e128,0x34edb3b,0x12dcd2c,0x3899af0,
0x24224c6,0x3a1914b,0x0f4448a,0x026a2cb } },
/* 227 */
{ { 0x1d03b59,0x1c6fc82,0x32abf64,0x28ed96b,0x1c90e62,0x2f57bb2,
0x3ff168e,0x04de7fd,0x0f4d449,0x01af6d8 },
{ 0x255bc30,0x2bfaf22,0x3fe0dad,0x0584025,0x1c79ead,0x3078ef7,
0x2197414,0x022a50b,0x0fd94ba,0x0007b0f } },
/* 228 */
{ { 0x09485c2,0x09dfaf7,0x10c7ba6,0x1e48bec,0x248cc9a,0x028a362,
0x21d60f7,0x193d93d,0x1c04754,0x0346b2c },
{ 0x2f36612,0x240ac49,0x0d8bd26,0x13b8186,0x259c3a4,0x020d5fb,
0x38a8133,0x09b0937,0x39d4056,0x01f7341 } },
/* 229 */
{ { 0x05a4b48,0x1f534fc,0x07725ce,0x148dc8c,0x2adcd29,0x04aa456,
0x0f79718,0x066e346,0x189377d,0x002fd4d },
{ 0x068ea73,0x336569b,0x184d35e,0x32a08e9,0x3c7f3bb,0x11ce9c8,
0x3674c6f,0x21bf27e,0x0d9e166,0x034a2f9 } },
/* 230 */
{ { 0x0fa8e4b,0x2e6418e,0x18fc5d2,0x1ba24ff,0x0559f18,0x0dbedbf,
0x2de2aa4,0x22338e9,0x3aa510f,0x035d801 },
{ 0x23a4988,0x02aad94,0x02732d1,0x111d374,0x0b455cf,0x0d01c9e,
0x067082a,0x2ec05fd,0x368b303,0x03cad4b } },
/* 231 */
{ { 0x035b4ca,0x1fabea6,0x1cbc0d5,0x3f2ed9a,0x02d2232,0x1990c66,
0x2eb680c,0x3b4ea3b,0x18ecc5a,0x03636fa },
{ 0x1a02709,0x26f8ff1,0x1fa8cba,0x397d6e8,0x230be68,0x043aa14,
0x3d43cdf,0x25c17fa,0x3a3ee55,0x0380564 } },
/* 232 */
{ { 0x275a0a6,0x16bd43a,0x0033d3e,0x2b15e16,0x2512226,0x005d901,
0x26d50fd,0x3bc19bf,0x3b1aeb8,0x02bfb01 },
{ 0x0bb0a31,0x26559e0,0x1aae7fb,0x330dcc2,0x16f1af3,0x06afce2,
0x13a15a0,0x2ff7645,0x3546e2d,0x029c6e4 } },
/* 233 */
{ { 0x0f593d2,0x384b806,0x122bbf8,0x0a281e0,0x1d1a904,0x2e93cab,
0x0505db0,0x08f6454,0x05c6285,0x014e880 },
{ 0x3f2b935,0x22d8e79,0x161a07c,0x16b060a,0x02bff97,0x146328b,
0x3ceea77,0x238f61a,0x19b3d58,0x02fd1f4 } },
/* 234 */
{ { 0x17665d5,0x259e9f7,0x0de5672,0x15cbcbd,0x34e3030,0x035240f,
0x0005ae8,0x286d851,0x07f39c9,0x000070b },
{ 0x1efc6d6,0x2a0051a,0x2724143,0x2a9ef1e,0x0c810bd,0x1e05429,
0x25670ba,0x2e66d7d,0x0e786ff,0x03f6b7e } },
/* 235 */
{ { 0x3c00785,0x232e23f,0x2b67fd3,0x244ed23,0x077fa75,0x3cda3ef,
0x14d055b,0x0f25011,0x24d5aa4,0x00ea0e3 },
{ 0x297bb9a,0x198ca4f,0x14d9561,0x18d1076,0x39eb933,0x2b6caa0,
0x1591a60,0x0768d45,0x257873e,0x00f36e0 } },
/* 236 */
{ { 0x1e77eab,0x0502a5f,0x0109137,0x0350592,0x3f7e1c5,0x3ac7437,
0x2dcad2c,0x1fee9d8,0x089f1f5,0x0169833 },
{ 0x0d45673,0x0d8e090,0x065580b,0x065644f,0x11b82be,0x3592dd0,
0x3284b8d,0x23f0015,0x16fdbfd,0x0248bfd } },
/* 237 */
{ { 0x1a129a1,0x1977bb2,0x0e041b2,0x15f30a1,0x0a5b1ce,0x3afef8f,
0x380c46c,0x3358810,0x27df6c5,0x01ca466 },
{ 0x3b90f9a,0x3d14ea3,0x031b298,0x02e2390,0x2d719c0,0x25bc615,
0x2c0e777,0x0226b8c,0x3803624,0x0179e45 } },
/* 238 */
{ { 0x363cdfb,0x1bb155f,0x24fd5c1,0x1c7c72b,0x28e6a35,0x18165f2,
0x226bea5,0x0beaff3,0x371e24c,0x0138294 },
{ 0x1765357,0x29034e9,0x22b4276,0x11035ce,0x23c89af,0x074468c,
0x3370ae4,0x013bae3,0x018d566,0x03d7fde } },
/* 239 */
{ { 0x209df21,0x0f8ff86,0x0e47fbf,0x23b99ba,0x126d5d2,0x2722405,
0x16bd0a2,0x1799082,0x0e9533f,0x039077c },
{ 0x3ba9e3f,0x3f6902c,0x1895305,0x3ac9813,0x3f2340c,0x3c0d9f1,
0x26e1927,0x0557c21,0x16eac4f,0x023b75f } },
/* 240 */
{ { 0x3fc8ff3,0x0770382,0x342fc9a,0x0afa4db,0x314efd8,0x328e07b,
0x016f7cc,0x3ba599c,0x1caed8a,0x0050cb0 },
{ 0x0b23c26,0x2120a5c,0x3273ec6,0x1cc1cd6,0x2a64fe8,0x2bbc3d6,
0x09f6e5e,0x34b1b8e,0x00b5ac8,0x032bbd2 } },
/* 241 */
{ { 0x1315922,0x1725e1d,0x0ca5524,0x1c4c18f,0x3d82951,0x193bcb2,
0x0e60d0b,0x388dbcf,0x37e8efa,0x0342e85 },
{ 0x1b3af60,0x26ba3ec,0x220e53a,0x394f4b6,0x01a796a,0x3e7bbca,
0x163605d,0x2b85807,0x17c1c54,0x03cc725 } },
/* 242 */
{ { 0x1cc4597,0x1635492,0x2028c0f,0x2c2eb82,0x2dc5015,0x0d2a052,
0x05fc557,0x1f0ebbf,0x0cb96e1,0x0004d01 },
{ 0x1a824bf,0x3896172,0x2ed7b29,0x178007a,0x0d59318,0x07bda2b,
0x2ee6826,0x0f9b235,0x04b9193,0x01bcddf } },
/* 243 */
{ { 0x0333fd2,0x0eeb46a,0x15b89f9,0x00968aa,0x2a89302,0x2bdd6b3,
0x1e5037e,0x2541884,0x24ed2d0,0x01b6e8f },
{ 0x04399cd,0x3be6334,0x3adea48,0x1bb9adc,0x31811c6,0x05fb2bc,
0x360752c,0x3d29dcb,0x3423bec,0x03c4f3c } },
/* 244 */
{ { 0x119e2eb,0x2e7b02a,0x0f68cee,0x257d8b0,0x183a9a1,0x2ae88a6,
0x3a3bb67,0x2eb4f3e,0x1a9274b,0x0320fea },
{ 0x2fa1ce0,0x346c2d8,0x2fbf0d7,0x3d4d063,0x0e58b60,0x09c1bc1,
0x28ef9e5,0x09a0efe,0x0f45d70,0x02d275c } },
/* 245 */
{ { 0x2d5513b,0x31d443e,0x1e2d914,0x3b2c5d4,0x105f32e,0x27ee756,
0x050418d,0x3c73db6,0x1bb0c30,0x01673eb },
{ 0x1cb7fd6,0x1eb08d5,0x26a3e16,0x2e20810,0x0249367,0x029e219,
0x2ec58c9,0x12d9fab,0x362354a,0x016eafc } },
/* 246 */
{ { 0x2424865,0x260747b,0x177f37c,0x1e3cb95,0x08b0028,0x2783016,
0x2970f1b,0x323c1c0,0x2a79026,0x0186231 },
{ 0x0f244da,0x26866f4,0x087306f,0x173ec20,0x31ecced,0x3c84d8d,
0x070f9b9,0x2e764d5,0x075df50,0x0264ff9 } },
/* 247 */
{ { 0x32c3609,0x0c737e6,0x14ea68e,0x300b11b,0x184eb19,0x29dd440,
0x09ec1a9,0x185adeb,0x0664c80,0x0207dd9 },
{ 0x1fbe978,0x30a969d,0x33561d7,0x34fc60e,0x36743fe,0x00774af,
0x0d1f045,0x018360e,0x12a5fe9,0x01592a0 } },
/* 248 */
{ { 0x2817d1d,0x2993d3e,0x2e0f7a5,0x112faa0,0x255f968,0x355fe6a,
0x3f5a0fc,0x075b2d7,0x3cf00e5,0x0089afc },
{ 0x32833cf,0x06a7e4b,0x09a8d6d,0x1693d3e,0x320a0a3,0x3cfdfdd,
0x136c498,0x1e0d845,0x347ff25,0x01a1de7 } },
/* 249 */
{ { 0x3043d08,0x030705c,0x20fa79b,0x1d07f00,0x0a54467,0x29b49b4,
0x367e289,0x0b82f4d,0x0d1eb09,0x025ef2c },
{ 0x32ed3c3,0x1baaa3c,0x3c482ab,0x146ca06,0x3c8a4f1,0x3e85e3c,
0x1bf4f3b,0x1195534,0x3e80a78,0x02a1cbf } },
/* 250 */
{ { 0x32b2086,0x2de4d68,0x3486b1a,0x03a0583,0x2e1eb71,0x2dab9af,
0x10cd913,0x28daa6f,0x3fcb732,0x000a04a },
{ 0x3605318,0x3f5f2b3,0x2d1da63,0x143f7f5,0x1646e5d,0x040b586,
0x1683982,0x25abe87,0x0c9fe53,0x001ce47 } },
/* 251 */
{ { 0x380d02b,0x055fc22,0x3f7fc50,0x3458a1d,0x26b8333,0x23550ab,
0x0a1af87,0x0a821eb,0x2dc7e6d,0x00d574a },
{ 0x07386e1,0x3ccd68a,0x3275b41,0x253e390,0x2fd272a,0x1e6627a,
0x2ca2cde,0x0e9e4a1,0x1e37c2a,0x00f70ac } },
/* 252 */
{ { 0x0581352,0x2748701,0x02bed68,0x094dd9e,0x30a00c8,0x3fb5c07,
0x3bd5909,0x211ac80,0x1103ccd,0x0311e1a },
{ 0x0c768ed,0x29dc209,0x36575db,0x009a107,0x272feea,0x2b33383,
0x313ed56,0x134c9cc,0x168d5bb,0x033310a } },
/* 253 */
{ { 0x17620b9,0x143784f,0x256a94e,0x229664a,0x1d89a5c,0x1d521f2,
0x0076406,0x1c73f70,0x342aa48,0x03851fa },
{ 0x0f3ae46,0x2ad3bab,0x0fbe274,0x3ed40d4,0x2fd4936,0x232103a,
0x2afe474,0x25b8f7c,0x047080e,0x008e6b0 } },
/* 254 */
{ { 0x3fee8d4,0x347cd4a,0x0fec481,0x33fe9ec,0x0ce80b5,0x33a6bcf,
0x1c4c9e2,0x3967441,0x1a3f5f7,0x03157e8 },
{ 0x257c227,0x1bc53a0,0x200b318,0x0fcd0af,0x2c5b165,0x2a413ec,
0x2fc998a,0x2da6426,0x19cd4f4,0x0025336 } },
/* 255 */
{ { 0x303beba,0x2072135,0x32918a9,0x140cb3a,0x08631d1,0x0ef527b,
0x05f2c9e,0x2b4ce91,0x0b642ab,0x02e428c },
{ 0x0a5abf9,0x15013ed,0x3603b46,0x30dd76d,0x3004750,0x28d7627,
0x1a42ccc,0x093ddbe,0x39a1b79,0x00067e2 } },
};
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_256_ecc_mulmod_base_10(sp_point_256* r, const sp_digit* k,
int map, void* heap)
{
return sp_256_ecc_mulmod_stripe_10(r, &p256_base, p256_table,
k, map, heap);
}
#endif
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* km Scalar to multiply by.
* r Resulting point.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_mulmod_base_256(mp_int* km, ecc_point* r, int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 p;
sp_digit kd[10];
#endif
sp_point_256* point;
sp_digit* k = NULL;
int err = MP_OKAY;
err = sp_256_point_new_10(heap, p, point);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL) {
err = MEMORY_E;
}
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(k, 10, km);
err = sp_256_ecc_mulmod_base_10(point, k, map, heap);
}
if (err == MP_OKAY) {
err = sp_256_point_to_ecc_point_10(point, r);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(point, 0, heap);
return err;
}
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* Returns 1 if the number of zero.
* Implementation is constant time.
*
* a Number to check.
* returns 1 if the number is zero and 0 otherwise.
*/
static int sp_256_iszero_10(const sp_digit* a)
{
return (a[0] | a[1] | a[2] | a[3] | a[4] | a[5] | a[6] | a[7] |
a[8] | a[9]) == 0;
}
#endif /* WOLFSSL_VALIDATE_ECC_KEYGEN || HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
/* Add 1 to a. (a = a + 1)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_add_one_10(sp_digit* a)
{
a[0]++;
sp_256_norm_10(a);
}
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_256_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 18U) {
r[j] &= 0x3ffffff;
s = 26U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Generates a scalar that is in the range 1..order-1.
*
* rng Random number generator.
* k Scalar value.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
static int sp_256_ecc_gen_k_10(WC_RNG* rng, sp_digit* k)
{
int err;
byte buf[32];
do {
err = wc_RNG_GenerateBlock(rng, buf, sizeof(buf));
if (err == 0) {
sp_256_from_bin(k, 10, buf, (int)sizeof(buf));
if (sp_256_cmp_10(k, p256_order2) < 0) {
sp_256_add_one_10(k);
break;
}
}
}
while (err == 0);
return err;
}
/* Makes a random EC key pair.
*
* rng Random number generator.
* priv Generated private value.
* pub Generated public point.
* heap Heap to use for allocation.
* returns ECC_INF_E when the point does not have the correct order, RNG
* failures, MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_make_key_256(WC_RNG* rng, mp_int* priv, ecc_point* pub, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 p;
sp_digit kd[10];
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_point_256 inf;
#endif
#endif
sp_point_256* point;
sp_digit* k = NULL;
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_point_256* infinity;
#endif
int err;
(void)heap;
err = sp_256_point_new_10(heap, p, point);
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, inf, infinity);
}
#endif
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL) {
err = MEMORY_E;
}
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
err = sp_256_ecc_gen_k_10(rng, k);
}
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_base_10(point, k, 1, NULL);
}
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_10(infinity, point, p256_order, 1, NULL);
}
if (err == MP_OKAY) {
if ((sp_256_iszero_10(point->x) == 0) || (sp_256_iszero_10(point->y) == 0)) {
err = ECC_INF_E;
}
}
#endif
if (err == MP_OKAY) {
err = sp_256_to_mp(k, priv);
}
if (err == MP_OKAY) {
err = sp_256_point_to_ecc_point_10(point, pub);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_256_point_free_10(infinity, 1, heap);
#endif
sp_256_point_free_10(point, 1, heap);
return err;
}
#ifdef HAVE_ECC_DHE
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 32
*
* r A single precision integer.
* a Byte array.
*/
static void sp_256_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<9; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
j = 256 / 8 - 1;
a[j] = 0;
for (i=0; i<10 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); /*lint !e9033*/
b += 8 - s;
if (j < 0) {
break;
}
while (b < 26) {
a[j--] = (byte)(r[i] >> b);
b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 26);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
/* Multiply the point by the scalar and serialize the X ordinate.
* The number is 0 padded to maximum size on output.
*
* priv Scalar to multiply the point by.
* pub Point to multiply.
* out Buffer to hold X ordinate.
* outLen On entry, size of the buffer in bytes.
* On exit, length of data in buffer in bytes.
* heap Heap to use for allocation.
* returns BUFFER_E if the buffer is to small for output size,
* MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_secret_gen_256(mp_int* priv, ecc_point* pub, byte* out,
word32* outLen, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 p;
sp_digit kd[10];
#endif
sp_point_256* point = NULL;
sp_digit* k = NULL;
int err = MP_OKAY;
if (*outLen < 32U) {
err = BUFFER_E;
}
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, p, point);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL)
err = MEMORY_E;
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(k, 10, priv);
sp_256_point_from_ecc_point_10(point, pub);
err = sp_256_ecc_mulmod_10(point, point, k, 1, heap);
}
if (err == MP_OKAY) {
sp_256_to_bin(point->x, out);
*outLen = 32;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(point, 0, heap);
return err;
}
#endif /* HAVE_ECC_DHE */
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_256_mul_d_10(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 10; i++) {
t += tb * a[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[10] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[10];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
t[ 5] = tb * a[ 5];
t[ 6] = tb * a[ 6];
t[ 7] = tb * a[ 7];
t[ 8] = tb * a[ 8];
t[ 9] = tb * a[ 9];
r[ 0] = (t[ 0] & 0x3ffffff);
r[ 1] = (sp_digit)(t[ 0] >> 26) + (t[ 1] & 0x3ffffff);
r[ 2] = (sp_digit)(t[ 1] >> 26) + (t[ 2] & 0x3ffffff);
r[ 3] = (sp_digit)(t[ 2] >> 26) + (t[ 3] & 0x3ffffff);
r[ 4] = (sp_digit)(t[ 3] >> 26) + (t[ 4] & 0x3ffffff);
r[ 5] = (sp_digit)(t[ 4] >> 26) + (t[ 5] & 0x3ffffff);
r[ 6] = (sp_digit)(t[ 5] >> 26) + (t[ 6] & 0x3ffffff);
r[ 7] = (sp_digit)(t[ 6] >> 26) + (t[ 7] & 0x3ffffff);
r[ 8] = (sp_digit)(t[ 7] >> 26) + (t[ 8] & 0x3ffffff);
r[ 9] = (sp_digit)(t[ 8] >> 26) + (t[ 9] & 0x3ffffff);
r[10] = (sp_digit)(t[ 9] >> 26);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_256_div_word_10(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 26 bits from d1 and top 5 bits from d0. */
d = (d1 << 5) | (d0 >> 21);
r = d / dv;
d -= r * dv;
/* Up to 6 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 16) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 11 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 11) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 16 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 6) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 21 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 1) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 26 bits in r */
/* Remaining 1 bits from d0. */
r <<= 1;
d <<= 1;
d |= d0 & ((1 << 1) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Number to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_256_div_10(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[20], t2d[10 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (3 * 10 + 1), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 2 * 10;
#else
t1 = t1d;
t2 = t2d;
#endif
dv = d[9];
XMEMCPY(t1, a, sizeof(*t1) * 2U * 10U);
for (i=9; i>=0; i--) {
t1[10 + i] += t1[10 + i - 1] >> 26;
t1[10 + i - 1] &= 0x3ffffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[10 + i];
d1 <<= 26;
d1 += t1[10 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_256_div_word_10(t1[10 + i], t1[10 + i - 1], dv);
#endif
sp_256_mul_d_10(t2, d, r1);
(void)sp_256_sub_10(&t1[i], &t1[i], t2);
t1[10 + i] -= t2[10];
t1[10 + i] += t1[10 + i - 1] >> 26;
t1[10 + i - 1] &= 0x3ffffff;
r1 = (((-t1[10 + i]) << 26) - t1[10 + i - 1]) / dv;
r1++;
sp_256_mul_d_10(t2, d, r1);
(void)sp_256_add_10(&t1[i], &t1[i], t2);
t1[10 + i] += t1[10 + i - 1] >> 26;
t1[10 + i - 1] &= 0x3ffffff;
}
t1[10 - 1] += t1[10 - 2] >> 26;
t1[10 - 2] &= 0x3ffffff;
r1 = t1[10 - 1] / dv;
sp_256_mul_d_10(t2, d, r1);
(void)sp_256_sub_10(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 10U);
for (i=0; i<8; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
sp_256_cond_add_10(r, r, d, 0 - ((r[9] < 0) ?
(sp_digit)1 : (sp_digit)0));
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_256_mod_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_256_div_10(a, m, NULL, r);
}
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
#ifdef WOLFSSL_SP_SMALL
/* Order-2 for the P256 curve. */
static const uint32_t p256_order_minus_2[8] = {
0xfc63254fU,0xf3b9cac2U,0xa7179e84U,0xbce6faadU,0xffffffffU,0xffffffffU,
0x00000000U,0xffffffffU
};
#else
/* The low half of the order-2 of the P256 curve. */
static const uint32_t p256_order_low[4] = {
0xfc63254fU,0xf3b9cac2U,0xa7179e84U,0xbce6faadU
};
#endif /* WOLFSSL_SP_SMALL */
/* Multiply two number mod the order of P256 curve. (r = a * b mod order)
*
* r Result of the multiplication.
* a First operand of the multiplication.
* b Second operand of the multiplication.
*/
static void sp_256_mont_mul_order_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
sp_256_mul_10(r, a, b);
sp_256_mont_reduce_order_10(r, p256_order, p256_mp_order);
}
/* Square number mod the order of P256 curve. (r = a * a mod order)
*
* r Result of the squaring.
* a Number to square.
*/
static void sp_256_mont_sqr_order_10(sp_digit* r, const sp_digit* a)
{
sp_256_sqr_10(r, a);
sp_256_mont_reduce_order_10(r, p256_order, p256_mp_order);
}
#ifndef WOLFSSL_SP_SMALL
/* Square number mod the order of P256 curve a number of times.
* (r = a ^ n mod order)
*
* r Result of the squaring.
* a Number to square.
*/
static void sp_256_mont_sqr_n_order_10(sp_digit* r, const sp_digit* a, int n)
{
int i;
sp_256_mont_sqr_order_10(r, a);
for (i=1; i<n; i++) {
sp_256_mont_sqr_order_10(r, r);
}
}
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the order of the P256 curve.
* (r = 1 / a mod order)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_256_mont_inv_order_10(sp_digit* r, const sp_digit* a,
sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 10);
for (i=254; i>=0; i--) {
sp_256_mont_sqr_order_10(t, t);
if ((p256_order_minus_2[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t, t, a);
}
}
XMEMCPY(r, t, sizeof(sp_digit) * 10U);
#else
sp_digit* t = td;
sp_digit* t2 = td + 2 * 10;
sp_digit* t3 = td + 4 * 10;
int i;
/* t = a^2 */
sp_256_mont_sqr_order_10(t, a);
/* t = a^3 = t * a */
sp_256_mont_mul_order_10(t, t, a);
/* t2= a^c = t ^ 2 ^ 2 */
sp_256_mont_sqr_n_order_10(t2, t, 2);
/* t3= a^f = t2 * t */
sp_256_mont_mul_order_10(t3, t2, t);
/* t2= a^f0 = t3 ^ 2 ^ 4 */
sp_256_mont_sqr_n_order_10(t2, t3, 4);
/* t = a^ff = t2 * t3 */
sp_256_mont_mul_order_10(t, t2, t3);
/* t3= a^ff00 = t ^ 2 ^ 8 */
sp_256_mont_sqr_n_order_10(t2, t, 8);
/* t = a^ffff = t2 * t */
sp_256_mont_mul_order_10(t, t2, t);
/* t2= a^ffff0000 = t ^ 2 ^ 16 */
sp_256_mont_sqr_n_order_10(t2, t, 16);
/* t = a^ffffffff = t2 * t */
sp_256_mont_mul_order_10(t, t2, t);
/* t2= a^ffffffff0000000000000000 = t ^ 2 ^ 64 */
sp_256_mont_sqr_n_order_10(t2, t, 64);
/* t2= a^ffffffff00000000ffffffff = t2 * t */
sp_256_mont_mul_order_10(t2, t2, t);
/* t2= a^ffffffff00000000ffffffff00000000 = t2 ^ 2 ^ 32 */
sp_256_mont_sqr_n_order_10(t2, t2, 32);
/* t2= a^ffffffff00000000ffffffffffffffff = t2 * t */
sp_256_mont_mul_order_10(t2, t2, t);
/* t2= a^ffffffff00000000ffffffffffffffffbce6 */
for (i=127; i>=112; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6f */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
sp_256_mont_mul_order_10(t2, t2, t3);
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84 */
for (i=107; i>=64; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
sp_256_mont_mul_order_10(t2, t2, t3);
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2 */
for (i=59; i>=32; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2f */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
sp_256_mont_mul_order_10(t2, t2, t3);
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254 */
for (i=27; i>=0; i--) {
sp_256_mont_sqr_order_10(t2, t2);
if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_256_mont_mul_order_10(t2, t2, a);
}
}
/* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632540 */
sp_256_mont_sqr_n_order_10(t2, t2, 4);
/* r = a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254f */
sp_256_mont_mul_order_10(r, t2, t3);
#endif /* WOLFSSL_SP_SMALL */
}
#endif /* HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_SIGN
#ifndef SP_ECC_MAX_SIG_GEN
#define SP_ECC_MAX_SIG_GEN 64
#endif
/* Sign the hash using the private key.
* e = [hash, 256 bits] from binary
* r = (k.G)->x mod order
* s = (r * x + e) / k mod order
* The hash is truncated to the first 256 bits.
*
* hash Hash to sign.
* hashLen Length of the hash data.
* rng Random number generator.
* priv Private part of key - scalar.
* rm First part of result as an mp_int.
* sm Sirst part of result as an mp_int.
* heap Heap to use for allocation.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
int sp_ecc_sign_256(const byte* hash, word32 hashLen, WC_RNG* rng, mp_int* priv,
mp_int* rm, mp_int* sm, mp_int* km, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d = NULL;
#else
sp_digit ed[2*10];
sp_digit xd[2*10];
sp_digit kd[2*10];
sp_digit rd[2*10];
sp_digit td[3 * 2*10];
sp_point_256 p;
#endif
sp_digit* e = NULL;
sp_digit* x = NULL;
sp_digit* k = NULL;
sp_digit* r = NULL;
sp_digit* tmp = NULL;
sp_point_256* point = NULL;
sp_digit carry;
sp_digit* s = NULL;
sp_digit* kInv = NULL;
int err = MP_OKAY;
int32_t c;
int i;
(void)heap;
err = sp_256_point_new_10(heap, p, point);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 7 * 2 * 10, heap,
DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
e = d + 0 * 10;
x = d + 2 * 10;
k = d + 4 * 10;
r = d + 6 * 10;
tmp = d + 8 * 10;
#else
e = ed;
x = xd;
k = kd;
r = rd;
tmp = td;
#endif
s = e;
kInv = k;
if (hashLen > 32U) {
hashLen = 32U;
}
sp_256_from_bin(e, 10, hash, (int)hashLen);
}
for (i = SP_ECC_MAX_SIG_GEN; err == MP_OKAY && i > 0; i--) {
sp_256_from_mp(x, 10, priv);
/* New random point. */
if (km == NULL || mp_iszero(km)) {
err = sp_256_ecc_gen_k_10(rng, k);
}
else {
sp_256_from_mp(k, 10, km);
mp_zero(km);
}
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_base_10(point, k, 1, NULL);
}
if (err == MP_OKAY) {
/* r = point->x mod order */
XMEMCPY(r, point->x, sizeof(sp_digit) * 10U);
sp_256_norm_10(r);
c = sp_256_cmp_10(r, p256_order);
sp_256_cond_sub_10(r, r, p256_order, 0L - (sp_digit)(c >= 0));
sp_256_norm_10(r);
/* Conv k to Montgomery form (mod order) */
sp_256_mul_10(k, k, p256_norm_order);
err = sp_256_mod_10(k, k, p256_order);
}
if (err == MP_OKAY) {
sp_256_norm_10(k);
/* kInv = 1/k mod order */
sp_256_mont_inv_order_10(kInv, k, tmp);
sp_256_norm_10(kInv);
/* s = r * x + e */
sp_256_mul_10(x, x, r);
err = sp_256_mod_10(x, x, p256_order);
}
if (err == MP_OKAY) {
sp_256_norm_10(x);
carry = sp_256_add_10(s, e, x);
sp_256_cond_sub_10(s, s, p256_order, 0 - carry);
sp_256_norm_10(s);
c = sp_256_cmp_10(s, p256_order);
sp_256_cond_sub_10(s, s, p256_order, 0L - (sp_digit)(c >= 0));
sp_256_norm_10(s);
/* s = s * k^-1 mod order */
sp_256_mont_mul_order_10(s, s, kInv);
sp_256_norm_10(s);
/* Check that signature is usable. */
if (sp_256_iszero_10(s) == 0) {
break;
}
}
}
if (i == 0) {
err = RNG_FAILURE_E;
}
if (err == MP_OKAY) {
err = sp_256_to_mp(r, rm);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(s, sm);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 8 * 10);
XFREE(d, heap, DYNAMIC_TYPE_ECC);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(x, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(k, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(r, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(r, 0, sizeof(sp_digit) * 2U * 10U);
XMEMSET(tmp, 0, sizeof(sp_digit) * 3U * 2U * 10U);
#endif
sp_256_point_free_10(point, 1, heap);
return err;
}
#endif /* HAVE_ECC_SIGN */
#ifdef HAVE_ECC_VERIFY
/* Verify the signature values with the hash and public key.
* e = Truncate(hash, 256)
* u1 = e/s mod order
* u2 = r/s mod order
* r == (u1.G + u2.Q)->x mod order
* Optimization: Leave point in projective form.
* (x, y, 1) == (x' / z'*z', y' / z'*z'*z', z' / z')
* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x'
* The hash is truncated to the first 256 bits.
*
* hash Hash to sign.
* hashLen Length of the hash data.
* rng Random number generator.
* priv Private part of key - scalar.
* rm First part of result as an mp_int.
* sm Sirst part of result as an mp_int.
* heap Heap to use for allocation.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
int sp_ecc_verify_256(const byte* hash, word32 hashLen, mp_int* pX,
mp_int* pY, mp_int* pZ, mp_int* r, mp_int* sm, int* res, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d = NULL;
#else
sp_digit u1d[2*10];
sp_digit u2d[2*10];
sp_digit sd[2*10];
sp_digit tmpd[2*10 * 5];
sp_point_256 p1d;
sp_point_256 p2d;
#endif
sp_digit* u1 = NULL;
sp_digit* u2 = NULL;
sp_digit* s = NULL;
sp_digit* tmp = NULL;
sp_point_256* p1;
sp_point_256* p2 = NULL;
sp_digit carry;
int32_t c;
int err;
err = sp_256_point_new_10(heap, p1d, p1);
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, p2d, p2);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 16 * 10, heap,
DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
u1 = d + 0 * 10;
u2 = d + 2 * 10;
s = d + 4 * 10;
tmp = d + 6 * 10;
#else
u1 = u1d;
u2 = u2d;
s = sd;
tmp = tmpd;
#endif
if (hashLen > 32U) {
hashLen = 32U;
}
sp_256_from_bin(u1, 10, hash, (int)hashLen);
sp_256_from_mp(u2, 10, r);
sp_256_from_mp(s, 10, sm);
sp_256_from_mp(p2->x, 10, pX);
sp_256_from_mp(p2->y, 10, pY);
sp_256_from_mp(p2->z, 10, pZ);
{
sp_256_mul_10(s, s, p256_norm_order);
}
err = sp_256_mod_10(s, s, p256_order);
}
if (err == MP_OKAY) {
sp_256_norm_10(s);
{
sp_256_mont_inv_order_10(s, s, tmp);
sp_256_mont_mul_order_10(u1, u1, s);
sp_256_mont_mul_order_10(u2, u2, s);
}
err = sp_256_ecc_mulmod_base_10(p1, u1, 0, heap);
}
if (err == MP_OKAY) {
err = sp_256_ecc_mulmod_10(p2, p2, u2, 0, heap);
}
if (err == MP_OKAY) {
{
sp_256_proj_point_add_10(p1, p1, p2, tmp);
if (sp_256_iszero_10(p1->z)) {
if (sp_256_iszero_10(p1->x) && sp_256_iszero_10(p1->y)) {
sp_256_proj_point_dbl_10(p1, p2, tmp);
}
else {
/* Y ordinate is not used from here - don't set. */
p1->x[0] = 0;
p1->x[1] = 0;
p1->x[2] = 0;
p1->x[3] = 0;
p1->x[4] = 0;
p1->x[5] = 0;
p1->x[6] = 0;
p1->x[7] = 0;
p1->x[8] = 0;
p1->x[9] = 0;
XMEMCPY(p1->z, p256_norm_mod, sizeof(p256_norm_mod));
}
}
}
/* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x' */
/* Reload r and convert to Montgomery form. */
sp_256_from_mp(u2, 10, r);
err = sp_256_mod_mul_norm_10(u2, u2, p256_mod);
}
if (err == MP_OKAY) {
/* u1 = r.z'.z' mod prime */
sp_256_mont_sqr_10(p1->z, p1->z, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(u1, u2, p1->z, p256_mod, p256_mp_mod);
*res = (int)(sp_256_cmp_10(p1->x, u1) == 0);
if (*res == 0) {
/* Reload r and add order. */
sp_256_from_mp(u2, 10, r);
carry = sp_256_add_10(u2, u2, p256_order);
/* Carry means result is greater than mod and is not valid. */
if (carry == 0) {
sp_256_norm_10(u2);
/* Compare with mod and if greater or equal then not valid. */
c = sp_256_cmp_10(u2, p256_mod);
if (c < 0) {
/* Convert to Montogomery form */
err = sp_256_mod_mul_norm_10(u2, u2, p256_mod);
if (err == MP_OKAY) {
/* u1 = (r + 1*order).z'.z' mod prime */
sp_256_mont_mul_10(u1, u2, p1->z, p256_mod,
p256_mp_mod);
*res = (int)(sp_256_cmp_10(p1->x, u1) == 0);
}
}
}
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL)
XFREE(d, heap, DYNAMIC_TYPE_ECC);
#endif
sp_256_point_free_10(p1, 0, heap);
sp_256_point_free_10(p2, 0, heap);
return err;
}
#endif /* HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_CHECK_KEY
/* Check that the x and y oridinates are a valid point on the curve.
*
* point EC point.
* heap Heap to use if dynamically allocating.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve and MP_OKAY otherwise.
*/
static int sp_256_ecc_is_point_10(sp_point_256* point, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d = NULL;
#else
sp_digit t1d[2*10];
sp_digit t2d[2*10];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10 * 4, heap, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = d + 0 * 10;
t2 = d + 2 * 10;
#else
(void)heap;
t1 = t1d;
t2 = t2d;
#endif
sp_256_sqr_10(t1, point->y);
(void)sp_256_mod_10(t1, t1, p256_mod);
sp_256_sqr_10(t2, point->x);
(void)sp_256_mod_10(t2, t2, p256_mod);
sp_256_mul_10(t2, t2, point->x);
(void)sp_256_mod_10(t2, t2, p256_mod);
(void)sp_256_sub_10(t2, p256_mod, t2);
sp_256_mont_add_10(t1, t1, t2, p256_mod);
sp_256_mont_add_10(t1, t1, point->x, p256_mod);
sp_256_mont_add_10(t1, t1, point->x, p256_mod);
sp_256_mont_add_10(t1, t1, point->x, p256_mod);
if (sp_256_cmp_10(t1, p256_b) != 0) {
err = MP_VAL;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, heap, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Check that the x and y oridinates are a valid point on the curve.
*
* pX X ordinate of EC point.
* pY Y ordinate of EC point.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve and MP_OKAY otherwise.
*/
int sp_ecc_is_point_256(mp_int* pX, mp_int* pY)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_256 pubd;
#endif
sp_point_256* pub;
byte one[1] = { 1 };
int err;
err = sp_256_point_new_10(NULL, pubd, pub);
if (err == MP_OKAY) {
sp_256_from_mp(pub->x, 10, pX);
sp_256_from_mp(pub->y, 10, pY);
sp_256_from_bin(pub->z, 10, one, (int)sizeof(one));
err = sp_256_ecc_is_point_10(pub, NULL);
}
sp_256_point_free_10(pub, 0, NULL);
return err;
}
/* Check that the private scalar generates the EC point (px, py), the point is
* on the curve and the point has the correct order.
*
* pX X ordinate of EC point.
* pY Y ordinate of EC point.
* privm Private scalar that generates EC point.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve, ECC_INF_E if the point does not have the correct order,
* ECC_PRIV_KEY_E when the private scalar doesn't generate the EC point and
* MP_OKAY otherwise.
*/
int sp_ecc_check_key_256(mp_int* pX, mp_int* pY, mp_int* privm, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit privd[10];
sp_point_256 pubd;
sp_point_256 pd;
#endif
sp_digit* priv = NULL;
sp_point_256* pub;
sp_point_256* p = NULL;
byte one[1] = { 1 };
int err;
err = sp_256_point_new_10(heap, pubd, pub);
if (err == MP_OKAY) {
err = sp_256_point_new_10(heap, pd, p);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
priv = (sp_digit*)XMALLOC(sizeof(sp_digit) * 10, heap,
DYNAMIC_TYPE_ECC);
if (priv == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
priv = privd;
#endif
sp_256_from_mp(pub->x, 10, pX);
sp_256_from_mp(pub->y, 10, pY);
sp_256_from_bin(pub->z, 10, one, (int)sizeof(one));
sp_256_from_mp(priv, 10, privm);
/* Check point at infinitiy. */
if ((sp_256_iszero_10(pub->x) != 0) &&
(sp_256_iszero_10(pub->y) != 0)) {
err = ECC_INF_E;
}
}
if (err == MP_OKAY) {
/* Check range of X and Y */
if (sp_256_cmp_10(pub->x, p256_mod) >= 0 ||
sp_256_cmp_10(pub->y, p256_mod) >= 0) {
err = ECC_OUT_OF_RANGE_E;
}
}
if (err == MP_OKAY) {
/* Check point is on curve */
err = sp_256_ecc_is_point_10(pub, heap);
}
if (err == MP_OKAY) {
/* Point * order = infinity */
err = sp_256_ecc_mulmod_10(p, pub, p256_order, 1, heap);
}
if (err == MP_OKAY) {
/* Check result is infinity */
if ((sp_256_iszero_10(p->x) == 0) ||
(sp_256_iszero_10(p->y) == 0)) {
err = ECC_INF_E;
}
}
if (err == MP_OKAY) {
/* Base * private = point */
err = sp_256_ecc_mulmod_base_10(p, priv, 1, heap);
}
if (err == MP_OKAY) {
/* Check result is public key */
if (sp_256_cmp_10(p->x, pub->x) != 0 ||
sp_256_cmp_10(p->y, pub->y) != 0) {
err = ECC_PRIV_KEY_E;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (priv != NULL) {
XFREE(priv, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(p, 0, heap);
sp_256_point_free_10(pub, 0, heap);
return err;
}
#endif
#ifdef WOLFSSL_PUBLIC_ECC_ADD_DBL
/* Add two projective EC points together.
* (pX, pY, pZ) + (qX, qY, qZ) = (rX, rY, rZ)
*
* pX First EC point's X ordinate.
* pY First EC point's Y ordinate.
* pZ First EC point's Z ordinate.
* qX Second EC point's X ordinate.
* qY Second EC point's Y ordinate.
* qZ Second EC point's Z ordinate.
* rX Resultant EC point's X ordinate.
* rY Resultant EC point's Y ordinate.
* rZ Resultant EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_proj_add_point_256(mp_int* pX, mp_int* pY, mp_int* pZ,
mp_int* qX, mp_int* qY, mp_int* qZ,
mp_int* rX, mp_int* rY, mp_int* rZ)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit tmpd[2 * 10 * 5];
sp_point_256 pd;
sp_point_256 qd;
#endif
sp_digit* tmp;
sp_point_256* p;
sp_point_256* q = NULL;
int err;
err = sp_256_point_new_10(NULL, pd, p);
if (err == MP_OKAY) {
err = sp_256_point_new_10(NULL, qd, q);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(p->x, 10, pX);
sp_256_from_mp(p->y, 10, pY);
sp_256_from_mp(p->z, 10, pZ);
sp_256_from_mp(q->x, 10, qX);
sp_256_from_mp(q->y, 10, qY);
sp_256_from_mp(q->z, 10, qZ);
sp_256_proj_point_add_10(p, p, q, tmp);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->x, rX);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, rY);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, rZ);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(q, 0, NULL);
sp_256_point_free_10(p, 0, NULL);
return err;
}
/* Double a projective EC point.
* (pX, pY, pZ) + (pX, pY, pZ) = (rX, rY, rZ)
*
* pX EC point's X ordinate.
* pY EC point's Y ordinate.
* pZ EC point's Z ordinate.
* rX Resultant EC point's X ordinate.
* rY Resultant EC point's Y ordinate.
* rZ Resultant EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_proj_dbl_point_256(mp_int* pX, mp_int* pY, mp_int* pZ,
mp_int* rX, mp_int* rY, mp_int* rZ)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit tmpd[2 * 10 * 2];
sp_point_256 pd;
#endif
sp_digit* tmp;
sp_point_256* p;
int err;
err = sp_256_point_new_10(NULL, pd, p);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 2, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(p->x, 10, pX);
sp_256_from_mp(p->y, 10, pY);
sp_256_from_mp(p->z, 10, pZ);
sp_256_proj_point_dbl_10(p, p, tmp);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->x, rX);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, rY);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, rZ);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(p, 0, NULL);
return err;
}
/* Map a projective EC point to affine in place.
* pZ will be one.
*
* pX EC point's X ordinate.
* pY EC point's Y ordinate.
* pZ EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_map_256(mp_int* pX, mp_int* pY, mp_int* pZ)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit tmpd[2 * 10 * 4];
sp_point_256 pd;
#endif
sp_digit* tmp;
sp_point_256* p;
int err;
err = sp_256_point_new_10(NULL, pd, p);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 4, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_256_from_mp(p->x, 10, pX);
sp_256_from_mp(p->y, 10, pY);
sp_256_from_mp(p->z, 10, pZ);
sp_256_map_10(p, p, tmp);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->x, pX);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, pY);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, pZ);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_256_point_free_10(p, 0, NULL);
return err;
}
#endif /* WOLFSSL_PUBLIC_ECC_ADD_DBL */
#ifdef HAVE_COMP_KEY
/* Find the square root of a number mod the prime of the curve.
*
* y The number to operate on and the result.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
static int sp_256_mont_sqrt_10(sp_digit* y)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d;
#else
sp_digit t1d[2 * 10];
sp_digit t2d[2 * 10];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 10, NULL, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = d + 0 * 10;
t2 = d + 2 * 10;
#else
t1 = t1d;
t2 = t2d;
#endif
{
/* t2 = y ^ 0x2 */
sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
/* t1 = y ^ 0x3 */
sp_256_mont_mul_10(t1, t2, y, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xc */
sp_256_mont_sqr_n_10(t2, t1, 2, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xf */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xf0 */
sp_256_mont_sqr_n_10(t2, t1, 4, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xff */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xff00 */
sp_256_mont_sqr_n_10(t2, t1, 8, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffff */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t2 = y ^ 0xffff0000 */
sp_256_mont_sqr_n_10(t2, t1, 16, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff */
sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000000 */
sp_256_mont_sqr_n_10(t1, t1, 32, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000001 */
sp_256_mont_mul_10(t1, t1, y, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000001000000000000000000000000 */
sp_256_mont_sqr_n_10(t1, t1, 96, p256_mod, p256_mp_mod);
/* t1 = y ^ 0xffffffff00000001000000000000000000000001 */
sp_256_mont_mul_10(t1, t1, y, p256_mod, p256_mp_mod);
sp_256_mont_sqr_n_10(y, t1, 94, p256_mod, p256_mp_mod);
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Uncompress the point given the X ordinate.
*
* xm X ordinate.
* odd Whether the Y ordinate is odd.
* ym Calculated Y ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_uncompress_256(mp_int* xm, int odd, mp_int* ym)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d;
#else
sp_digit xd[2 * 10];
sp_digit yd[2 * 10];
#endif
sp_digit* x = NULL;
sp_digit* y = NULL;
int err = MP_OKAY;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 10, NULL, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
x = d + 0 * 10;
y = d + 2 * 10;
#else
x = xd;
y = yd;
#endif
sp_256_from_mp(x, 10, xm);
err = sp_256_mod_mul_norm_10(x, x, p256_mod);
}
if (err == MP_OKAY) {
/* y = x^3 */
{
sp_256_mont_sqr_10(y, x, p256_mod, p256_mp_mod);
sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
}
/* y = x^3 - 3x */
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_sub_10(y, y, x, p256_mod);
sp_256_mont_sub_10(y, y, x, p256_mod);
/* y = x^3 - 3x + b */
err = sp_256_mod_mul_norm_10(x, p256_b, p256_mod);
}
if (err == MP_OKAY) {
sp_256_mont_add_10(y, y, x, p256_mod);
/* y = sqrt(x^3 - 3x + b) */
err = sp_256_mont_sqrt_10(y);
}
if (err == MP_OKAY) {
XMEMSET(y + 10, 0, 10U * sizeof(sp_digit));
sp_256_mont_reduce_10(y, p256_mod, p256_mp_mod);
if ((((word32)y[0] ^ (word32)odd) & 1U) != 0U) {
sp_256_mont_sub_10(y, p256_mod, y, p256_mod);
}
err = sp_256_to_mp(y, ym);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
#endif
#endif /* !WOLFSSL_SP_NO_256 */
#ifdef WOLFSSL_SP_384
/* Point structure to use. */
typedef struct sp_point_384 {
sp_digit x[2 * 15];
sp_digit y[2 * 15];
sp_digit z[2 * 15];
int infinity;
} sp_point_384;
/* The modulus (prime) of the curve P384. */
static const sp_digit p384_mod[15] = {
0x3ffffff,0x000003f,0x0000000,0x3fc0000,0x2ffffff,0x3ffffff,0x3ffffff,
0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x00fffff
};
/* The Montogmery normalizer for modulus of the curve P384. */
static const sp_digit p384_norm_mod[15] = {
0x0000001,0x3ffffc0,0x3ffffff,0x003ffff,0x1000000,0x0000000,0x0000000,
0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000
};
/* The Montogmery multiplier for modulus of the curve P384. */
static sp_digit p384_mp_mod = 0x000001;
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* The order of the curve P384. */
static const sp_digit p384_order[15] = {
0x0c52973,0x3065ab3,0x277aece,0x2c922c2,0x3581a0d,0x10dcb77,0x234d81f,
0x3ffff1d,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x00fffff
};
#endif
/* The order of the curve P384 minus 2. */
static const sp_digit p384_order2[15] = {
0x0c52971,0x3065ab3,0x277aece,0x2c922c2,0x3581a0d,0x10dcb77,0x234d81f,
0x3ffff1d,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x3ffffff,0x00fffff
};
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* The Montogmery normalizer for order of the curve P384. */
static const sp_digit p384_norm_order[15] = {
0x33ad68d,0x0f9a54c,0x1885131,0x136dd3d,0x0a7e5f2,0x2f23488,0x1cb27e0,
0x00000e2,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000
};
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* The Montogmery multiplier for order of the curve P384. */
static sp_digit p384_mp_order = 0x8fdc45;
#endif
/* The base point of curve P384. */
static const sp_point_384 p384_base = {
/* X ordinate */
{
0x2760ab7,0x1178e1c,0x296c3a5,0x176fd54,0x05502f2,0x0950a8e,0x3741e08,
0x26e6167,0x3628ba7,0x11b874e,0x3320ad7,0x2c71c7b,0x305378e,0x288afa2,0x00aa87c,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* Y ordinate */
{
0x0ea0e5f,0x0c75f24,0x019d7a4,0x33875fa,0x00a60b1,0x17c2e30,0x1a3113b,
0x051f3a7,0x1bd289a,0x27e3d07,0x1292dc2,0x27a62fe,0x22c6f5d,0x392a589,0x003617d,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* Z ordinate */
{
0x0000001,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,
0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
},
/* infinity */
0
};
#if defined(HAVE_ECC_CHECK_KEY) || defined(HAVE_COMP_KEY)
static const sp_digit p384_b[15] = {
0x3ec2aef,0x1723b74,0x119d2a8,0x23628bb,0x2c65639,0x004e1d6,0x14088f5,
0x104480c,0x06efe81,0x2460767,0x23f82d1,0x23815af,0x2e7e498,0x3e9f88f,0x00b3312
};
#endif
static int sp_384_point_new_ex_15(void* heap, sp_point_384* sp, sp_point_384** p)
{
int ret = MP_OKAY;
(void)heap;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
(void)sp;
*p = (sp_point_384*)XMALLOC(sizeof(sp_point_384), heap, DYNAMIC_TYPE_ECC);
#else
*p = sp;
#endif
if (*p == NULL) {
ret = MEMORY_E;
}
return ret;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
/* Allocate memory for point and return error. */
#define sp_384_point_new_15(heap, sp, p) sp_384_point_new_ex_15((heap), NULL, &(p))
#else
/* Set pointer to data and return no error. */
#define sp_384_point_new_15(heap, sp, p) sp_384_point_new_ex_15((heap), &(sp), &(p))
#endif
static void sp_384_point_free_15(sp_point_384* p, int clear, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
/* If valid pointer then clear point data if requested and free data. */
if (p != NULL) {
if (clear != 0) {
XMEMSET(p, 0, sizeof(*p));
}
XFREE(p, heap, DYNAMIC_TYPE_ECC);
}
#else
/* Clear point data if requested. */
if (clear != 0) {
XMEMSET(p, 0, sizeof(*p));
}
#endif
(void)heap;
}
/* Multiply a number by Montogmery normalizer mod modulus (prime).
*
* r The resulting Montgomery form number.
* a The number to convert.
* m The modulus (prime).
* returns MEMORY_E when memory allocation fails and MP_OKAY otherwise.
*/
static int sp_384_mod_mul_norm_15(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
int64_t* td;
#else
int64_t td[12];
int64_t a32d[12];
#endif
int64_t* t;
int64_t* a32;
int64_t o;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (int64_t*)XMALLOC(sizeof(int64_t) * 2 * 12, NULL, DYNAMIC_TYPE_ECC);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = td;
a32 = td + 12;
#else
t = td;
a32 = a32d;
#endif
a32[0] = a[0];
a32[0] |= a[1] << 26U;
a32[0] &= 0xffffffffL;
a32[1] = (sp_digit)(a[1] >> 6);
a32[1] |= a[2] << 20U;
a32[1] &= 0xffffffffL;
a32[2] = (sp_digit)(a[2] >> 12);
a32[2] |= a[3] << 14U;
a32[2] &= 0xffffffffL;
a32[3] = (sp_digit)(a[3] >> 18);
a32[3] |= a[4] << 8U;
a32[3] &= 0xffffffffL;
a32[4] = (sp_digit)(a[4] >> 24);
a32[4] |= a[5] << 2U;
a32[4] |= a[6] << 28U;
a32[4] &= 0xffffffffL;
a32[5] = (sp_digit)(a[6] >> 4);
a32[5] |= a[7] << 22U;
a32[5] &= 0xffffffffL;
a32[6] = (sp_digit)(a[7] >> 10);
a32[6] |= a[8] << 16U;
a32[6] &= 0xffffffffL;
a32[7] = (sp_digit)(a[8] >> 16);
a32[7] |= a[9] << 10U;
a32[7] &= 0xffffffffL;
a32[8] = (sp_digit)(a[9] >> 22);
a32[8] |= a[10] << 4U;
a32[8] |= a[11] << 30U;
a32[8] &= 0xffffffffL;
a32[9] = (sp_digit)(a[11] >> 2);
a32[9] |= a[12] << 24U;
a32[9] &= 0xffffffffL;
a32[10] = (sp_digit)(a[12] >> 8);
a32[10] |= a[13] << 18U;
a32[10] &= 0xffffffffL;
a32[11] = (sp_digit)(a[13] >> 14);
a32[11] |= a[14] << 12U;
a32[11] &= 0xffffffffL;
/* 1 0 0 0 0 0 0 0 1 1 0 -1 */
t[0] = 0 + a32[0] + a32[8] + a32[9] - a32[11];
/* -1 1 0 0 0 0 0 0 -1 0 1 1 */
t[1] = 0 - a32[0] + a32[1] - a32[8] + a32[10] + a32[11];
/* 0 -1 1 0 0 0 0 0 0 -1 0 1 */
t[2] = 0 - a32[1] + a32[2] - a32[9] + a32[11];
/* 1 0 -1 1 0 0 0 0 1 1 -1 -1 */
t[3] = 0 + a32[0] - a32[2] + a32[3] + a32[8] + a32[9] - a32[10] - a32[11];
/* 1 1 0 -1 1 0 0 0 1 2 1 -2 */
t[4] = 0 + a32[0] + a32[1] - a32[3] + a32[4] + a32[8] + 2 * a32[9] + a32[10] - 2 * a32[11];
/* 0 1 1 0 -1 1 0 0 0 1 2 1 */
t[5] = 0 + a32[1] + a32[2] - a32[4] + a32[5] + a32[9] + 2 * a32[10] + a32[11];
/* 0 0 1 1 0 -1 1 0 0 0 1 2 */
t[6] = 0 + a32[2] + a32[3] - a32[5] + a32[6] + a32[10] + 2 * a32[11];
/* 0 0 0 1 1 0 -1 1 0 0 0 1 */
t[7] = 0 + a32[3] + a32[4] - a32[6] + a32[7] + a32[11];
/* 0 0 0 0 1 1 0 -1 1 0 0 0 */
t[8] = 0 + a32[4] + a32[5] - a32[7] + a32[8];
/* 0 0 0 0 0 1 1 0 -1 1 0 0 */
t[9] = 0 + a32[5] + a32[6] - a32[8] + a32[9];
/* 0 0 0 0 0 0 1 1 0 -1 1 0 */
t[10] = 0 + a32[6] + a32[7] - a32[9] + a32[10];
/* 0 0 0 0 0 0 0 1 1 0 -1 1 */
t[11] = 0 + a32[7] + a32[8] - a32[10] + a32[11];
t[1] += t[0] >> 32; t[0] &= 0xffffffff;
t[2] += t[1] >> 32; t[1] &= 0xffffffff;
t[3] += t[2] >> 32; t[2] &= 0xffffffff;
t[4] += t[3] >> 32; t[3] &= 0xffffffff;
t[5] += t[4] >> 32; t[4] &= 0xffffffff;
t[6] += t[5] >> 32; t[5] &= 0xffffffff;
t[7] += t[6] >> 32; t[6] &= 0xffffffff;
t[8] += t[7] >> 32; t[7] &= 0xffffffff;
t[9] += t[8] >> 32; t[8] &= 0xffffffff;
t[10] += t[9] >> 32; t[9] &= 0xffffffff;
t[11] += t[10] >> 32; t[10] &= 0xffffffff;
o = t[11] >> 32; t[11] &= 0xffffffff;
t[0] += o;
t[1] -= o;
t[3] += o;
t[4] += o;
t[1] += t[0] >> 32; t[0] &= 0xffffffff;
t[2] += t[1] >> 32; t[1] &= 0xffffffff;
t[3] += t[2] >> 32; t[2] &= 0xffffffff;
t[4] += t[3] >> 32; t[3] &= 0xffffffff;
t[5] += t[4] >> 32; t[4] &= 0xffffffff;
t[6] += t[5] >> 32; t[5] &= 0xffffffff;
t[7] += t[6] >> 32; t[6] &= 0xffffffff;
t[8] += t[7] >> 32; t[7] &= 0xffffffff;
t[9] += t[8] >> 32; t[8] &= 0xffffffff;
t[10] += t[9] >> 32; t[9] &= 0xffffffff;
t[11] += t[10] >> 32; t[10] &= 0xffffffff;
r[0] = (sp_digit)(t[0]) & 0x3ffffffL;
r[1] = (sp_digit)(t[0] >> 26U);
r[1] |= t[1] << 6U;
r[1] &= 0x3ffffffL;
r[2] = (sp_digit)(t[1] >> 20U);
r[2] |= t[2] << 12U;
r[2] &= 0x3ffffffL;
r[3] = (sp_digit)(t[2] >> 14U);
r[3] |= t[3] << 18U;
r[3] &= 0x3ffffffL;
r[4] = (sp_digit)(t[3] >> 8U);
r[4] |= t[4] << 24U;
r[4] &= 0x3ffffffL;
r[5] = (sp_digit)(t[4] >> 2U) & 0x3ffffffL;
r[6] = (sp_digit)(t[4] >> 28U);
r[6] |= t[5] << 4U;
r[6] &= 0x3ffffffL;
r[7] = (sp_digit)(t[5] >> 22U);
r[7] |= t[6] << 10U;
r[7] &= 0x3ffffffL;
r[8] = (sp_digit)(t[6] >> 16U);
r[8] |= t[7] << 16U;
r[8] &= 0x3ffffffL;
r[9] = (sp_digit)(t[7] >> 10U);
r[9] |= t[8] << 22U;
r[9] &= 0x3ffffffL;
r[10] = (sp_digit)(t[8] >> 4U) & 0x3ffffffL;
r[11] = (sp_digit)(t[8] >> 30U);
r[11] |= t[9] << 2U;
r[11] &= 0x3ffffffL;
r[12] = (sp_digit)(t[9] >> 24U);
r[12] |= t[10] << 8U;
r[12] &= 0x3ffffffL;
r[13] = (sp_digit)(t[10] >> 18U);
r[13] |= t[11] << 14U;
r[13] &= 0x3ffffffL;
r[14] = (sp_digit)(t[11] >> 12U);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL)
XFREE(td, NULL, DYNAMIC_TYPE_ECC);
#endif
return err;
}
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_384_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 26
int j;
XMEMCPY(r, a->dp, sizeof(sp_digit) * a->used);
for (j = a->used; j < size; j++) {
r[j] = 0;
}
#elif DIGIT_BIT > 26
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0x3ffffff;
s = 26U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 26U) <= (word32)DIGIT_BIT) {
s += 26U;
r[j] &= 0x3ffffff;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = 0L;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
int i, j = 0, s = 0;
r[0] = 0;
for (i = 0; i < a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 26) {
r[j] &= 0x3ffffff;
if (j + 1 >= size) {
break;
}
s = 26 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Convert a point of type ecc_point to type sp_point_384.
*
* p Point of type sp_point_384 (result).
* pm Point of type ecc_point.
*/
static void sp_384_point_from_ecc_point_15(sp_point_384* p, const ecc_point* pm)
{
XMEMSET(p->x, 0, sizeof(p->x));
XMEMSET(p->y, 0, sizeof(p->y));
XMEMSET(p->z, 0, sizeof(p->z));
sp_384_from_mp(p->x, 15, pm->x);
sp_384_from_mp(p->y, 15, pm->y);
sp_384_from_mp(p->z, 15, pm->z);
p->infinity = 0;
}
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_384_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (384 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 26
XMEMCPY(r->dp, a, sizeof(sp_digit) * 15);
r->used = 15;
mp_clamp(r);
#elif DIGIT_BIT < 26
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 15; i++) {
r->dp[j] |= (mp_digit)(a[i] << s);
r->dp[j] &= (1L << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = (mp_digit)(a[i] >> s);
while (s + DIGIT_BIT <= 26) {
s += DIGIT_BIT;
r->dp[j++] &= (1L << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = (mp_digit)(a[i] >> s);
}
}
s = 26 - s;
}
r->used = (384 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i, j = 0, s = 0;
r->dp[0] = 0;
for (i = 0; i < 15; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 26 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= (1L << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 26 - s;
}
else {
s += 26;
}
}
r->used = (384 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Convert a point of type sp_point_384 to type ecc_point.
*
* p Point of type sp_point_384.
* pm Point of type ecc_point (result).
* returns MEMORY_E when allocation of memory in ecc_point fails otherwise
* MP_OKAY.
*/
static int sp_384_point_to_ecc_point_15(const sp_point_384* p, ecc_point* pm)
{
int err;
err = sp_384_to_mp(p->x, pm->x);
if (err == MP_OKAY) {
err = sp_384_to_mp(p->y, pm->y);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->z, pm->z);
}
return err;
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_384_mul_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[14]) * b[14];
r[29] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 27; k >= 0; k--) {
for (i = 14; i >= 0; i--) {
j = k - i;
if (j >= 15) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * b[j];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
#else
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_384_mul_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int64_t t0 = ((int64_t)a[ 0]) * b[ 0];
int64_t t1 = ((int64_t)a[ 0]) * b[ 1]
+ ((int64_t)a[ 1]) * b[ 0];
int64_t t2 = ((int64_t)a[ 0]) * b[ 2]
+ ((int64_t)a[ 1]) * b[ 1]
+ ((int64_t)a[ 2]) * b[ 0];
int64_t t3 = ((int64_t)a[ 0]) * b[ 3]
+ ((int64_t)a[ 1]) * b[ 2]
+ ((int64_t)a[ 2]) * b[ 1]
+ ((int64_t)a[ 3]) * b[ 0];
int64_t t4 = ((int64_t)a[ 0]) * b[ 4]
+ ((int64_t)a[ 1]) * b[ 3]
+ ((int64_t)a[ 2]) * b[ 2]
+ ((int64_t)a[ 3]) * b[ 1]
+ ((int64_t)a[ 4]) * b[ 0];
int64_t t5 = ((int64_t)a[ 0]) * b[ 5]
+ ((int64_t)a[ 1]) * b[ 4]
+ ((int64_t)a[ 2]) * b[ 3]
+ ((int64_t)a[ 3]) * b[ 2]
+ ((int64_t)a[ 4]) * b[ 1]
+ ((int64_t)a[ 5]) * b[ 0];
int64_t t6 = ((int64_t)a[ 0]) * b[ 6]
+ ((int64_t)a[ 1]) * b[ 5]
+ ((int64_t)a[ 2]) * b[ 4]
+ ((int64_t)a[ 3]) * b[ 3]
+ ((int64_t)a[ 4]) * b[ 2]
+ ((int64_t)a[ 5]) * b[ 1]
+ ((int64_t)a[ 6]) * b[ 0];
int64_t t7 = ((int64_t)a[ 0]) * b[ 7]
+ ((int64_t)a[ 1]) * b[ 6]
+ ((int64_t)a[ 2]) * b[ 5]
+ ((int64_t)a[ 3]) * b[ 4]
+ ((int64_t)a[ 4]) * b[ 3]
+ ((int64_t)a[ 5]) * b[ 2]
+ ((int64_t)a[ 6]) * b[ 1]
+ ((int64_t)a[ 7]) * b[ 0];
int64_t t8 = ((int64_t)a[ 0]) * b[ 8]
+ ((int64_t)a[ 1]) * b[ 7]
+ ((int64_t)a[ 2]) * b[ 6]
+ ((int64_t)a[ 3]) * b[ 5]
+ ((int64_t)a[ 4]) * b[ 4]
+ ((int64_t)a[ 5]) * b[ 3]
+ ((int64_t)a[ 6]) * b[ 2]
+ ((int64_t)a[ 7]) * b[ 1]
+ ((int64_t)a[ 8]) * b[ 0];
int64_t t9 = ((int64_t)a[ 0]) * b[ 9]
+ ((int64_t)a[ 1]) * b[ 8]
+ ((int64_t)a[ 2]) * b[ 7]
+ ((int64_t)a[ 3]) * b[ 6]
+ ((int64_t)a[ 4]) * b[ 5]
+ ((int64_t)a[ 5]) * b[ 4]
+ ((int64_t)a[ 6]) * b[ 3]
+ ((int64_t)a[ 7]) * b[ 2]
+ ((int64_t)a[ 8]) * b[ 1]
+ ((int64_t)a[ 9]) * b[ 0];
int64_t t10 = ((int64_t)a[ 0]) * b[10]
+ ((int64_t)a[ 1]) * b[ 9]
+ ((int64_t)a[ 2]) * b[ 8]
+ ((int64_t)a[ 3]) * b[ 7]
+ ((int64_t)a[ 4]) * b[ 6]
+ ((int64_t)a[ 5]) * b[ 5]
+ ((int64_t)a[ 6]) * b[ 4]
+ ((int64_t)a[ 7]) * b[ 3]
+ ((int64_t)a[ 8]) * b[ 2]
+ ((int64_t)a[ 9]) * b[ 1]
+ ((int64_t)a[10]) * b[ 0];
int64_t t11 = ((int64_t)a[ 0]) * b[11]
+ ((int64_t)a[ 1]) * b[10]
+ ((int64_t)a[ 2]) * b[ 9]
+ ((int64_t)a[ 3]) * b[ 8]
+ ((int64_t)a[ 4]) * b[ 7]
+ ((int64_t)a[ 5]) * b[ 6]
+ ((int64_t)a[ 6]) * b[ 5]
+ ((int64_t)a[ 7]) * b[ 4]
+ ((int64_t)a[ 8]) * b[ 3]
+ ((int64_t)a[ 9]) * b[ 2]
+ ((int64_t)a[10]) * b[ 1]
+ ((int64_t)a[11]) * b[ 0];
int64_t t12 = ((int64_t)a[ 0]) * b[12]
+ ((int64_t)a[ 1]) * b[11]
+ ((int64_t)a[ 2]) * b[10]
+ ((int64_t)a[ 3]) * b[ 9]
+ ((int64_t)a[ 4]) * b[ 8]
+ ((int64_t)a[ 5]) * b[ 7]
+ ((int64_t)a[ 6]) * b[ 6]
+ ((int64_t)a[ 7]) * b[ 5]
+ ((int64_t)a[ 8]) * b[ 4]
+ ((int64_t)a[ 9]) * b[ 3]
+ ((int64_t)a[10]) * b[ 2]
+ ((int64_t)a[11]) * b[ 1]
+ ((int64_t)a[12]) * b[ 0];
int64_t t13 = ((int64_t)a[ 0]) * b[13]
+ ((int64_t)a[ 1]) * b[12]
+ ((int64_t)a[ 2]) * b[11]
+ ((int64_t)a[ 3]) * b[10]
+ ((int64_t)a[ 4]) * b[ 9]
+ ((int64_t)a[ 5]) * b[ 8]
+ ((int64_t)a[ 6]) * b[ 7]
+ ((int64_t)a[ 7]) * b[ 6]
+ ((int64_t)a[ 8]) * b[ 5]
+ ((int64_t)a[ 9]) * b[ 4]
+ ((int64_t)a[10]) * b[ 3]
+ ((int64_t)a[11]) * b[ 2]
+ ((int64_t)a[12]) * b[ 1]
+ ((int64_t)a[13]) * b[ 0];
int64_t t14 = ((int64_t)a[ 0]) * b[14]
+ ((int64_t)a[ 1]) * b[13]
+ ((int64_t)a[ 2]) * b[12]
+ ((int64_t)a[ 3]) * b[11]
+ ((int64_t)a[ 4]) * b[10]
+ ((int64_t)a[ 5]) * b[ 9]
+ ((int64_t)a[ 6]) * b[ 8]
+ ((int64_t)a[ 7]) * b[ 7]
+ ((int64_t)a[ 8]) * b[ 6]
+ ((int64_t)a[ 9]) * b[ 5]
+ ((int64_t)a[10]) * b[ 4]
+ ((int64_t)a[11]) * b[ 3]
+ ((int64_t)a[12]) * b[ 2]
+ ((int64_t)a[13]) * b[ 1]
+ ((int64_t)a[14]) * b[ 0];
int64_t t15 = ((int64_t)a[ 1]) * b[14]
+ ((int64_t)a[ 2]) * b[13]
+ ((int64_t)a[ 3]) * b[12]
+ ((int64_t)a[ 4]) * b[11]
+ ((int64_t)a[ 5]) * b[10]
+ ((int64_t)a[ 6]) * b[ 9]
+ ((int64_t)a[ 7]) * b[ 8]
+ ((int64_t)a[ 8]) * b[ 7]
+ ((int64_t)a[ 9]) * b[ 6]
+ ((int64_t)a[10]) * b[ 5]
+ ((int64_t)a[11]) * b[ 4]
+ ((int64_t)a[12]) * b[ 3]
+ ((int64_t)a[13]) * b[ 2]
+ ((int64_t)a[14]) * b[ 1];
int64_t t16 = ((int64_t)a[ 2]) * b[14]
+ ((int64_t)a[ 3]) * b[13]
+ ((int64_t)a[ 4]) * b[12]
+ ((int64_t)a[ 5]) * b[11]
+ ((int64_t)a[ 6]) * b[10]
+ ((int64_t)a[ 7]) * b[ 9]
+ ((int64_t)a[ 8]) * b[ 8]
+ ((int64_t)a[ 9]) * b[ 7]
+ ((int64_t)a[10]) * b[ 6]
+ ((int64_t)a[11]) * b[ 5]
+ ((int64_t)a[12]) * b[ 4]
+ ((int64_t)a[13]) * b[ 3]
+ ((int64_t)a[14]) * b[ 2];
int64_t t17 = ((int64_t)a[ 3]) * b[14]
+ ((int64_t)a[ 4]) * b[13]
+ ((int64_t)a[ 5]) * b[12]
+ ((int64_t)a[ 6]) * b[11]
+ ((int64_t)a[ 7]) * b[10]
+ ((int64_t)a[ 8]) * b[ 9]
+ ((int64_t)a[ 9]) * b[ 8]
+ ((int64_t)a[10]) * b[ 7]
+ ((int64_t)a[11]) * b[ 6]
+ ((int64_t)a[12]) * b[ 5]
+ ((int64_t)a[13]) * b[ 4]
+ ((int64_t)a[14]) * b[ 3];
int64_t t18 = ((int64_t)a[ 4]) * b[14]
+ ((int64_t)a[ 5]) * b[13]
+ ((int64_t)a[ 6]) * b[12]
+ ((int64_t)a[ 7]) * b[11]
+ ((int64_t)a[ 8]) * b[10]
+ ((int64_t)a[ 9]) * b[ 9]
+ ((int64_t)a[10]) * b[ 8]
+ ((int64_t)a[11]) * b[ 7]
+ ((int64_t)a[12]) * b[ 6]
+ ((int64_t)a[13]) * b[ 5]
+ ((int64_t)a[14]) * b[ 4];
int64_t t19 = ((int64_t)a[ 5]) * b[14]
+ ((int64_t)a[ 6]) * b[13]
+ ((int64_t)a[ 7]) * b[12]
+ ((int64_t)a[ 8]) * b[11]
+ ((int64_t)a[ 9]) * b[10]
+ ((int64_t)a[10]) * b[ 9]
+ ((int64_t)a[11]) * b[ 8]
+ ((int64_t)a[12]) * b[ 7]
+ ((int64_t)a[13]) * b[ 6]
+ ((int64_t)a[14]) * b[ 5];
int64_t t20 = ((int64_t)a[ 6]) * b[14]
+ ((int64_t)a[ 7]) * b[13]
+ ((int64_t)a[ 8]) * b[12]
+ ((int64_t)a[ 9]) * b[11]
+ ((int64_t)a[10]) * b[10]
+ ((int64_t)a[11]) * b[ 9]
+ ((int64_t)a[12]) * b[ 8]
+ ((int64_t)a[13]) * b[ 7]
+ ((int64_t)a[14]) * b[ 6];
int64_t t21 = ((int64_t)a[ 7]) * b[14]
+ ((int64_t)a[ 8]) * b[13]
+ ((int64_t)a[ 9]) * b[12]
+ ((int64_t)a[10]) * b[11]
+ ((int64_t)a[11]) * b[10]
+ ((int64_t)a[12]) * b[ 9]
+ ((int64_t)a[13]) * b[ 8]
+ ((int64_t)a[14]) * b[ 7];
int64_t t22 = ((int64_t)a[ 8]) * b[14]
+ ((int64_t)a[ 9]) * b[13]
+ ((int64_t)a[10]) * b[12]
+ ((int64_t)a[11]) * b[11]
+ ((int64_t)a[12]) * b[10]
+ ((int64_t)a[13]) * b[ 9]
+ ((int64_t)a[14]) * b[ 8];
int64_t t23 = ((int64_t)a[ 9]) * b[14]
+ ((int64_t)a[10]) * b[13]
+ ((int64_t)a[11]) * b[12]
+ ((int64_t)a[12]) * b[11]
+ ((int64_t)a[13]) * b[10]
+ ((int64_t)a[14]) * b[ 9];
int64_t t24 = ((int64_t)a[10]) * b[14]
+ ((int64_t)a[11]) * b[13]
+ ((int64_t)a[12]) * b[12]
+ ((int64_t)a[13]) * b[11]
+ ((int64_t)a[14]) * b[10];
int64_t t25 = ((int64_t)a[11]) * b[14]
+ ((int64_t)a[12]) * b[13]
+ ((int64_t)a[13]) * b[12]
+ ((int64_t)a[14]) * b[11];
int64_t t26 = ((int64_t)a[12]) * b[14]
+ ((int64_t)a[13]) * b[13]
+ ((int64_t)a[14]) * b[12];
int64_t t27 = ((int64_t)a[13]) * b[14]
+ ((int64_t)a[14]) * b[13];
int64_t t28 = ((int64_t)a[14]) * b[14];
t1 += t0 >> 26; r[ 0] = t0 & 0x3ffffff;
t2 += t1 >> 26; r[ 1] = t1 & 0x3ffffff;
t3 += t2 >> 26; r[ 2] = t2 & 0x3ffffff;
t4 += t3 >> 26; r[ 3] = t3 & 0x3ffffff;
t5 += t4 >> 26; r[ 4] = t4 & 0x3ffffff;
t6 += t5 >> 26; r[ 5] = t5 & 0x3ffffff;
t7 += t6 >> 26; r[ 6] = t6 & 0x3ffffff;
t8 += t7 >> 26; r[ 7] = t7 & 0x3ffffff;
t9 += t8 >> 26; r[ 8] = t8 & 0x3ffffff;
t10 += t9 >> 26; r[ 9] = t9 & 0x3ffffff;
t11 += t10 >> 26; r[10] = t10 & 0x3ffffff;
t12 += t11 >> 26; r[11] = t11 & 0x3ffffff;
t13 += t12 >> 26; r[12] = t12 & 0x3ffffff;
t14 += t13 >> 26; r[13] = t13 & 0x3ffffff;
t15 += t14 >> 26; r[14] = t14 & 0x3ffffff;
t16 += t15 >> 26; r[15] = t15 & 0x3ffffff;
t17 += t16 >> 26; r[16] = t16 & 0x3ffffff;
t18 += t17 >> 26; r[17] = t17 & 0x3ffffff;
t19 += t18 >> 26; r[18] = t18 & 0x3ffffff;
t20 += t19 >> 26; r[19] = t19 & 0x3ffffff;
t21 += t20 >> 26; r[20] = t20 & 0x3ffffff;
t22 += t21 >> 26; r[21] = t21 & 0x3ffffff;
t23 += t22 >> 26; r[22] = t22 & 0x3ffffff;
t24 += t23 >> 26; r[23] = t23 & 0x3ffffff;
t25 += t24 >> 26; r[24] = t24 & 0x3ffffff;
t26 += t25 >> 26; r[25] = t25 & 0x3ffffff;
t27 += t26 >> 26; r[26] = t26 & 0x3ffffff;
t28 += t27 >> 26; r[27] = t27 & 0x3ffffff;
r[29] = (sp_digit)(t28 >> 26);
r[28] = t28 & 0x3ffffff;
}
#endif /* WOLFSSL_SP_SMALL */
#define sp_384_mont_reduce_order_15 sp_384_mont_reduce_15
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_384_cmp_15(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=14; i>=0; i--) {
r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
}
#else
r |= (a[14] - b[14]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[13] - b[13]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[12] - b[12]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[11] - b[11]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[10] - b[10]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 9] - b[ 9]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 8] - b[ 8]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 7] - b[ 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 6] - b[ 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 5] - b[ 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 4] - b[ 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 3] - b[ 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 2] - b[ 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 1] - b[ 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
r |= (a[ 0] - b[ 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_384_cond_sub_15(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 15; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
r[ 0] = a[ 0] - (b[ 0] & m);
r[ 1] = a[ 1] - (b[ 1] & m);
r[ 2] = a[ 2] - (b[ 2] & m);
r[ 3] = a[ 3] - (b[ 3] & m);
r[ 4] = a[ 4] - (b[ 4] & m);
r[ 5] = a[ 5] - (b[ 5] & m);
r[ 6] = a[ 6] - (b[ 6] & m);
r[ 7] = a[ 7] - (b[ 7] & m);
r[ 8] = a[ 8] - (b[ 8] & m);
r[ 9] = a[ 9] - (b[ 9] & m);
r[10] = a[10] - (b[10] & m);
r[11] = a[11] - (b[11] & m);
r[12] = a[12] - (b[12] & m);
r[13] = a[13] - (b[13] & m);
r[14] = a[14] - (b[14] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_384_mul_add_15(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 15; i++) {
t += (tb * a[i]) + r[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[15] += t;
#else
int64_t tb = b;
int64_t t[15];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
t[ 5] = tb * a[ 5];
t[ 6] = tb * a[ 6];
t[ 7] = tb * a[ 7];
t[ 8] = tb * a[ 8];
t[ 9] = tb * a[ 9];
t[10] = tb * a[10];
t[11] = tb * a[11];
t[12] = tb * a[12];
t[13] = tb * a[13];
t[14] = tb * a[14];
r[ 0] += (sp_digit) (t[ 0] & 0x3ffffff);
r[ 1] += (sp_digit)((t[ 0] >> 26) + (t[ 1] & 0x3ffffff));
r[ 2] += (sp_digit)((t[ 1] >> 26) + (t[ 2] & 0x3ffffff));
r[ 3] += (sp_digit)((t[ 2] >> 26) + (t[ 3] & 0x3ffffff));
r[ 4] += (sp_digit)((t[ 3] >> 26) + (t[ 4] & 0x3ffffff));
r[ 5] += (sp_digit)((t[ 4] >> 26) + (t[ 5] & 0x3ffffff));
r[ 6] += (sp_digit)((t[ 5] >> 26) + (t[ 6] & 0x3ffffff));
r[ 7] += (sp_digit)((t[ 6] >> 26) + (t[ 7] & 0x3ffffff));
r[ 8] += (sp_digit)((t[ 7] >> 26) + (t[ 8] & 0x3ffffff));
r[ 9] += (sp_digit)((t[ 8] >> 26) + (t[ 9] & 0x3ffffff));
r[10] += (sp_digit)((t[ 9] >> 26) + (t[10] & 0x3ffffff));
r[11] += (sp_digit)((t[10] >> 26) + (t[11] & 0x3ffffff));
r[12] += (sp_digit)((t[11] >> 26) + (t[12] & 0x3ffffff));
r[13] += (sp_digit)((t[12] >> 26) + (t[13] & 0x3ffffff));
r[14] += (sp_digit)((t[13] >> 26) + (t[14] & 0x3ffffff));
r[15] += (sp_digit) (t[14] >> 26);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 26.
*
* a Array of sp_digit to normalize.
*/
static void sp_384_norm_15(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 14; i++) {
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
}
#else
a[1] += a[0] >> 26; a[0] &= 0x3ffffff;
a[2] += a[1] >> 26; a[1] &= 0x3ffffff;
a[3] += a[2] >> 26; a[2] &= 0x3ffffff;
a[4] += a[3] >> 26; a[3] &= 0x3ffffff;
a[5] += a[4] >> 26; a[4] &= 0x3ffffff;
a[6] += a[5] >> 26; a[5] &= 0x3ffffff;
a[7] += a[6] >> 26; a[6] &= 0x3ffffff;
a[8] += a[7] >> 26; a[7] &= 0x3ffffff;
a[9] += a[8] >> 26; a[8] &= 0x3ffffff;
a[10] += a[9] >> 26; a[9] &= 0x3ffffff;
a[11] += a[10] >> 26; a[10] &= 0x3ffffff;
a[12] += a[11] >> 26; a[11] &= 0x3ffffff;
a[13] += a[12] >> 26; a[12] &= 0x3ffffff;
a[14] += a[13] >> 26; a[13] &= 0x3ffffff;
#endif
}
/* Shift the result in the high 384 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_384_mont_shift_15(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
int64_t n = a[14] >> 20;
n += ((int64_t)a[15]) << 6;
for (i = 0; i < 14; i++) {
r[i] = n & 0x3ffffff;
n >>= 26;
n += ((int64_t)a[16 + i]) << 6;
}
r[14] = (sp_digit)n;
#else
int64_t n = a[14] >> 20;
n += ((int64_t)a[15]) << 6;
r[ 0] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[16]) << 6;
r[ 1] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[17]) << 6;
r[ 2] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[18]) << 6;
r[ 3] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[19]) << 6;
r[ 4] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[20]) << 6;
r[ 5] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[21]) << 6;
r[ 6] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[22]) << 6;
r[ 7] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[23]) << 6;
r[ 8] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[24]) << 6;
r[ 9] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[25]) << 6;
r[10] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[26]) << 6;
r[11] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[27]) << 6;
r[12] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[28]) << 6;
r[13] = n & 0x3ffffff; n >>= 26; n += ((int64_t)a[29]) << 6;
r[14] = (sp_digit)n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[15], 0, sizeof(*r) * 15U);
}
/* Reduce the number back to 384 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_384_mont_reduce_15(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
sp_384_norm_15(a + 15);
for (i=0; i<14; i++) {
mu = (a[i] * mp) & 0x3ffffff;
sp_384_mul_add_15(a+i, m, mu);
a[i+1] += a[i] >> 26;
}
mu = (a[i] * mp) & 0xfffffL;
sp_384_mul_add_15(a+i, m, mu);
a[i+1] += a[i] >> 26;
a[i] &= 0x3ffffff;
sp_384_mont_shift_15(a, a);
sp_384_cond_sub_15(a, a, m, 0 - (((a[14] >> 20) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(a);
}
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_384_mont_mul_15(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m, sp_digit mp)
{
sp_384_mul_15(r, a, b);
sp_384_mont_reduce_15(r, m, mp);
}
#ifdef WOLFSSL_SP_SMALL
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_384_sqr_15(sp_digit* r, const sp_digit* a)
{
int i, j, k;
int64_t c;
c = ((int64_t)a[14]) * a[14];
r[29] = (sp_digit)(c >> 26);
c = (c & 0x3ffffff) << 26;
for (k = 27; k >= 0; k--) {
for (i = 14; i >= 0; i--) {
j = k - i;
if (j >= 15 || i <= j) {
break;
}
if (j < 0) {
continue;
}
c += ((int64_t)a[i]) * a[j] * 2;
}
if (i == j) {
c += ((int64_t)a[i]) * a[i];
}
r[k + 2] += c >> 52;
r[k + 1] = (c >> 26) & 0x3ffffff;
c = (c & 0x3ffffff) << 26;
}
r[0] = (sp_digit)(c >> 26);
}
#else
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_384_sqr_15(sp_digit* r, const sp_digit* a)
{
int64_t t0 = ((int64_t)a[ 0]) * a[ 0];
int64_t t1 = (((int64_t)a[ 0]) * a[ 1]) * 2;
int64_t t2 = (((int64_t)a[ 0]) * a[ 2]) * 2
+ ((int64_t)a[ 1]) * a[ 1];
int64_t t3 = (((int64_t)a[ 0]) * a[ 3]
+ ((int64_t)a[ 1]) * a[ 2]) * 2;
int64_t t4 = (((int64_t)a[ 0]) * a[ 4]
+ ((int64_t)a[ 1]) * a[ 3]) * 2
+ ((int64_t)a[ 2]) * a[ 2];
int64_t t5 = (((int64_t)a[ 0]) * a[ 5]
+ ((int64_t)a[ 1]) * a[ 4]
+ ((int64_t)a[ 2]) * a[ 3]) * 2;
int64_t t6 = (((int64_t)a[ 0]) * a[ 6]
+ ((int64_t)a[ 1]) * a[ 5]
+ ((int64_t)a[ 2]) * a[ 4]) * 2
+ ((int64_t)a[ 3]) * a[ 3];
int64_t t7 = (((int64_t)a[ 0]) * a[ 7]
+ ((int64_t)a[ 1]) * a[ 6]
+ ((int64_t)a[ 2]) * a[ 5]
+ ((int64_t)a[ 3]) * a[ 4]) * 2;
int64_t t8 = (((int64_t)a[ 0]) * a[ 8]
+ ((int64_t)a[ 1]) * a[ 7]
+ ((int64_t)a[ 2]) * a[ 6]
+ ((int64_t)a[ 3]) * a[ 5]) * 2
+ ((int64_t)a[ 4]) * a[ 4];
int64_t t9 = (((int64_t)a[ 0]) * a[ 9]
+ ((int64_t)a[ 1]) * a[ 8]
+ ((int64_t)a[ 2]) * a[ 7]
+ ((int64_t)a[ 3]) * a[ 6]
+ ((int64_t)a[ 4]) * a[ 5]) * 2;
int64_t t10 = (((int64_t)a[ 0]) * a[10]
+ ((int64_t)a[ 1]) * a[ 9]
+ ((int64_t)a[ 2]) * a[ 8]
+ ((int64_t)a[ 3]) * a[ 7]
+ ((int64_t)a[ 4]) * a[ 6]) * 2
+ ((int64_t)a[ 5]) * a[ 5];
int64_t t11 = (((int64_t)a[ 0]) * a[11]
+ ((int64_t)a[ 1]) * a[10]
+ ((int64_t)a[ 2]) * a[ 9]
+ ((int64_t)a[ 3]) * a[ 8]
+ ((int64_t)a[ 4]) * a[ 7]
+ ((int64_t)a[ 5]) * a[ 6]) * 2;
int64_t t12 = (((int64_t)a[ 0]) * a[12]
+ ((int64_t)a[ 1]) * a[11]
+ ((int64_t)a[ 2]) * a[10]
+ ((int64_t)a[ 3]) * a[ 9]
+ ((int64_t)a[ 4]) * a[ 8]
+ ((int64_t)a[ 5]) * a[ 7]) * 2
+ ((int64_t)a[ 6]) * a[ 6];
int64_t t13 = (((int64_t)a[ 0]) * a[13]
+ ((int64_t)a[ 1]) * a[12]
+ ((int64_t)a[ 2]) * a[11]
+ ((int64_t)a[ 3]) * a[10]
+ ((int64_t)a[ 4]) * a[ 9]
+ ((int64_t)a[ 5]) * a[ 8]
+ ((int64_t)a[ 6]) * a[ 7]) * 2;
int64_t t14 = (((int64_t)a[ 0]) * a[14]
+ ((int64_t)a[ 1]) * a[13]
+ ((int64_t)a[ 2]) * a[12]
+ ((int64_t)a[ 3]) * a[11]
+ ((int64_t)a[ 4]) * a[10]
+ ((int64_t)a[ 5]) * a[ 9]
+ ((int64_t)a[ 6]) * a[ 8]) * 2
+ ((int64_t)a[ 7]) * a[ 7];
int64_t t15 = (((int64_t)a[ 1]) * a[14]
+ ((int64_t)a[ 2]) * a[13]
+ ((int64_t)a[ 3]) * a[12]
+ ((int64_t)a[ 4]) * a[11]
+ ((int64_t)a[ 5]) * a[10]
+ ((int64_t)a[ 6]) * a[ 9]
+ ((int64_t)a[ 7]) * a[ 8]) * 2;
int64_t t16 = (((int64_t)a[ 2]) * a[14]
+ ((int64_t)a[ 3]) * a[13]
+ ((int64_t)a[ 4]) * a[12]
+ ((int64_t)a[ 5]) * a[11]
+ ((int64_t)a[ 6]) * a[10]
+ ((int64_t)a[ 7]) * a[ 9]) * 2
+ ((int64_t)a[ 8]) * a[ 8];
int64_t t17 = (((int64_t)a[ 3]) * a[14]
+ ((int64_t)a[ 4]) * a[13]
+ ((int64_t)a[ 5]) * a[12]
+ ((int64_t)a[ 6]) * a[11]
+ ((int64_t)a[ 7]) * a[10]
+ ((int64_t)a[ 8]) * a[ 9]) * 2;
int64_t t18 = (((int64_t)a[ 4]) * a[14]
+ ((int64_t)a[ 5]) * a[13]
+ ((int64_t)a[ 6]) * a[12]
+ ((int64_t)a[ 7]) * a[11]
+ ((int64_t)a[ 8]) * a[10]) * 2
+ ((int64_t)a[ 9]) * a[ 9];
int64_t t19 = (((int64_t)a[ 5]) * a[14]
+ ((int64_t)a[ 6]) * a[13]
+ ((int64_t)a[ 7]) * a[12]
+ ((int64_t)a[ 8]) * a[11]
+ ((int64_t)a[ 9]) * a[10]) * 2;
int64_t t20 = (((int64_t)a[ 6]) * a[14]
+ ((int64_t)a[ 7]) * a[13]
+ ((int64_t)a[ 8]) * a[12]
+ ((int64_t)a[ 9]) * a[11]) * 2
+ ((int64_t)a[10]) * a[10];
int64_t t21 = (((int64_t)a[ 7]) * a[14]
+ ((int64_t)a[ 8]) * a[13]
+ ((int64_t)a[ 9]) * a[12]
+ ((int64_t)a[10]) * a[11]) * 2;
int64_t t22 = (((int64_t)a[ 8]) * a[14]
+ ((int64_t)a[ 9]) * a[13]
+ ((int64_t)a[10]) * a[12]) * 2
+ ((int64_t)a[11]) * a[11];
int64_t t23 = (((int64_t)a[ 9]) * a[14]
+ ((int64_t)a[10]) * a[13]
+ ((int64_t)a[11]) * a[12]) * 2;
int64_t t24 = (((int64_t)a[10]) * a[14]
+ ((int64_t)a[11]) * a[13]) * 2
+ ((int64_t)a[12]) * a[12];
int64_t t25 = (((int64_t)a[11]) * a[14]
+ ((int64_t)a[12]) * a[13]) * 2;
int64_t t26 = (((int64_t)a[12]) * a[14]) * 2
+ ((int64_t)a[13]) * a[13];
int64_t t27 = (((int64_t)a[13]) * a[14]) * 2;
int64_t t28 = ((int64_t)a[14]) * a[14];
t1 += t0 >> 26; r[ 0] = t0 & 0x3ffffff;
t2 += t1 >> 26; r[ 1] = t1 & 0x3ffffff;
t3 += t2 >> 26; r[ 2] = t2 & 0x3ffffff;
t4 += t3 >> 26; r[ 3] = t3 & 0x3ffffff;
t5 += t4 >> 26; r[ 4] = t4 & 0x3ffffff;
t6 += t5 >> 26; r[ 5] = t5 & 0x3ffffff;
t7 += t6 >> 26; r[ 6] = t6 & 0x3ffffff;
t8 += t7 >> 26; r[ 7] = t7 & 0x3ffffff;
t9 += t8 >> 26; r[ 8] = t8 & 0x3ffffff;
t10 += t9 >> 26; r[ 9] = t9 & 0x3ffffff;
t11 += t10 >> 26; r[10] = t10 & 0x3ffffff;
t12 += t11 >> 26; r[11] = t11 & 0x3ffffff;
t13 += t12 >> 26; r[12] = t12 & 0x3ffffff;
t14 += t13 >> 26; r[13] = t13 & 0x3ffffff;
t15 += t14 >> 26; r[14] = t14 & 0x3ffffff;
t16 += t15 >> 26; r[15] = t15 & 0x3ffffff;
t17 += t16 >> 26; r[16] = t16 & 0x3ffffff;
t18 += t17 >> 26; r[17] = t17 & 0x3ffffff;
t19 += t18 >> 26; r[18] = t18 & 0x3ffffff;
t20 += t19 >> 26; r[19] = t19 & 0x3ffffff;
t21 += t20 >> 26; r[20] = t20 & 0x3ffffff;
t22 += t21 >> 26; r[21] = t21 & 0x3ffffff;
t23 += t22 >> 26; r[22] = t22 & 0x3ffffff;
t24 += t23 >> 26; r[23] = t23 & 0x3ffffff;
t25 += t24 >> 26; r[24] = t24 & 0x3ffffff;
t26 += t25 >> 26; r[25] = t25 & 0x3ffffff;
t27 += t26 >> 26; r[26] = t26 & 0x3ffffff;
t28 += t27 >> 26; r[27] = t27 & 0x3ffffff;
r[29] = (sp_digit)(t28 >> 26);
r[28] = t28 & 0x3ffffff;
}
#endif /* WOLFSSL_SP_SMALL */
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_384_mont_sqr_15(sp_digit* r, const sp_digit* a, const sp_digit* m,
sp_digit mp)
{
sp_384_sqr_15(r, a);
sp_384_mont_reduce_15(r, m, mp);
}
#if !defined(WOLFSSL_SP_SMALL) || defined(HAVE_COMP_KEY)
/* Square the Montgomery form number a number of times. (r = a ^ n mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* n Number of times to square.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
static void sp_384_mont_sqr_n_15(sp_digit* r, const sp_digit* a, int n,
const sp_digit* m, sp_digit mp)
{
sp_384_mont_sqr_15(r, a, m, mp);
for (; n > 1; n--) {
sp_384_mont_sqr_15(r, r, m, mp);
}
}
#endif /* !WOLFSSL_SP_SMALL || HAVE_COMP_KEY */
#ifdef WOLFSSL_SP_SMALL
/* Mod-2 for the P384 curve. */
static const uint32_t p384_mod_minus_2[12] = {
0xfffffffdU,0x00000000U,0x00000000U,0xffffffffU,0xfffffffeU,0xffffffffU,
0xffffffffU,0xffffffffU,0xffffffffU,0xffffffffU,0xffffffffU,0xffffffffU
};
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
* P384 curve. (r = 1 / a mod m)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_384_mont_inv_15(sp_digit* r, const sp_digit* a, sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 15);
for (i=382; i>=0; i--) {
sp_384_mont_sqr_15(t, t, p384_mod, p384_mp_mod);
if (p384_mod_minus_2[i / 32] & ((sp_digit)1 << (i % 32)))
sp_384_mont_mul_15(t, t, a, p384_mod, p384_mp_mod);
}
XMEMCPY(r, t, sizeof(sp_digit) * 15);
#else
sp_digit* t1 = td;
sp_digit* t2 = td + 2 * 15;
sp_digit* t3 = td + 4 * 15;
sp_digit* t4 = td + 6 * 15;
sp_digit* t5 = td + 8 * 15;
/* 0x2 */
sp_384_mont_sqr_15(t1, a, p384_mod, p384_mp_mod);
/* 0x3 */
sp_384_mont_mul_15(t5, t1, a, p384_mod, p384_mp_mod);
/* 0xc */
sp_384_mont_sqr_n_15(t1, t5, 2, p384_mod, p384_mp_mod);
/* 0xf */
sp_384_mont_mul_15(t2, t5, t1, p384_mod, p384_mp_mod);
/* 0x1e */
sp_384_mont_sqr_15(t1, t2, p384_mod, p384_mp_mod);
/* 0x1f */
sp_384_mont_mul_15(t4, t1, a, p384_mod, p384_mp_mod);
/* 0x3e0 */
sp_384_mont_sqr_n_15(t1, t4, 5, p384_mod, p384_mp_mod);
/* 0x3ff */
sp_384_mont_mul_15(t2, t4, t1, p384_mod, p384_mp_mod);
/* 0x7fe0 */
sp_384_mont_sqr_n_15(t1, t2, 5, p384_mod, p384_mp_mod);
/* 0x7fff */
sp_384_mont_mul_15(t4, t4, t1, p384_mod, p384_mp_mod);
/* 0x3fff8000 */
sp_384_mont_sqr_n_15(t1, t4, 15, p384_mod, p384_mp_mod);
/* 0x3fffffff */
sp_384_mont_mul_15(t2, t4, t1, p384_mod, p384_mp_mod);
/* 0xfffffffc */
sp_384_mont_sqr_n_15(t3, t2, 2, p384_mod, p384_mp_mod);
/* 0xfffffffd */
sp_384_mont_mul_15(r, t3, a, p384_mod, p384_mp_mod);
/* 0xffffffff */
sp_384_mont_mul_15(t3, t5, t3, p384_mod, p384_mp_mod);
/* 0xfffffffc0000000 */
sp_384_mont_sqr_n_15(t1, t2, 30, p384_mod, p384_mp_mod);
/* 0xfffffffffffffff */
sp_384_mont_mul_15(t2, t2, t1, p384_mod, p384_mp_mod);
/* 0xfffffffffffffff000000000000000 */
sp_384_mont_sqr_n_15(t1, t2, 60, p384_mod, p384_mp_mod);
/* 0xffffffffffffffffffffffffffffff */
sp_384_mont_mul_15(t2, t2, t1, p384_mod, p384_mp_mod);
/* 0xffffffffffffffffffffffffffffff000000000000000000000000000000 */
sp_384_mont_sqr_n_15(t1, t2, 120, p384_mod, p384_mp_mod);
/* 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff */
sp_384_mont_mul_15(t2, t2, t1, p384_mod, p384_mp_mod);
/* 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8000 */
sp_384_mont_sqr_n_15(t1, t2, 15, p384_mod, p384_mp_mod);
/* 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff */
sp_384_mont_mul_15(t2, t4, t1, p384_mod, p384_mp_mod);
/* 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe00000000 */
sp_384_mont_sqr_n_15(t1, t2, 33, p384_mod, p384_mp_mod);
/* 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff */
sp_384_mont_mul_15(t2, t3, t1, p384_mod, p384_mp_mod);
/* 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff000000000000000000000000 */
sp_384_mont_sqr_n_15(t1, t2, 96, p384_mod, p384_mp_mod);
/* 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffd */
sp_384_mont_mul_15(r, r, t1, p384_mod, p384_mp_mod);
#endif /* WOLFSSL_SP_SMALL */
}
/* Map the Montgomery form projective coordinate point to an affine point.
*
* r Resulting affine coordinate point.
* p Montgomery form projective coordinate point.
* t Temporary ordinate data.
*/
static void sp_384_map_15(sp_point_384* r, const sp_point_384* p, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*15;
int32_t n;
sp_384_mont_inv_15(t1, p->z, t + 2*15);
sp_384_mont_sqr_15(t2, t1, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t1, t2, t1, p384_mod, p384_mp_mod);
/* x /= z^2 */
sp_384_mont_mul_15(r->x, p->x, t2, p384_mod, p384_mp_mod);
XMEMSET(r->x + 15, 0, sizeof(r->x) / 2U);
sp_384_mont_reduce_15(r->x, p384_mod, p384_mp_mod);
/* Reduce x to less than modulus */
n = sp_384_cmp_15(r->x, p384_mod);
sp_384_cond_sub_15(r->x, r->x, p384_mod, 0 - ((n >= 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(r->x);
/* y /= z^3 */
sp_384_mont_mul_15(r->y, p->y, t1, p384_mod, p384_mp_mod);
XMEMSET(r->y + 15, 0, sizeof(r->y) / 2U);
sp_384_mont_reduce_15(r->y, p384_mod, p384_mp_mod);
/* Reduce y to less than modulus */
n = sp_384_cmp_15(r->y, p384_mod);
sp_384_cond_sub_15(r->y, r->y, p384_mod, 0 - ((n >= 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(r->y);
XMEMSET(r->z, 0, sizeof(r->z));
r->z[0] = 1;
}
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_384_add_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 15; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#else
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_384_add_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] + b[ 0];
r[ 1] = a[ 1] + b[ 1];
r[ 2] = a[ 2] + b[ 2];
r[ 3] = a[ 3] + b[ 3];
r[ 4] = a[ 4] + b[ 4];
r[ 5] = a[ 5] + b[ 5];
r[ 6] = a[ 6] + b[ 6];
r[ 7] = a[ 7] + b[ 7];
r[ 8] = a[ 8] + b[ 8];
r[ 9] = a[ 9] + b[ 9];
r[10] = a[10] + b[10];
r[11] = a[11] + b[11];
r[12] = a[12] + b[12];
r[13] = a[13] + b[13];
r[14] = a[14] + b[14];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Add two Montgomery form numbers (r = a + b % m).
*
* r Result of addition.
* a First number to add in Montogmery form.
* b Second number to add in Montogmery form.
* m Modulus (prime).
*/
static void sp_384_mont_add_15(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
(void)sp_384_add_15(r, a, b);
sp_384_norm_15(r);
sp_384_cond_sub_15(r, r, m, 0 - (((r[14] >> 20) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(r);
}
/* Double a Montgomery form number (r = a + a % m).
*
* r Result of doubling.
* a Number to double in Montogmery form.
* m Modulus (prime).
*/
static void sp_384_mont_dbl_15(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
(void)sp_384_add_15(r, a, a);
sp_384_norm_15(r);
sp_384_cond_sub_15(r, r, m, 0 - (((r[14] >> 20) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(r);
}
/* Triple a Montgomery form number (r = a + a + a % m).
*
* r Result of Tripling.
* a Number to triple in Montogmery form.
* m Modulus (prime).
*/
static void sp_384_mont_tpl_15(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
(void)sp_384_add_15(r, a, a);
sp_384_norm_15(r);
sp_384_cond_sub_15(r, r, m, 0 - (((r[14] >> 20) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(r);
(void)sp_384_add_15(r, r, a);
sp_384_norm_15(r);
sp_384_cond_sub_15(r, r, m, 0 - (((r[14] >> 20) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_384_norm_15(r);
}
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_384_sub_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 15; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_384_sub_15(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] - b[ 0];
r[ 1] = a[ 1] - b[ 1];
r[ 2] = a[ 2] - b[ 2];
r[ 3] = a[ 3] - b[ 3];
r[ 4] = a[ 4] - b[ 4];
r[ 5] = a[ 5] - b[ 5];
r[ 6] = a[ 6] - b[ 6];
r[ 7] = a[ 7] - b[ 7];
r[ 8] = a[ 8] - b[ 8];
r[ 9] = a[ 9] - b[ 9];
r[10] = a[10] - b[10];
r[11] = a[11] - b[11];
r[12] = a[12] - b[12];
r[13] = a[13] - b[13];
r[14] = a[14] - b[14];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Conditionally add a and b using the mask m.
* m is -1 to add and 0 when not.
*
* r A single precision number representing conditional add result.
* a A single precision number to add with.
* b A single precision number to add.
* m Mask value to apply.
*/
static void sp_384_cond_add_15(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 15; i++) {
r[i] = a[i] + (b[i] & m);
}
#else
r[ 0] = a[ 0] + (b[ 0] & m);
r[ 1] = a[ 1] + (b[ 1] & m);
r[ 2] = a[ 2] + (b[ 2] & m);
r[ 3] = a[ 3] + (b[ 3] & m);
r[ 4] = a[ 4] + (b[ 4] & m);
r[ 5] = a[ 5] + (b[ 5] & m);
r[ 6] = a[ 6] + (b[ 6] & m);
r[ 7] = a[ 7] + (b[ 7] & m);
r[ 8] = a[ 8] + (b[ 8] & m);
r[ 9] = a[ 9] + (b[ 9] & m);
r[10] = a[10] + (b[10] & m);
r[11] = a[11] + (b[11] & m);
r[12] = a[12] + (b[12] & m);
r[13] = a[13] + (b[13] & m);
r[14] = a[14] + (b[14] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Subtract two Montgomery form numbers (r = a - b % m).
*
* r Result of subtration.
* a Number to subtract from in Montogmery form.
* b Number to subtract with in Montogmery form.
* m Modulus (prime).
*/
static void sp_384_mont_sub_15(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
(void)sp_384_sub_15(r, a, b);
sp_384_cond_add_15(r, r, m, r[14] >> 20);
sp_384_norm_15(r);
}
/* Shift number left one bit.
* Bottom bit is lost.
*
* r Result of shift.
* a Number to shift.
*/
SP_NOINLINE static void sp_384_rshift1_15(sp_digit* r, sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=0; i<14; i++) {
r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
}
#else
r[0] = ((a[0] >> 1) | (a[1] << 25)) & 0x3ffffff;
r[1] = ((a[1] >> 1) | (a[2] << 25)) & 0x3ffffff;
r[2] = ((a[2] >> 1) | (a[3] << 25)) & 0x3ffffff;
r[3] = ((a[3] >> 1) | (a[4] << 25)) & 0x3ffffff;
r[4] = ((a[4] >> 1) | (a[5] << 25)) & 0x3ffffff;
r[5] = ((a[5] >> 1) | (a[6] << 25)) & 0x3ffffff;
r[6] = ((a[6] >> 1) | (a[7] << 25)) & 0x3ffffff;
r[7] = ((a[7] >> 1) | (a[8] << 25)) & 0x3ffffff;
r[8] = ((a[8] >> 1) | (a[9] << 25)) & 0x3ffffff;
r[9] = ((a[9] >> 1) | (a[10] << 25)) & 0x3ffffff;
r[10] = ((a[10] >> 1) | (a[11] << 25)) & 0x3ffffff;
r[11] = ((a[11] >> 1) | (a[12] << 25)) & 0x3ffffff;
r[12] = ((a[12] >> 1) | (a[13] << 25)) & 0x3ffffff;
r[13] = ((a[13] >> 1) | (a[14] << 25)) & 0x3ffffff;
#endif
r[14] = a[14] >> 1;
}
/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m)
*
* r Result of division by 2.
* a Number to divide.
* m Modulus (prime).
*/
static void sp_384_div2_15(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
sp_384_cond_add_15(r, a, m, 0 - (a[0] & 1));
sp_384_norm_15(r);
sp_384_rshift1_15(r, r);
}
/* Double the Montgomery form projective point p.
*
* r Result of doubling point.
* p Point to double.
* t Temporary ordinate data.
*/
static void sp_384_proj_point_dbl_15(sp_point_384* r, const sp_point_384* p, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*15;
sp_digit* x;
sp_digit* y;
sp_digit* z;
x = r->x;
y = r->y;
z = r->z;
/* Put infinity into result. */
if (r != p) {
r->infinity = p->infinity;
}
/* T1 = Z * Z */
sp_384_mont_sqr_15(t1, p->z, p384_mod, p384_mp_mod);
/* Z = Y * Z */
sp_384_mont_mul_15(z, p->y, p->z, p384_mod, p384_mp_mod);
/* Z = 2Z */
sp_384_mont_dbl_15(z, z, p384_mod);
/* T2 = X - T1 */
sp_384_mont_sub_15(t2, p->x, t1, p384_mod);
/* T1 = X + T1 */
sp_384_mont_add_15(t1, p->x, t1, p384_mod);
/* T2 = T1 * T2 */
sp_384_mont_mul_15(t2, t1, t2, p384_mod, p384_mp_mod);
/* T1 = 3T2 */
sp_384_mont_tpl_15(t1, t2, p384_mod);
/* Y = 2Y */
sp_384_mont_dbl_15(y, p->y, p384_mod);
/* Y = Y * Y */
sp_384_mont_sqr_15(y, y, p384_mod, p384_mp_mod);
/* T2 = Y * Y */
sp_384_mont_sqr_15(t2, y, p384_mod, p384_mp_mod);
/* T2 = T2/2 */
sp_384_div2_15(t2, t2, p384_mod);
/* Y = Y * X */
sp_384_mont_mul_15(y, y, p->x, p384_mod, p384_mp_mod);
/* X = T1 * T1 */
sp_384_mont_sqr_15(x, t1, p384_mod, p384_mp_mod);
/* X = X - Y */
sp_384_mont_sub_15(x, x, y, p384_mod);
/* X = X - Y */
sp_384_mont_sub_15(x, x, y, p384_mod);
/* Y = Y - X */
sp_384_mont_sub_15(y, y, x, p384_mod);
/* Y = Y * T1 */
sp_384_mont_mul_15(y, y, t1, p384_mod, p384_mp_mod);
/* Y = Y - T2 */
sp_384_mont_sub_15(y, y, t2, p384_mod);
}
/* Compare two numbers to determine if they are equal.
* Constant time implementation.
*
* a First number to compare.
* b Second number to compare.
* returns 1 when equal and 0 otherwise.
*/
static int sp_384_cmp_equal_15(const sp_digit* a, const sp_digit* b)
{
return ((a[0] ^ b[0]) | (a[1] ^ b[1]) | (a[2] ^ b[2]) | (a[3] ^ b[3]) |
(a[4] ^ b[4]) | (a[5] ^ b[5]) | (a[6] ^ b[6]) | (a[7] ^ b[7]) |
(a[8] ^ b[8]) | (a[9] ^ b[9]) | (a[10] ^ b[10]) | (a[11] ^ b[11]) |
(a[12] ^ b[12]) | (a[13] ^ b[13]) | (a[14] ^ b[14])) == 0;
}
/* Add two Montgomery form projective points.
*
* r Result of addition.
* p First point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_384_proj_point_add_15(sp_point_384* r, const sp_point_384* p, const sp_point_384* q,
sp_digit* t)
{
const sp_point_384* ap[2];
sp_point_384* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*15;
sp_digit* t3 = t + 4*15;
sp_digit* t4 = t + 6*15;
sp_digit* t5 = t + 8*15;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Ensure only the first point is the same as the result. */
if (q == r) {
const sp_point_384* a = p;
p = q;
q = a;
}
/* Check double */
(void)sp_384_sub_15(t1, p384_mod, q->y);
sp_384_norm_15(t1);
if ((sp_384_cmp_equal_15(p->x, q->x) & sp_384_cmp_equal_15(p->z, q->z) &
(sp_384_cmp_equal_15(p->y, q->y) | sp_384_cmp_equal_15(p->y, t1))) != 0) {
sp_384_proj_point_dbl_15(r, p, t);
}
else {
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point_384*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point_384));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<15; i++) {
r->x[i] = ap[p->infinity]->x[i];
}
for (i=0; i<15; i++) {
r->y[i] = ap[p->infinity]->y[i];
}
for (i=0; i<15; i++) {
r->z[i] = ap[p->infinity]->z[i];
}
r->infinity = ap[p->infinity]->infinity;
/* U1 = X1*Z2^2 */
sp_384_mont_sqr_15(t1, q->z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t3, t1, q->z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t1, t1, x, p384_mod, p384_mp_mod);
/* U2 = X2*Z1^2 */
sp_384_mont_sqr_15(t2, z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t4, t2, z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t2, t2, q->x, p384_mod, p384_mp_mod);
/* S1 = Y1*Z2^3 */
sp_384_mont_mul_15(t3, t3, y, p384_mod, p384_mp_mod);
/* S2 = Y2*Z1^3 */
sp_384_mont_mul_15(t4, t4, q->y, p384_mod, p384_mp_mod);
/* H = U2 - U1 */
sp_384_mont_sub_15(t2, t2, t1, p384_mod);
/* R = S2 - S1 */
sp_384_mont_sub_15(t4, t4, t3, p384_mod);
/* Z3 = H*Z1*Z2 */
sp_384_mont_mul_15(z, z, q->z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(z, z, t2, p384_mod, p384_mp_mod);
/* X3 = R^2 - H^3 - 2*U1*H^2 */
sp_384_mont_sqr_15(x, t4, p384_mod, p384_mp_mod);
sp_384_mont_sqr_15(t5, t2, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(y, t1, t5, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t5, t5, t2, p384_mod, p384_mp_mod);
sp_384_mont_sub_15(x, x, t5, p384_mod);
sp_384_mont_dbl_15(t1, y, p384_mod);
sp_384_mont_sub_15(x, x, t1, p384_mod);
/* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
sp_384_mont_sub_15(y, y, x, p384_mod);
sp_384_mont_mul_15(y, y, t4, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t5, t5, t3, p384_mod, p384_mp_mod);
sp_384_mont_sub_15(y, y, t5, p384_mod);
}
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_15(sp_point_384* r, const sp_point_384* g, const sp_digit* k,
int map, void* heap)
{
#ifdef WOLFSSL_SP_NO_MALLOC
sp_point_384 t[3];
sp_digit tmp[2 * 15 * 6];
#else
sp_point_384* t;
sp_digit* tmp;
#endif
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
(void)heap;
#ifndef WOLFSSL_SP_NO_MALLOC
t = (sp_point_384*)XMALLOC(sizeof(sp_point_384) * 3, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 6, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#endif
if (err == MP_OKAY) {
XMEMSET(t, 0, sizeof(sp_point_384) * 3);
/* t[0] = {0, 0, 1} * norm */
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
err = sp_384_mod_mul_norm_15(t[1].x, g->x, p384_mod);
}
if (err == MP_OKAY)
err = sp_384_mod_mul_norm_15(t[1].y, g->y, p384_mod);
if (err == MP_OKAY)
err = sp_384_mod_mul_norm_15(t[1].z, g->z, p384_mod);
if (err == MP_OKAY) {
i = 14;
c = 20;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_384_proj_point_add_15(&t[y^1], &t[0], &t[1], tmp);
XMEMCPY(&t[2], (void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])),
sizeof(sp_point_384));
sp_384_proj_point_dbl_15(&t[2], &t[2], tmp);
XMEMCPY((void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), &t[2],
sizeof(sp_point_384));
}
if (map != 0) {
sp_384_map_15(r, &t[0], tmp);
}
else {
XMEMCPY(r, &t[0], sizeof(sp_point_384));
}
}
#ifndef WOLFSSL_SP_NO_MALLOC
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 15 * 6);
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point_384) * 3);
XFREE(t, NULL, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmp, sizeof(tmp));
ForceZero(t, sizeof(t));
#endif
return err;
}
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_15(sp_point_384* r, const sp_point_384* g, const sp_digit* k,
int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 t[3];
sp_digit tmp[2 * 15 * 6];
#else
sp_point_384* t;
sp_digit* tmp;
#endif
sp_digit n;
int i;
int c, y;
int err = MP_OKAY;
(void)heap;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = (sp_point*)XMALLOC(sizeof(*t) * 3, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 6, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#endif
if (err == MP_OKAY) {
/* t[0] = {0, 0, 1} * norm */
XMEMSET(&t[0], 0, sizeof(t[0]));
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
t[1].infinity = 0;
err = sp_384_mod_mul_norm_15(t[1].x, g->x, p384_mod);
}
if (err == MP_OKAY)
err = sp_384_mod_mul_norm_15(t[1].y, g->y, p384_mod);
if (err == MP_OKAY)
err = sp_384_mod_mul_norm_15(t[1].z, g->z, p384_mod);
if (err == MP_OKAY) {
i = 14;
c = 20;
n = k[i--] << (26 - c);
for (; ; c--) {
if (c == 0) {
if (i == -1)
break;
n = k[i--];
c = 26;
}
y = (n >> 25) & 1;
n <<= 1;
sp_384_proj_point_add_15(&t[y^1], &t[0], &t[1], tmp);
XMEMCPY(&t[2], (void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), sizeof(t[2]));
sp_384_proj_point_dbl_15(&t[2], &t[2], tmp);
XMEMCPY((void*)(((size_t)&t[0] & addr_mask[y^1]) +
((size_t)&t[1] & addr_mask[y])), &t[2], sizeof(t[2]));
}
if (map != 0) {
sp_384_map_15(r, &t[0], tmp);
}
else {
XMEMCPY(r, &t[0], sizeof(sp_point_384));
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 15 * 6);
XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point_384) * 3);
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmp, sizeof(tmp));
ForceZero(t, sizeof(t));
#endif
return err;
}
#else
/* A table entry for pre-computed points. */
typedef struct sp_table_entry_384 {
sp_digit x[15];
sp_digit y[15];
} sp_table_entry_384;
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_fast_15(sp_point_384* r, const sp_point_384* g, const sp_digit* k,
int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 td[16];
sp_point_384 rtd;
sp_digit tmpd[2 * 15 * 6];
#endif
sp_point_384* t;
sp_point_384* rt;
sp_digit* tmp;
sp_digit n;
int i;
int c, y;
int err;
(void)heap;
err = sp_384_point_new_15(heap, rtd, rt);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = (sp_point_384*)XMALLOC(sizeof(sp_point_384) * 16, heap, DYNAMIC_TYPE_ECC);
if (t == NULL)
err = MEMORY_E;
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 6, heap,
DYNAMIC_TYPE_ECC);
if (tmp == NULL)
err = MEMORY_E;
#else
t = td;
tmp = tmpd;
#endif
if (err == MP_OKAY) {
/* t[0] = {0, 0, 1} * norm */
XMEMSET(&t[0], 0, sizeof(t[0]));
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
(void)sp_384_mod_mul_norm_15(t[1].x, g->x, p384_mod);
(void)sp_384_mod_mul_norm_15(t[1].y, g->y, p384_mod);
(void)sp_384_mod_mul_norm_15(t[1].z, g->z, p384_mod);
t[1].infinity = 0;
sp_384_proj_point_dbl_15(&t[ 2], &t[ 1], tmp);
t[ 2].infinity = 0;
sp_384_proj_point_add_15(&t[ 3], &t[ 2], &t[ 1], tmp);
t[ 3].infinity = 0;
sp_384_proj_point_dbl_15(&t[ 4], &t[ 2], tmp);
t[ 4].infinity = 0;
sp_384_proj_point_add_15(&t[ 5], &t[ 3], &t[ 2], tmp);
t[ 5].infinity = 0;
sp_384_proj_point_dbl_15(&t[ 6], &t[ 3], tmp);
t[ 6].infinity = 0;
sp_384_proj_point_add_15(&t[ 7], &t[ 4], &t[ 3], tmp);
t[ 7].infinity = 0;
sp_384_proj_point_dbl_15(&t[ 8], &t[ 4], tmp);
t[ 8].infinity = 0;
sp_384_proj_point_add_15(&t[ 9], &t[ 5], &t[ 4], tmp);
t[ 9].infinity = 0;
sp_384_proj_point_dbl_15(&t[10], &t[ 5], tmp);
t[10].infinity = 0;
sp_384_proj_point_add_15(&t[11], &t[ 6], &t[ 5], tmp);
t[11].infinity = 0;
sp_384_proj_point_dbl_15(&t[12], &t[ 6], tmp);
t[12].infinity = 0;
sp_384_proj_point_add_15(&t[13], &t[ 7], &t[ 6], tmp);
t[13].infinity = 0;
sp_384_proj_point_dbl_15(&t[14], &t[ 7], tmp);
t[14].infinity = 0;
sp_384_proj_point_add_15(&t[15], &t[ 8], &t[ 7], tmp);
t[15].infinity = 0;
i = 13;
n = k[i+1] << 6;
c = 16;
y = n >> 22;
XMEMCPY(rt, &t[y], sizeof(sp_point_384));
n <<= 10;
for (; i>=0 || c>=4; ) {
if (c < 4) {
n |= k[i--] << (6 - c);
c += 26;
}
y = (n >> 28) & 0xf;
n <<= 4;
c -= 4;
sp_384_proj_point_dbl_15(rt, rt, tmp);
sp_384_proj_point_dbl_15(rt, rt, tmp);
sp_384_proj_point_dbl_15(rt, rt, tmp);
sp_384_proj_point_dbl_15(rt, rt, tmp);
sp_384_proj_point_add_15(rt, rt, &t[y], tmp);
}
if (map != 0) {
sp_384_map_15(r, rt, tmp);
}
else {
XMEMCPY(r, rt, sizeof(sp_point_384));
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 15 * 6);
XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
}
if (t != NULL) {
XMEMSET(t, 0, sizeof(sp_point_384) * 16);
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#else
ForceZero(tmpd, sizeof(tmpd));
ForceZero(td, sizeof(td));
#endif
sp_384_point_free_15(rt, 1, heap);
return err;
}
#ifdef FP_ECC
/* Double the Montgomery form projective point p a number of times.
*
* r Result of repeated doubling of point.
* p Point to double.
* n Number of times to double
* t Temporary ordinate data.
*/
static void sp_384_proj_point_dbl_n_15(sp_point_384* p, int n, sp_digit* t)
{
sp_digit* w = t;
sp_digit* a = t + 2*15;
sp_digit* b = t + 4*15;
sp_digit* t1 = t + 6*15;
sp_digit* t2 = t + 8*15;
sp_digit* x;
sp_digit* y;
sp_digit* z;
x = p->x;
y = p->y;
z = p->z;
/* Y = 2*Y */
sp_384_mont_dbl_15(y, y, p384_mod);
/* W = Z^4 */
sp_384_mont_sqr_15(w, z, p384_mod, p384_mp_mod);
sp_384_mont_sqr_15(w, w, p384_mod, p384_mp_mod);
#ifndef WOLFSSL_SP_SMALL
while (--n > 0)
#else
while (--n >= 0)
#endif
{
/* A = 3*(X^2 - W) */
sp_384_mont_sqr_15(t1, x, p384_mod, p384_mp_mod);
sp_384_mont_sub_15(t1, t1, w, p384_mod);
sp_384_mont_tpl_15(a, t1, p384_mod);
/* B = X*Y^2 */
sp_384_mont_sqr_15(t1, y, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(b, t1, x, p384_mod, p384_mp_mod);
/* X = A^2 - 2B */
sp_384_mont_sqr_15(x, a, p384_mod, p384_mp_mod);
sp_384_mont_dbl_15(t2, b, p384_mod);
sp_384_mont_sub_15(x, x, t2, p384_mod);
/* Z = Z*Y */
sp_384_mont_mul_15(z, z, y, p384_mod, p384_mp_mod);
/* t2 = Y^4 */
sp_384_mont_sqr_15(t1, t1, p384_mod, p384_mp_mod);
#ifdef WOLFSSL_SP_SMALL
if (n != 0)
#endif
{
/* W = W*Y^4 */
sp_384_mont_mul_15(w, w, t1, p384_mod, p384_mp_mod);
}
/* y = 2*A*(B - X) - Y^4 */
sp_384_mont_sub_15(y, b, x, p384_mod);
sp_384_mont_mul_15(y, y, a, p384_mod, p384_mp_mod);
sp_384_mont_dbl_15(y, y, p384_mod);
sp_384_mont_sub_15(y, y, t1, p384_mod);
}
#ifndef WOLFSSL_SP_SMALL
/* A = 3*(X^2 - W) */
sp_384_mont_sqr_15(t1, x, p384_mod, p384_mp_mod);
sp_384_mont_sub_15(t1, t1, w, p384_mod);
sp_384_mont_tpl_15(a, t1, p384_mod);
/* B = X*Y^2 */
sp_384_mont_sqr_15(t1, y, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(b, t1, x, p384_mod, p384_mp_mod);
/* X = A^2 - 2B */
sp_384_mont_sqr_15(x, a, p384_mod, p384_mp_mod);
sp_384_mont_dbl_15(t2, b, p384_mod);
sp_384_mont_sub_15(x, x, t2, p384_mod);
/* Z = Z*Y */
sp_384_mont_mul_15(z, z, y, p384_mod, p384_mp_mod);
/* t2 = Y^4 */
sp_384_mont_sqr_15(t1, t1, p384_mod, p384_mp_mod);
/* y = 2*A*(B - X) - Y^4 */
sp_384_mont_sub_15(y, b, x, p384_mod);
sp_384_mont_mul_15(y, y, a, p384_mod, p384_mp_mod);
sp_384_mont_dbl_15(y, y, p384_mod);
sp_384_mont_sub_15(y, y, t1, p384_mod);
#endif
/* Y = Y/2 */
sp_384_div2_15(y, y, p384_mod);
}
#endif /* FP_ECC */
/* Add two Montgomery form projective points. The second point has a q value of
* one.
* Only the first point can be the same pointer as the result point.
*
* r Result of addition.
* p First point to add.
* q Second point to add.
* t Temporary ordinate data.
*/
static void sp_384_proj_point_add_qz1_15(sp_point_384* r, const sp_point_384* p,
const sp_point_384* q, sp_digit* t)
{
const sp_point_384* ap[2];
sp_point_384* rp[2];
sp_digit* t1 = t;
sp_digit* t2 = t + 2*15;
sp_digit* t3 = t + 4*15;
sp_digit* t4 = t + 6*15;
sp_digit* t5 = t + 8*15;
sp_digit* x;
sp_digit* y;
sp_digit* z;
int i;
/* Check double */
(void)sp_384_sub_15(t1, p384_mod, q->y);
sp_384_norm_15(t1);
if ((sp_384_cmp_equal_15(p->x, q->x) & sp_384_cmp_equal_15(p->z, q->z) &
(sp_384_cmp_equal_15(p->y, q->y) | sp_384_cmp_equal_15(p->y, t1))) != 0) {
sp_384_proj_point_dbl_15(r, p, t);
}
else {
rp[0] = r;
/*lint allow cast to different type of pointer*/
rp[1] = (sp_point_384*)t; /*lint !e9087 !e740*/
XMEMSET(rp[1], 0, sizeof(sp_point_384));
x = rp[p->infinity | q->infinity]->x;
y = rp[p->infinity | q->infinity]->y;
z = rp[p->infinity | q->infinity]->z;
ap[0] = p;
ap[1] = q;
for (i=0; i<15; i++) {
r->x[i] = ap[p->infinity]->x[i];
}
for (i=0; i<15; i++) {
r->y[i] = ap[p->infinity]->y[i];
}
for (i=0; i<15; i++) {
r->z[i] = ap[p->infinity]->z[i];
}
r->infinity = ap[p->infinity]->infinity;
/* U2 = X2*Z1^2 */
sp_384_mont_sqr_15(t2, z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t4, t2, z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t2, t2, q->x, p384_mod, p384_mp_mod);
/* S2 = Y2*Z1^3 */
sp_384_mont_mul_15(t4, t4, q->y, p384_mod, p384_mp_mod);
/* H = U2 - X1 */
sp_384_mont_sub_15(t2, t2, x, p384_mod);
/* R = S2 - Y1 */
sp_384_mont_sub_15(t4, t4, y, p384_mod);
/* Z3 = H*Z1 */
sp_384_mont_mul_15(z, z, t2, p384_mod, p384_mp_mod);
/* X3 = R^2 - H^3 - 2*X1*H^2 */
sp_384_mont_sqr_15(t1, t4, p384_mod, p384_mp_mod);
sp_384_mont_sqr_15(t5, t2, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t3, x, t5, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t5, t5, t2, p384_mod, p384_mp_mod);
sp_384_mont_sub_15(x, t1, t5, p384_mod);
sp_384_mont_dbl_15(t1, t3, p384_mod);
sp_384_mont_sub_15(x, x, t1, p384_mod);
/* Y3 = R*(X1*H^2 - X3) - Y1*H^3 */
sp_384_mont_sub_15(t3, t3, x, p384_mod);
sp_384_mont_mul_15(t3, t3, t4, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t5, t5, y, p384_mod, p384_mp_mod);
sp_384_mont_sub_15(y, t3, t5, p384_mod);
}
}
#ifdef FP_ECC
/* Convert the projective point to affine.
* Ordinates are in Montgomery form.
*
* a Point to convert.
* t Temporary data.
*/
static void sp_384_proj_to_affine_15(sp_point_384* a, sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2 * 15;
sp_digit* tmp = t + 4 * 15;
sp_384_mont_inv_15(t1, a->z, tmp);
sp_384_mont_sqr_15(t2, t1, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(t1, t2, t1, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(a->x, a->x, t2, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(a->y, a->y, t1, p384_mod, p384_mp_mod);
XMEMCPY(a->z, p384_norm_mod, sizeof(p384_norm_mod));
}
/* Generate the pre-computed table of points for the base point.
*
* a The base point.
* table Place to store generated point data.
* tmp Temporary data.
* heap Heap to use for allocation.
*/
static int sp_384_gen_stripe_table_15(const sp_point_384* a,
sp_table_entry_384* table, sp_digit* tmp, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 td, s1d, s2d;
#endif
sp_point_384* t;
sp_point_384* s1 = NULL;
sp_point_384* s2 = NULL;
int i, j;
int err;
(void)heap;
err = sp_384_point_new_15(heap, td, t);
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, s1d, s1);
}
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, s2d, s2);
}
if (err == MP_OKAY) {
err = sp_384_mod_mul_norm_15(t->x, a->x, p384_mod);
}
if (err == MP_OKAY) {
err = sp_384_mod_mul_norm_15(t->y, a->y, p384_mod);
}
if (err == MP_OKAY) {
err = sp_384_mod_mul_norm_15(t->z, a->z, p384_mod);
}
if (err == MP_OKAY) {
t->infinity = 0;
sp_384_proj_to_affine_15(t, tmp);
XMEMCPY(s1->z, p384_norm_mod, sizeof(p384_norm_mod));
s1->infinity = 0;
XMEMCPY(s2->z, p384_norm_mod, sizeof(p384_norm_mod));
s2->infinity = 0;
/* table[0] = {0, 0, infinity} */
XMEMSET(&table[0], 0, sizeof(sp_table_entry_384));
/* table[1] = Affine version of 'a' in Montgomery form */
XMEMCPY(table[1].x, t->x, sizeof(table->x));
XMEMCPY(table[1].y, t->y, sizeof(table->y));
for (i=1; i<8; i++) {
sp_384_proj_point_dbl_n_15(t, 48, tmp);
sp_384_proj_to_affine_15(t, tmp);
XMEMCPY(table[1<<i].x, t->x, sizeof(table->x));
XMEMCPY(table[1<<i].y, t->y, sizeof(table->y));
}
for (i=1; i<8; i++) {
XMEMCPY(s1->x, table[1<<i].x, sizeof(table->x));
XMEMCPY(s1->y, table[1<<i].y, sizeof(table->y));
for (j=(1<<i)+1; j<(1<<(i+1)); j++) {
XMEMCPY(s2->x, table[j-(1<<i)].x, sizeof(table->x));
XMEMCPY(s2->y, table[j-(1<<i)].y, sizeof(table->y));
sp_384_proj_point_add_qz1_15(t, s1, s2, tmp);
sp_384_proj_to_affine_15(t, tmp);
XMEMCPY(table[j].x, t->x, sizeof(table->x));
XMEMCPY(table[j].y, t->y, sizeof(table->y));
}
}
}
sp_384_point_free_15(s2, 0, heap);
sp_384_point_free_15(s1, 0, heap);
sp_384_point_free_15( t, 0, heap);
return err;
}
#endif /* FP_ECC */
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_stripe_15(sp_point_384* r, const sp_point_384* g,
const sp_table_entry_384* table, const sp_digit* k, int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 rtd;
sp_point_384 pd;
sp_digit td[2 * 15 * 6];
#endif
sp_point_384* rt;
sp_point_384* p = NULL;
sp_digit* t;
int i, j;
int y, x;
int err;
(void)g;
(void)heap;
err = sp_384_point_new_15(heap, rtd, rt);
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, pd, p);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 6, heap,
DYNAMIC_TYPE_ECC);
if (t == NULL) {
err = MEMORY_E;
}
#else
t = td;
#endif
if (err == MP_OKAY) {
XMEMCPY(p->z, p384_norm_mod, sizeof(p384_norm_mod));
XMEMCPY(rt->z, p384_norm_mod, sizeof(p384_norm_mod));
y = 0;
for (j=0,x=47; j<8; j++,x+=48) {
y |= ((k[x / 26] >> (x % 26)) & 1) << j;
}
XMEMCPY(rt->x, table[y].x, sizeof(table[y].x));
XMEMCPY(rt->y, table[y].y, sizeof(table[y].y));
rt->infinity = !y;
for (i=46; i>=0; i--) {
y = 0;
for (j=0,x=i; j<8; j++,x+=48) {
y |= ((k[x / 26] >> (x % 26)) & 1) << j;
}
sp_384_proj_point_dbl_15(rt, rt, t);
XMEMCPY(p->x, table[y].x, sizeof(table[y].x));
XMEMCPY(p->y, table[y].y, sizeof(table[y].y));
p->infinity = !y;
sp_384_proj_point_add_qz1_15(rt, rt, p, t);
}
if (map != 0) {
sp_384_map_15(r, rt, t);
}
else {
XMEMCPY(r, rt, sizeof(sp_point_384));
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (t != NULL) {
XFREE(t, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(p, 0, heap);
sp_384_point_free_15(rt, 0, heap);
return err;
}
#ifdef FP_ECC
#ifndef FP_ENTRIES
#define FP_ENTRIES 16
#endif
typedef struct sp_cache_384_t {
sp_digit x[15];
sp_digit y[15];
sp_table_entry_384 table[256];
uint32_t cnt;
int set;
} sp_cache_384_t;
static THREAD_LS_T sp_cache_384_t sp_cache_384[FP_ENTRIES];
static THREAD_LS_T int sp_cache_384_last = -1;
static THREAD_LS_T int sp_cache_384_inited = 0;
#ifndef HAVE_THREAD_LS
static volatile int initCacheMutex_384 = 0;
static wolfSSL_Mutex sp_cache_384_lock;
#endif
static void sp_ecc_get_cache_384(const sp_point_384* g, sp_cache_384_t** cache)
{
int i, j;
uint32_t least;
if (sp_cache_384_inited == 0) {
for (i=0; i<FP_ENTRIES; i++) {
sp_cache_384[i].set = 0;
}
sp_cache_384_inited = 1;
}
/* Compare point with those in cache. */
for (i=0; i<FP_ENTRIES; i++) {
if (!sp_cache_384[i].set)
continue;
if (sp_384_cmp_equal_15(g->x, sp_cache_384[i].x) &
sp_384_cmp_equal_15(g->y, sp_cache_384[i].y)) {
sp_cache_384[i].cnt++;
break;
}
}
/* No match. */
if (i == FP_ENTRIES) {
/* Find empty entry. */
i = (sp_cache_384_last + 1) % FP_ENTRIES;
for (; i != sp_cache_384_last; i=(i+1)%FP_ENTRIES) {
if (!sp_cache_384[i].set) {
break;
}
}
/* Evict least used. */
if (i == sp_cache_384_last) {
least = sp_cache_384[0].cnt;
for (j=1; j<FP_ENTRIES; j++) {
if (sp_cache_384[j].cnt < least) {
i = j;
least = sp_cache_384[i].cnt;
}
}
}
XMEMCPY(sp_cache_384[i].x, g->x, sizeof(sp_cache_384[i].x));
XMEMCPY(sp_cache_384[i].y, g->y, sizeof(sp_cache_384[i].y));
sp_cache_384[i].set = 1;
sp_cache_384[i].cnt = 1;
}
*cache = &sp_cache_384[i];
sp_cache_384_last = i;
}
#endif /* FP_ECC */
/* Multiply the base point of P384 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_15(sp_point_384* r, const sp_point_384* g, const sp_digit* k,
int map, void* heap)
{
#ifndef FP_ECC
return sp_384_ecc_mulmod_fast_15(r, g, k, map, heap);
#else
sp_digit tmp[2 * 15 * 7];
sp_cache_384_t* cache;
int err = MP_OKAY;
#ifndef HAVE_THREAD_LS
if (initCacheMutex_384 == 0) {
wc_InitMutex(&sp_cache_384_lock);
initCacheMutex_384 = 1;
}
if (wc_LockMutex(&sp_cache_384_lock) != 0)
err = BAD_MUTEX_E;
#endif /* HAVE_THREAD_LS */
if (err == MP_OKAY) {
sp_ecc_get_cache_384(g, &cache);
if (cache->cnt == 2)
sp_384_gen_stripe_table_15(g, cache->table, tmp, heap);
#ifndef HAVE_THREAD_LS
wc_UnLockMutex(&sp_cache_384_lock);
#endif /* HAVE_THREAD_LS */
if (cache->cnt < 2) {
err = sp_384_ecc_mulmod_fast_15(r, g, k, map, heap);
}
else {
err = sp_384_ecc_mulmod_stripe_15(r, g, cache->table, k,
map, heap);
}
}
return err;
#endif
}
#endif
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* km Scalar to multiply by.
* p Point to multiply.
* r Resulting point.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_mulmod_384(mp_int* km, ecc_point* gm, ecc_point* r, int map,
void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 p;
sp_digit kd[15];
#endif
sp_point_384* point;
sp_digit* k = NULL;
int err = MP_OKAY;
err = sp_384_point_new_15(heap, p, point);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 15, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL)
err = MEMORY_E;
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_384_from_mp(k, 15, km);
sp_384_point_from_ecc_point_15(point, gm);
err = sp_384_ecc_mulmod_15(point, point, k, map, heap);
}
if (err == MP_OKAY) {
err = sp_384_point_to_ecc_point_15(point, r);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(point, 0, heap);
return err;
}
#ifdef WOLFSSL_SP_SMALL
/* Multiply the base point of P384 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_base_15(sp_point_384* r, const sp_digit* k,
int map, void* heap)
{
/* No pre-computed values. */
return sp_384_ecc_mulmod_15(r, &p384_base, k, map, heap);
}
#elif defined(WOLFSSL_SP_CACHE_RESISTANT)
/* Multiply the base point of P384 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_base_15(sp_point_384* r, const sp_digit* k,
int map, void* heap)
{
/* No pre-computed values. */
return sp_384_ecc_mulmod_15(r, &p384_base, k, map, heap);
}
#else
static const sp_table_entry_384 p384_table[256] = {
/* 0 */
{ { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
{ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
/* 1 */
{ { 0x1c0b528,0x01d5992,0x0e383dd,0x38a835b,0x220e378,0x106d35b,
0x1c3afc5,0x03bfe1e,0x28459a3,0x2d91521,0x214ede2,0x0bfdc8d,
0x2151381,0x3708a67,0x004d3aa },
{ 0x303a4fe,0x10f6b52,0x29ac230,0x2fdeed2,0x0a1bfa8,0x3a0ec14,
0x2de7562,0x3ff662e,0x21968f4,0x031b0d4,0x3969a84,0x2000898,
0x1c5e9dd,0x2f09685,0x002b78a } },
/* 2 */
{ { 0x30c535b,0x191d4ca,0x2296298,0x14dc141,0x090dd69,0x05aae6b,
0x0cd6b42,0x35da80e,0x3b7be12,0x2cf7e6d,0x1f347bd,0x3d365e1,
0x1448913,0x32704fa,0x00222c5 },
{ 0x280dc64,0x39e5bc9,0x24175f8,0x2dd60d4,0x0120e7c,0x041d02e,
0x0b5d8ad,0x37b9895,0x2fb5337,0x1f0e2e3,0x14f0224,0x2230b86,
0x1bc4cf6,0x17cdb09,0x007b5c7 } },
/* 3 */
{ { 0x2dffea5,0x28f30e7,0x29fce26,0x070df5f,0x235bbfd,0x2f78fbd,
0x27700d9,0x23d6bc3,0x3471a53,0x0c0e03a,0x05bf9eb,0x276a2ec,
0x20c3e2e,0x31cc691,0x00dbb93 },
{ 0x126b605,0x2e8983d,0x153737d,0x23bf5e1,0x295d497,0x35ca812,
0x2d793ae,0x16c6893,0x3777600,0x089a520,0x1e681f8,0x3d55ee6,
0x154ef99,0x155f592,0x00ae5f9 } },
/* 4 */
{ { 0x26feef9,0x20315fc,0x1240244,0x250e838,0x3c31a26,0x1cf8af1,
0x1002c32,0x3b531cd,0x1c53ef1,0x22310ba,0x3f4948e,0x22eafd9,
0x3863202,0x3d0e2a5,0x006a502 },
{ 0x34536fe,0x04e91ad,0x30ebf5f,0x2af62a7,0x01d218b,0x1c8c9da,
0x336bcc3,0x23060c3,0x331576e,0x1b14c5e,0x1bbcb76,0x0755e9a,
0x3d4dcef,0x24c2cf8,0x00917c4 } },
/* 5 */
{ { 0x349ddd0,0x09b8bb8,0x0250114,0x3e66cbf,0x29f117e,0x3005d29,
0x36b480e,0x2119bfc,0x2761845,0x253d2f7,0x0580604,0x0bb6db4,
0x3ca922f,0x1744677,0x008adc7 },
{ 0x3d5a7ce,0x27425ed,0x11e9a61,0x3968d10,0x3874275,0x3692d3b,
0x03e0470,0x0763d50,0x3d97790,0x3cbaeab,0x2747170,0x18faf3a,
0x180365e,0x2511fe7,0x0012a36 } },
/* 6 */
{ { 0x3c52870,0x2701e93,0x296128f,0x120694e,0x1ce0b37,0x3860a36,
0x10fa180,0x0896b55,0x2f76adb,0x22892ae,0x2e58a34,0x07b4295,
0x2cb62d1,0x079a522,0x00f3d81 },
{ 0x061ed22,0x2375dd3,0x3c9d861,0x3e602d1,0x10bb747,0x39ae156,
0x3f796fd,0x087a48a,0x06d680a,0x37f7f47,0x2af2c9d,0x36c55dc,
0x10f3dc0,0x279b07a,0x00a0937 } },
/* 7 */
{ { 0x085c629,0x319bbf8,0x089a386,0x184256f,0x15fc2a4,0x00fd2d0,
0x13d6312,0x363d44d,0x32b7e4b,0x25f2865,0x27df8ce,0x1dce02a,
0x24ea3b0,0x0e27b9f,0x00d8a90 },
{ 0x3b14461,0x1d371f9,0x0f781bc,0x0503271,0x0dc2cb0,0x13bc284,
0x34b3a68,0x1ff894a,0x25d2032,0x16f79ba,0x260f961,0x07b10d5,
0x18173b7,0x2812e2b,0x00eede5 } },
/* 8 */
{ { 0x13b9a2d,0x132ece2,0x0c5d558,0x02c0214,0x1820c66,0x37cb50f,
0x26d8267,0x3a00504,0x3f00109,0x33756ee,0x38172f1,0x2e4bb8c,
0x030d985,0x3e4fcc5,0x00609d4 },
{ 0x2daf9d6,0x16681fa,0x1fb01e0,0x1b03c49,0x370e653,0x183c839,
0x2207515,0x0ea6b58,0x1ae7aaf,0x3a96522,0x24bae14,0x1c38bd9,
0x082497b,0x1c05db4,0x000dd03 } },
/* 9 */
{ { 0x110521f,0x04efa21,0x0c174cc,0x2a7dc93,0x387315b,0x14f7098,
0x1d83bb3,0x2495ed2,0x2fe0c27,0x1e2d9df,0x093c953,0x0287073,
0x02c9951,0x336291c,0x0033e30 },
{ 0x208353f,0x3f22748,0x2b2bf0f,0x2373b50,0x10170fa,0x1b8a97d,
0x0851ed2,0x0b25824,0x055ecb5,0x12049d9,0x3fe1adf,0x11b1385,
0x28eab06,0x11fac21,0x00513f0 } },
/* 10 */
{ { 0x35bdf53,0x1847d37,0x1a6dc07,0x29d62c4,0x045d331,0x313b8e5,
0x165daf1,0x1e34562,0x3e75a58,0x16ea2fa,0x02dd302,0x3302862,
0x3eb8bae,0x2266a48,0x00cf2a3 },
{ 0x24fd048,0x324a074,0x025df98,0x1662eec,0x3841bfb,0x26ae754,
0x1df8cec,0x0113ae3,0x0b67fef,0x094e293,0x2323666,0x0ab087c,
0x2f06509,0x0e142d9,0x00a919d } },
/* 11 */
{ { 0x1d480d8,0x00ed021,0x3a7d3db,0x1e46ca1,0x28cd9f4,0x2a3ceeb,
0x24dc754,0x0624a3c,0x0003db4,0x1520bae,0x1c56e0f,0x2fe7ace,
0x1dc6f38,0x0c826a4,0x008b977 },
{ 0x209cfc2,0x2c16c9c,0x1b70a31,0x21416cb,0x34c49bf,0x186549e,
0x062498d,0x146e959,0x0391fac,0x08ff944,0x2b4b834,0x013d57a,
0x2eabffb,0x0370131,0x00c07c1 } },
/* 12 */
{ { 0x332f048,0x0bf9336,0x16dfad2,0x2451d7b,0x35f23bf,0x299adb2,
0x0ce0c0a,0x0170294,0x289f034,0x2b7d89e,0x395e2d6,0x1d20df7,
0x2e64e36,0x16dae90,0x00081c9 },
{ 0x31d6ceb,0x0f80db9,0x0271eba,0x33db1ac,0x1b45bcc,0x1a11c07,
0x347e630,0x148fd9e,0x142e712,0x3183e3e,0x1cd47ad,0x108d1c9,
0x09cbb82,0x35e61d9,0x0083027 } },
/* 13 */
{ { 0x215b0b8,0x0a7a98d,0x2c41b39,0x3f69536,0x0b41441,0x16da8da,
0x15d556b,0x3c17a26,0x129167e,0x3ea0351,0x2d25a27,0x2f2d285,
0x15b68f6,0x2931ef5,0x00210d6 },
{ 0x1351130,0x012aec9,0x37ebf38,0x26640f8,0x01d2df6,0x2130972,
0x201efc0,0x23a457c,0x087a1c6,0x14c68a3,0x163f62a,0x36b494d,
0x015d481,0x39c35b1,0x005dd6d } },
/* 14 */
{ { 0x06612ce,0x11c3f61,0x199729f,0x3b36863,0x2986f3e,0x3cd2be1,
0x04c1612,0x2be2dae,0x00846dd,0x3d7bc29,0x249e795,0x1016803,
0x37a3714,0x2c5aa8b,0x005f491 },
{ 0x341b38d,0x01eb936,0x3caac7f,0x27863ef,0x1ef7d11,0x1110ec6,
0x18e0761,0x26498e8,0x01a79a1,0x390d5a1,0x22226fb,0x3d2a473,
0x0872191,0x1230f32,0x00dc772 } },
/* 15 */
{ { 0x0b1ec9d,0x03fc6b9,0x3706d57,0x03b9fbb,0x221d23e,0x2867821,
0x1e40f4c,0x2c9c0f3,0x3c4cd4b,0x31f5948,0x3f13aa6,0x307c1b2,
0x04b6016,0x116b453,0x005aa72 },
{ 0x0b74de8,0x20519d1,0x134e37f,0x05d882a,0x1839e7a,0x3a2c6a8,
0x0d14e8d,0x1d78bdd,0x251f30d,0x3a1e27e,0x081c261,0x2c9014b,
0x165ee09,0x19e0cf1,0x00654e2 } },
/* 16 */
{ { 0x39fbe67,0x081778b,0x0e44378,0x20dfdca,0x1c4afcb,0x20b803c,
0x0ec06c6,0x1508f6f,0x1c3114d,0x3bca851,0x3a52463,0x07661d1,
0x17b0aa0,0x16c5f5c,0x00fc093 },
{ 0x0d01f95,0x0ef13f5,0x2d34965,0x2a25582,0x39aa83e,0x3e38fcf,
0x3943dca,0x385bbdd,0x210e86f,0x3dc1dd2,0x3f9ffdc,0x18b9bc6,
0x345c96b,0x0e79621,0x008a72f } },
/* 17 */
{ { 0x341c342,0x3793688,0x042273a,0x153a9c1,0x3dd326e,0x1d073bc,
0x2c7d983,0x05524cd,0x00d59e6,0x347abe8,0x3d9a3ef,0x0fb624a,
0x2c7e4cd,0x09b3171,0x0003faf },
{ 0x045f8ac,0x38bf3cc,0x1e73087,0x0c85d3c,0x314a655,0x382be69,
0x384f28f,0x24d6cb3,0x2842cdc,0x1777f5e,0x2929c89,0x03c45ed,
0x3cfcc4c,0x0b59322,0x0035657 } },
/* 18 */
{ { 0x18c1bba,0x2eb005f,0x33d57ec,0x30e42c3,0x36058f9,0x1865f43,
0x2116e3f,0x2c4a2bb,0x0684033,0x0f1375c,0x0209b98,0x2136e9b,
0x1bc4af0,0x0b3e0c7,0x0097c7c },
{ 0x16010e8,0x398777e,0x2a172f4,0x0814a7e,0x0d97e4e,0x274dfc8,
0x2666606,0x1b5c93b,0x1ed3d36,0x3f3304e,0x13488e0,0x02dbb88,
0x2d53369,0x3717ce9,0x007cad1 } },
/* 19 */
{ { 0x257a41f,0x2a6a076,0x39b6660,0x04bb000,0x1e74a04,0x3876b45,
0x343c6b5,0x0753108,0x3f54668,0x24a13cf,0x23749e8,0x0421fc5,
0x32f13b5,0x0f31be7,0x00070f2 },
{ 0x1186e14,0x0847697,0x0dff542,0x0dff76c,0x084748f,0x2c7d060,
0x23aab4d,0x0b43906,0x27ba640,0x1497b59,0x02f5835,0x0a492a4,
0x0a6892f,0x39f3e91,0x005844e } },
/* 20 */
{ { 0x33b236f,0x02181cf,0x21dafab,0x0760788,0x019e9d4,0x249ed0a,
0x36571e3,0x3c7dbcf,0x1337550,0x010d22a,0x285e62f,0x19ee65a,
0x052bf71,0x1d65fd5,0x0062d43 },
{ 0x2955926,0x3fae7bc,0x0353d85,0x07db7de,0x1440a56,0x328dad6,
0x1668ec9,0x28058e2,0x1a1a22d,0x1014afc,0x3609325,0x3effdcb,
0x209f3bd,0x3ca3888,0x0094e50 } },
/* 21 */
{ { 0x062e8af,0x0b96ccc,0x136990b,0x1d7a28f,0x1a85723,0x0076dec,
0x21b00b2,0x06a88ff,0x2f0ee65,0x1fa49b7,0x39b10ad,0x10b26fa,
0x0be7465,0x026e8bf,0x00098e3 },
{ 0x3f1d63f,0x37bacff,0x1374779,0x02882ff,0x323d0e8,0x1da3de5,
0x12bb3b8,0x0a15a11,0x34d1f95,0x2b3dd6e,0x29ea3fa,0x39ad000,
0x33a538f,0x390204d,0x0012bd3 } },
/* 22 */
{ { 0x04cbba5,0x0de0344,0x1d4cc02,0x11fe8d7,0x36207e7,0x32a6da8,
0x0239281,0x1ec40d7,0x3e89798,0x213fc66,0x0022eee,0x11daefe,
0x3e74db8,0x28534ee,0x00aa0a4 },
{ 0x07d4543,0x250cc46,0x206620f,0x1c1e7db,0x1321538,0x31fa0b8,
0x30f74ea,0x01aae0e,0x3a2828f,0x3e9dd22,0x026ef35,0x3c0a62b,
0x27dbdc5,0x01c23a6,0x000f0c5 } },
/* 23 */
{ { 0x2f029dd,0x3091337,0x21b80c5,0x21e1419,0x13dabc6,0x3847660,
0x12b865f,0x36eb666,0x38f6274,0x0ba6006,0x098da24,0x1398c64,
0x13d08e5,0x246a469,0x009929a },
{ 0x1285887,0x3ff5c8d,0x010237b,0x097c506,0x0bc7594,0x34b9b88,
0x00cc35f,0x0bb964a,0x00cfbc4,0x29cd718,0x0837619,0x2b4a192,
0x0c57bb7,0x08c69de,0x00a3627 } },
/* 24 */
{ { 0x1361ed8,0x266d724,0x366cae7,0x1d5b18c,0x247d71b,0x2c9969a,
0x0dd5211,0x1edd153,0x25998d7,0x0380856,0x3ab29db,0x09366de,
0x1e53644,0x2b31ff6,0x008b0ff },
{ 0x3b5d9ef,0x217448d,0x174746d,0x18afea4,0x15b106d,0x3e66e8b,
0x0479f85,0x13793b4,0x1231d10,0x3c39bce,0x25e8983,0x2a13210,
0x05a7083,0x382be04,0x00a9507 } },
/* 25 */
{ { 0x0cf381c,0x1a29b85,0x31ccf6c,0x2f708b8,0x3af9d27,0x2a29732,
0x168d4da,0x393488d,0x2c0e338,0x3f90c7b,0x0f52ad1,0x2a0a3fa,
0x2cd80f1,0x15e7a1a,0x00db6a0 },
{ 0x107832a,0x159cb91,0x1289288,0x17e21f9,0x073fc27,0x1584342,
0x3802780,0x3d6c197,0x154075f,0x16366d1,0x09f712b,0x23a3ec4,
0x29cf23a,0x3218baf,0x0039f0a } },
/* 26 */
{ { 0x052edf5,0x2afde13,0x2e53d8f,0x3969626,0x3dcd737,0x1e46ac5,
0x118bf0d,0x01b2652,0x156bcff,0x16d7ef6,0x1ca46d4,0x34c0cbb,
0x3e486f6,0x1f85068,0x002cdff },
{ 0x1f47ec8,0x12cee98,0x0608667,0x18fbbe1,0x08a8821,0x31a1fe4,
0x17c7054,0x3c89e89,0x2edf6cd,0x1b8c32c,0x3f6ea84,0x1319329,
0x3cd3c2c,0x05f331a,0x00186fa } },
/* 27 */
{ { 0x1fcb91e,0x0fd4d87,0x358a48a,0x04d91b4,0x083595e,0x044a1e6,
0x15827b9,0x1d5eaf4,0x2b82187,0x08f3984,0x21bd737,0x0c54285,
0x2f56887,0x14c2d98,0x00f4684 },
{ 0x01896f6,0x0e542d0,0x2090883,0x269dfcf,0x1e11cb8,0x239fd29,
0x312cac4,0x19dfacb,0x369f606,0x0cc4f75,0x16579f9,0x33c22cc,
0x0f22bfd,0x3b251ae,0x006429c } },
/* 28 */
{ { 0x375f9a4,0x137552e,0x3570498,0x2e4a74e,0x24aef06,0x35b9307,
0x384ca23,0x3bcd6d7,0x011b083,0x3c93187,0x392ca9f,0x129ce48,
0x0a800ce,0x145d9cc,0x00865d6 },
{ 0x22b4a2b,0x37f9d9c,0x3e0eca3,0x3e5ec20,0x112c04b,0x2e1ae29,
0x3ce5b51,0x0f83200,0x32d6a7e,0x10ff1d8,0x081adbe,0x265c30b,
0x216b1c8,0x0eb4483,0x003cbcd } },
/* 29 */
{ { 0x030ce93,0x2d331fb,0x20a2fbf,0x1f6dc9c,0x010ed6c,0x1ed5540,
0x275bf74,0x3df0fb1,0x103333f,0x0241c96,0x1075bfc,0x30e5cf9,
0x0f31bc7,0x32c01eb,0x00b049e },
{ 0x358839c,0x1dbabd3,0x1e4fb40,0x36a8ac1,0x2101896,0x2d0319b,
0x2033b0a,0x192e8fd,0x2ebc8d8,0x2867ba7,0x07bf6d2,0x1b3c555,
0x2477deb,0x198fe09,0x008e5a9 } },
/* 30 */
{ { 0x3fbd5e1,0x18bf77d,0x2b1d69e,0x151da44,0x338ecfe,0x0768efe,
0x1a3d56d,0x3c35211,0x10e1c86,0x2012525,0x3bc36ce,0x32b6fe4,
0x0c8d183,0x15c93f3,0x0041fce },
{ 0x332c144,0x24e70a0,0x246e05f,0x22c21c7,0x2b17f24,0x1ba2bfd,
0x0534e26,0x318a4f6,0x1dc3b85,0x0c741bc,0x23131b7,0x01a8cba,
0x364e5db,0x21362cf,0x00f2951 } },
/* 31 */
{ { 0x2ddc103,0x14ffdcd,0x206fd96,0x0de57bd,0x025f43e,0x381b73a,
0x2301fcf,0x3bafc27,0x34130b6,0x0216bc8,0x0ff56b2,0x2c4ad4c,
0x23c6b79,0x1267fa6,0x009b4fb },
{ 0x1d27ac2,0x13e2494,0x1389015,0x38d5b29,0x2d33167,0x3f01969,
0x28ec1fa,0x1b26de0,0x2587f74,0x1c25668,0x0c44f83,0x23c6f8c,
0x32fdbb1,0x045f104,0x00a7946 } },
/* 32 */
{ { 0x23c647b,0x09addd7,0x1348c04,0x0e633c1,0x1bfcbd9,0x1cb034f,
0x1312e31,0x11cdcc7,0x1e6ee75,0x057d27f,0x2da7ee6,0x154c3c1,
0x3a5fb89,0x2c2ba2c,0x00cf281 },
{ 0x1b8a543,0x125cd50,0x1d30fd1,0x29cc203,0x341a625,0x14e4233,
0x3aae076,0x289e38a,0x036ba02,0x230f405,0x3b21b8f,0x34088b9,
0x01297a0,0x03a75fb,0x00fdc27 } },
/* 33 */
{ { 0x07f41d6,0x1cf032f,0x1641008,0x0f86deb,0x3d97611,0x0e110fe,
0x136ff42,0x0b914a9,0x0e241e6,0x180c340,0x1f545fc,0x0ba619d,
0x1208c53,0x04223a4,0x00cd033 },
{ 0x397612c,0x0132665,0x34e2d1a,0x00bba99,0x1d4393e,0x065d0a8,
0x2fa69ee,0x1643b55,0x08085f0,0x3774aad,0x08a2243,0x33bf149,
0x03f41a5,0x1ed950e,0x0048cc6 } },
/* 34 */
{ { 0x014ab48,0x010c3bf,0x2a744e5,0x13c99c1,0x2195b7f,0x32207fd,
0x28a228c,0x004f4bf,0x0e2d945,0x2ec6e5a,0x0b92162,0x1aa95e5,
0x2754a93,0x1adcd93,0x004fb76 },
{ 0x1e1ff7f,0x24ef28c,0x269113f,0x32b393c,0x2696eb5,0x0ac2780,
0x354bf8a,0x0ffe3fd,0x09ce58e,0x0163c4f,0x1678c0b,0x15cd1bc,
0x292b3b7,0x036ea19,0x00d5420 } },
/* 35 */
{ { 0x1da1265,0x0c2ef5b,0x18dd9a0,0x3f3a25c,0x0f7b4f3,0x0d8196e,
0x24931f9,0x090729a,0x1875f72,0x1ef39cb,0x2577585,0x2ed472d,
0x136756c,0x20553a6,0x00c7161 },
{ 0x2e32189,0x283de4b,0x00b2e81,0x0989df7,0x3ef2fab,0x1c7d1a7,
0x24f6feb,0x3e16679,0x233dfda,0x06d1233,0x3e6b5df,0x1707132,
0x05f7b3f,0x2c00779,0x00fb8df } },
/* 36 */
{ { 0x15bb921,0x117e9d3,0x267ec73,0x2f934ad,0x25c7e04,0x20b5e8f,
0x2d3a802,0x2ca911f,0x3f87e47,0x39709dd,0x08488e2,0x2cec400,
0x35b4589,0x1f0acba,0x009aad7 },
{ 0x2ac34ae,0x06f29f6,0x3326d68,0x3949abe,0x02452e4,0x0687b85,
0x0879244,0x1eb7832,0x0d4c240,0x31d0ec1,0x3c17a2a,0x17a666f,
0x01a06cb,0x3e0929c,0x004dca2 } },
/* 37 */
{ { 0x127bc1a,0x0c72984,0x13be68e,0x26c5fab,0x1a3edd5,0x097d685,
0x36b645e,0x385799e,0x394a420,0x39d8885,0x0b1e872,0x13f60ed,
0x2ce1b79,0x3c0ecb7,0x007cab3 },
{ 0x29b3586,0x26fc572,0x0bd7711,0x0913494,0x0a55459,0x31af3c9,
0x3633eac,0x3e2105c,0x0c2b1b6,0x0e6f4c2,0x047d38c,0x2b81bd5,
0x1fe1c3b,0x04d7cd0,0x0054dcc } },
/* 38 */
{ { 0x03caf0d,0x0d66365,0x313356d,0x2a4897f,0x2ce044e,0x18feb7a,
0x1f6a7c5,0x3709e7b,0x14473e8,0x2d8cbae,0x3190dca,0x12d19f8,
0x31e3181,0x3cc5b6e,0x002d4f4 },
{ 0x143b7ca,0x2604728,0x39508d6,0x0cb79f3,0x24ec1ac,0x1ed7fa0,
0x3ab5fd3,0x3c76488,0x2e49390,0x03a0985,0x3580461,0x3fd2c81,
0x308f0ab,0x38561d6,0x0011b9b } },
/* 39 */
{ { 0x3be682c,0x0c68f4e,0x32dd4ae,0x099d3bb,0x0bc7c5d,0x311f750,
0x2fd10a3,0x2e7864a,0x23bc14a,0x13b1f82,0x32e495e,0x1b0f746,
0x3cd856a,0x17a4c26,0x00085ee },
{ 0x02e67fd,0x06a4223,0x2af2f38,0x2038987,0x132083a,0x1b7bb85,
0x0d6a499,0x131e43f,0x3035e52,0x278ee3e,0x1d5b08b,0x30d8364,
0x2719f8d,0x0b21fc9,0x003a06e } },
/* 40 */
{ { 0x237cac0,0x27d6a1c,0x27945cd,0x2750d61,0x293f0b5,0x253db13,
0x04a764e,0x20b4d0e,0x12bb627,0x160c13b,0x0de0601,0x236e2cf,
0x2190f0b,0x354d76f,0x004336d },
{ 0x2ab473a,0x10d54e4,0x1046574,0x1d6f97b,0x0031c72,0x06426a9,
0x38678c2,0x0b76cf9,0x04f9920,0x152adf8,0x2977e63,0x1234819,
0x198be26,0x061024c,0x00d427d } },
/* 41 */
{ { 0x39b5a31,0x2123d43,0x362a822,0x1a2eab6,0x0bb0034,0x0d5d567,
0x3a04723,0x3a10c8c,0x08079ae,0x0d27bda,0x2eb9e1e,0x2619e82,
0x39a55a8,0x0c6c7db,0x00c1519 },
{ 0x174251e,0x13ac2eb,0x295ed26,0x18d2afc,0x037b9b2,0x1258344,
0x00921b0,0x1f702d8,0x1bc4da7,0x1c3794f,0x12b1869,0x366eacf,
0x16ddf01,0x31ebdc5,0x00ad54e } },
/* 42 */
{ { 0x1efdc58,0x1370d5e,0x0ddb8e7,0x1a53fda,0x1456bd3,0x0c825a9,
0x0e74ccd,0x20f41c9,0x3423867,0x139073f,0x3c70d8a,0x131fc85,
0x219a2a0,0x34bf986,0x0041199 },
{ 0x1c05dd2,0x268f80a,0x3da9d38,0x1af9f8f,0x0535f2a,0x30ad37e,
0x2cf72d7,0x14a509b,0x1f4fe74,0x259e09d,0x1d23f51,0x0672732,
0x08fc463,0x00b6201,0x001e05a } },
/* 43 */
{ { 0x0d5ffe8,0x3238bb5,0x17f275c,0x25b6fa8,0x2f8bb48,0x3b8f2d2,
0x059790c,0x18594d4,0x285a47c,0x3d301bb,0x12935d2,0x23ffc96,
0x3d7c7f9,0x15c8cbf,0x0034c4a },
{ 0x20376a2,0x05201ba,0x1e02c4b,0x1413c45,0x02ea5e7,0x39575f0,
0x2d76e21,0x113694c,0x011f310,0x0da3725,0x31b7799,0x1cb9195,
0x0cfd592,0x22ee4ea,0x00adaa3 } },
/* 44 */
{ { 0x14ed72a,0x031c49f,0x39a34bf,0x192e87d,0x0da0e92,0x130e7a9,
0x00258bf,0x144e123,0x2d82a71,0x0294e53,0x3f06c66,0x3d4473a,
0x037cd4a,0x3bbfb17,0x00fcebc },
{ 0x39ae8c1,0x2dd6a9d,0x206ef23,0x332b479,0x2deff59,0x09d5720,
0x3526fd2,0x33bf7cf,0x344bb32,0x359316a,0x115bdef,0x1b8468a,
0x3813ea9,0x11a8450,0x00ab197 } },
/* 45 */
{ { 0x0837d7d,0x1e1617b,0x0ba443c,0x2f2e3b8,0x2ca5b6f,0x176ed7b,
0x2924d9d,0x07294d3,0x104bb4f,0x1cfd3e8,0x398640f,0x1162dc8,
0x007ea15,0x2aa75fd,0x004231f },
{ 0x16e6896,0x01987be,0x0f9d53e,0x1a740ec,0x1554e4c,0x31e1634,
0x3cb07b9,0x013eb53,0x39352cb,0x1dfa549,0x0974e7f,0x17c55d2,
0x157c85f,0x1561adb,0x002e3fa } },
/* 46 */
{ { 0x29951a8,0x35200da,0x2ad042c,0x22109e4,0x3a8b15b,0x2eca69c,
0x28bcf9a,0x0cfa063,0x0924099,0x12ff668,0x2fb88dc,0x028d653,
0x2445876,0x218d01c,0x0014418 },
{ 0x1caedc7,0x295bba6,0x01c9162,0x3364744,0x28fb12e,0x24c80b6,
0x2719673,0x35e5ba9,0x04aa4cc,0x206ab23,0x1cf185a,0x2c140d8,
0x1095a7d,0x1b3633f,0x000c9f8 } },
/* 47 */
{ { 0x0b2a556,0x0a051c4,0x30b29a7,0x190c9ed,0x3767ca9,0x38de66d,
0x2d9e125,0x3aca813,0x2dc22a3,0x319e074,0x0d9450a,0x3445bac,
0x3e08a5b,0x07f29fa,0x00eccac },
{ 0x02d6e94,0x21113f7,0x321bde6,0x0a4d7b3,0x03621f4,0x2780e8b,
0x22d5432,0x1fc2853,0x0d57d3e,0x254f90b,0x33ed00b,0x289b025,
0x12272bb,0x30e715f,0x0000297 } },
/* 48 */
{ { 0x0243a7d,0x2aac42e,0x0c5b3aa,0x0fa3e96,0x06eeef9,0x2b9fdd9,
0x26fca39,0x0134fe1,0x22661ab,0x1990416,0x03945d6,0x15e3628,
0x3848ca3,0x0f91e46,0x00b08cd },
{ 0x16d2411,0x3717e1d,0x128c45e,0x3669d54,0x0d4a790,0x2797da8,
0x0f09634,0x2faab0b,0x27df649,0x3b19b49,0x0467039,0x39b65a2,
0x3816f3c,0x31ad0bd,0x0050046 } },
/* 49 */
{ { 0x2425043,0x3858099,0x389092a,0x3f7c236,0x11ff66a,0x3c58b39,
0x2f5a7f8,0x1663ce1,0x2a0fcf5,0x38634b7,0x1a8ca18,0x0dcace8,
0x0e6f778,0x03ae334,0x00df0d2 },
{ 0x1bb4045,0x357875d,0x14b77ed,0x33ae5b6,0x2252a47,0x31899dd,
0x3293582,0x040c6f6,0x14340dd,0x3614f0e,0x3d5f47f,0x326fb3d,
0x0044a9d,0x00beeb9,0x0027c23 } },
/* 50 */
{ { 0x32d49ce,0x34822a3,0x30a22d1,0x00858b7,0x10d91aa,0x2681fd9,
0x1cce870,0x2404a71,0x38b8433,0x377c1c8,0x019442c,0x0a38b21,
0x22aba50,0x0d61c81,0x002dcbd },
{ 0x0680967,0x2f0f2f9,0x172cb5f,0x1167e4b,0x12a7bc6,0x05b0da7,
0x2c76e11,0x3a36201,0x37a3177,0x1d71419,0x0569df5,0x0dce7ad,
0x3f40b75,0x3bd8db0,0x002d481 } },
/* 51 */
{ { 0x2a1103e,0x34e7f7f,0x1b171a2,0x24a57e0,0x2eaae55,0x166c992,
0x10aa18f,0x0bb836f,0x01acb59,0x0e430e7,0x1750cca,0x18be036,
0x3cc6cdf,0x0a0f7e5,0x00da4d8 },
{ 0x2201067,0x374d187,0x1f6b0a6,0x165a7ec,0x31531f8,0x3580487,
0x15e5521,0x0724522,0x2b04c04,0x202c86a,0x3cc1ccf,0x225b11a,
0x1bde79d,0x0eccc50,0x00d24da } },
/* 52 */
{ { 0x3b0a354,0x2814dd4,0x1cd8575,0x3d031b7,0x0392ff2,0x1855ee5,
0x0e8cff5,0x203442e,0x3bd3b1b,0x141cf95,0x3fedee1,0x1d783c0,
0x26f192a,0x0392aa3,0x0075238 },
{ 0x158ffe9,0x3889f19,0x14151f4,0x06067b1,0x13a3486,0x1e65c21,
0x382d5ef,0x1ab0aac,0x2ffddc4,0x3179b7a,0x3c8d094,0x05101e3,
0x237c6e5,0x3947d83,0x00f674f } },
/* 53 */
{ { 0x363408f,0x21eb96b,0x27376fb,0x2a735d6,0x1a39c36,0x3d31863,
0x33313fc,0x32235e0,0x082f034,0x23ef351,0x39b3528,0x1a69d84,
0x1d9c944,0x07159ad,0x0077a71 },
{ 0x04f8d65,0x25771e5,0x2ba84a6,0x194586a,0x1e6da5f,0x118059a,
0x14e9c32,0x1d24619,0x3f528ae,0x22f22e4,0x0f5580d,0x0747a0e,
0x32cc85f,0x286b3a8,0x008ccf9 } },
/* 54 */
{ { 0x196fee2,0x2c4431c,0x094528a,0x18e1d32,0x175799d,0x26bb6b7,
0x2293482,0x23fd289,0x07b2be8,0x1a5c533,0x158d60d,0x04a4f3f,
0x164e9f7,0x32ccca9,0x00da6b6 },
{ 0x1d821c2,0x3f76c4f,0x323df43,0x17e4374,0x0f2f278,0x121227e,
0x2464190,0x19d2644,0x326d24c,0x3185983,0x0803c15,0x0767a33,
0x1c4c996,0x0563eab,0x00631c6 } },
/* 55 */
{ { 0x1752366,0x0baf83f,0x288bacf,0x0384e6f,0x2b93c34,0x3c805e7,
0x3664850,0x29e1663,0x254ff1d,0x3852080,0x0f85c16,0x1e389d9,
0x3191352,0x3915eaa,0x00a246e },
{ 0x3763b33,0x187ad14,0x3c0d438,0x3f11702,0x1c49f03,0x35ac7a8,
0x3f16bca,0x27266bf,0x08b6fd4,0x0f38ce4,0x37fde8c,0x147a6ff,
0x02c5e5c,0x28e7fc5,0x00076a7 } },
/* 56 */
{ { 0x2338d10,0x0e77fa7,0x011b046,0x1bfd0ad,0x28ee699,0x21d73bc,
0x0461d1a,0x342ea58,0x2d695b4,0x30415ed,0x2906e0b,0x18e494a,
0x20f8a27,0x026b870,0x002c19f },
{ 0x2f4c43d,0x3f0fc3b,0x0aa95b8,0x2a01ea1,0x3e2e1b1,0x0d74af6,
0x0555288,0x0cb757d,0x24d2071,0x143d2bb,0x3907f67,0x3e0ce30,
0x131f0e9,0x3724381,0x007a874 } },
/* 57 */
{ { 0x3c27050,0x08b5165,0x0bf884b,0x3dd679c,0x3bd0b8d,0x25ce2e6,
0x1674057,0x1f13ed3,0x1f5cd91,0x0d1fd35,0x13ce6e3,0x2671338,
0x10f8b90,0x34e5487,0x00942bf },
{ 0x03b566d,0x23c3da9,0x37de502,0x1a486ff,0x1af6e86,0x1108cb3,
0x36f856c,0x01a6a0f,0x179f915,0x1595a01,0x2cfecb8,0x082568b,
0x1ba16d1,0x1abb6c0,0x00cf7f0 } },
/* 58 */
{ { 0x2f96c80,0x1b8f123,0x209c0f5,0x2ccf76d,0x1d521f2,0x3705143,
0x2941027,0x07f88af,0x07102a9,0x38b4868,0x1efa37d,0x1bdd3e8,
0x028a12e,0x02e055b,0x009a9a9 },
{ 0x1c7dfcb,0x3aa7aa7,0x1d62c54,0x3f0b0b0,0x3c74e66,0x274f819,
0x23f9674,0x0e2b67c,0x24654dd,0x0c71f0e,0x1946cee,0x0016211,
0x0045dc7,0x0da1173,0x0089856 } },
/* 59 */
{ { 0x0e73946,0x29f353f,0x056329d,0x2d48c5a,0x28f697d,0x2ea4bb1,
0x235e9cc,0x34faa38,0x15f9f91,0x3557519,0x2a50a6c,0x1a27c8e,
0x2a1a0f3,0x3098879,0x00dcf21 },
{ 0x1b818bf,0x2f20b98,0x2243cff,0x25b691e,0x3c74a2f,0x2f06833,
0x0e980a8,0x32db48d,0x2b57929,0x33cd7f5,0x2fe17d6,0x11a384b,
0x2dafb81,0x2b9562c,0x00ddea6 } },
/* 60 */
{ { 0x2787b2e,0x37a21df,0x310d294,0x07ce6a4,0x1258acc,0x3050997,
0x19714aa,0x122824b,0x11c708b,0x0462d56,0x21abbf7,0x331aec3,
0x307b927,0x3e8d5a0,0x00c0581 },
{ 0x24d4d58,0x3d628fc,0x23279e0,0x2e38338,0x2febe9b,0x346f9c0,
0x3d6a419,0x3264e47,0x245faca,0x3669f62,0x1e50d66,0x3028232,
0x18201ab,0x0bdc192,0x0002c34 } },
/* 61 */
{ { 0x17bdbc2,0x1c501c5,0x1605ccd,0x31ab438,0x372fa89,0x24a8057,
0x13da2bb,0x3f95ac7,0x3cda0a3,0x1e2b679,0x24f0673,0x03b72f4,
0x35be616,0x2ccd849,0x0079d4d },
{ 0x33497c4,0x0c7f657,0x2fb0d3d,0x3b81064,0x38cafea,0x0e942bc,
0x3ca7451,0x2ab9784,0x1678c85,0x3c62098,0x1eb556f,0x01b3aa2,
0x149f3ce,0x2656f6d,0x002eef1 } },
/* 62 */
{ { 0x0596edc,0x1f4fad4,0x03a28ed,0x18a4149,0x3aa3593,0x12db40a,
0x12c2c2a,0x3b1a288,0x327c4fb,0x35847f5,0x384f733,0x02e3fde,
0x1af0e8a,0x2e417c3,0x00d85a6 },
{ 0x0091cf7,0x2267d75,0x276860e,0x19cbbfc,0x04fef2b,0x030ce59,
0x3195cb1,0x1aa3f07,0x3699362,0x2a09d74,0x0d6c840,0x1e413d0,
0x28acdc7,0x1ff5ea1,0x0088d8b } },
/* 63 */
{ { 0x3d98425,0x08dc8de,0x154e85f,0x24b1c2c,0x2d44639,0x19a1e8b,
0x300ee29,0x053f72e,0x3f7c832,0x12417f6,0x1359368,0x0674a4c,
0x1218e20,0x0e4fbd4,0x000428c },
{ 0x01e909a,0x1d88fe6,0x12da40c,0x215ef86,0x2925133,0x004241f,
0x3e480f4,0x2d16523,0x07c3120,0x3375e86,0x21fd8f3,0x35dc0b6,
0x0efc5c9,0x14ef8d6,0x0066e47 } },
/* 64 */
{ { 0x2973cf4,0x34d3845,0x34f7070,0x22df93c,0x120aee0,0x3ae2b4a,
0x1af9b95,0x177689a,0x036a6a4,0x0377828,0x23df41e,0x22d4a39,
0x0df2aa1,0x06ca898,0x0003cc7 },
{ 0x06b1dd7,0x19dc2a8,0x35d324a,0x0467499,0x25bfa9c,0x1a1110c,
0x01e2a19,0x1b3c1cf,0x18d131a,0x10d9815,0x2ee7945,0x0a2720c,
0x0ddcdb0,0x2c071b6,0x00a6aef } },
/* 65 */
{ { 0x1ab5245,0x1192d00,0x13ffba1,0x1b71236,0x09b8d0b,0x0eb49cb,
0x1867dc9,0x371de4e,0x05eae9f,0x36faf82,0x094ea8b,0x2b9440e,
0x022e173,0x2268e6b,0x00740fc },
{ 0x0e23b23,0x22c28ca,0x04d05e2,0x0bb84c4,0x1235272,0x0289903,
0x267a18b,0x0df0fd1,0x32e49bb,0x2ab1d29,0x281e183,0x3dcd3c3,
0x1c0eb79,0x2db0ff6,0x00bffe5 } },
/* 66 */
{ { 0x2a2123f,0x0d63d71,0x1f6db1a,0x257f8a3,0x1927b2d,0x06674be,
0x302753f,0x20b7225,0x14c1a3f,0x0429cdd,0x377affe,0x0f40a75,
0x2d34d06,0x05fb6b9,0x0054398 },
{ 0x38b83c4,0x1e7bbda,0x1682f79,0x0527651,0x2615cb2,0x1795fab,
0x0e4facc,0x11f763c,0x1b81130,0x2010ae2,0x13f3650,0x20d5b72,
0x1f32f88,0x34617f4,0x00bf008 } },
/* 67 */
{ { 0x28068db,0x0aa8913,0x1a47801,0x10695ca,0x1c72cc6,0x0fc1a47,
0x33df2c4,0x0517cf0,0x3471d92,0x1be815c,0x397f794,0x3f03cbe,
0x121bfae,0x172cbe0,0x00813d7 },
{ 0x383bba6,0x04f1c90,0x0b3f056,0x1c29089,0x2a924ce,0x3c85e69,
0x1cecbe5,0x0ad8796,0x0aa79f6,0x25e38ba,0x13ad807,0x30b30ed,
0x0fa963a,0x35c763d,0x0055518 } },
/* 68 */
{ { 0x0623f3b,0x3ca4880,0x2bff03c,0x0457ca7,0x3095c71,0x02a9a08,
0x1722478,0x302c10b,0x3a17458,0x001131e,0x0959ec2,0x18bdfbc,
0x2929fca,0x2adfe32,0x0040ae2 },
{ 0x127b102,0x14ddeaa,0x1771b8c,0x283700c,0x2398a86,0x085a901,
0x108f9dc,0x0cc0012,0x33a918d,0x26d08e9,0x20b9473,0x12c3fc7,
0x1f69763,0x1c94b5a,0x00e29de } },
/* 69 */
{ { 0x035af04,0x3450021,0x12da744,0x077fb06,0x25f255b,0x0db7150,
0x17dc123,0x1a2a07c,0x2a7636a,0x3972430,0x3704ca1,0x0327add,
0x3d65a96,0x3c79bec,0x009de8c },
{ 0x11d3d06,0x3fb8354,0x12c7c60,0x04fe7ad,0x0466e23,0x01ac245,
0x3c0f5f2,0x2a935d0,0x3ac2191,0x090bd56,0x3febdbc,0x3f1f23f,
0x0ed1cce,0x02079ba,0x00d4fa6 } },
/* 70 */
{ { 0x0ab9645,0x10174ec,0x3711b5e,0x26357c7,0x2aeec7f,0x2170a9b,
0x1423115,0x1a5122b,0x39e512c,0x18116b2,0x290db1c,0x041b13a,
0x26563ae,0x0f56263,0x00b89f3 },
{ 0x3ed2ce4,0x01f365f,0x1b2043b,0x05f7605,0x1f9934e,0x2a068d2,
0x38d4d50,0x201859d,0x2de5291,0x0a7985a,0x17e6711,0x01b6c1b,
0x08091fa,0x33c6212,0x001da23 } },
/* 71 */
{ { 0x2f2c4b5,0x311acd0,0x1e47821,0x3bd9816,0x1931513,0x1bd4334,
0x30ae436,0x2c49dc0,0x2c943e7,0x010ed4d,0x1fca536,0x189633d,
0x17abf00,0x39e5ad5,0x00e4e3e },
{ 0x0c8b22f,0x2ce4009,0x1054bb6,0x307f2fc,0x32eb5e2,0x19d24ab,
0x3b18c95,0x0e55e4d,0x2e4acf5,0x1bc250c,0x1dbf3a5,0x17d6a74,
0x087cf58,0x07f6f82,0x00f8675 } },
/* 72 */
{ { 0x110e0b2,0x0e672e7,0x11b7157,0x1598371,0x01c0d59,0x3d60c24,
0x096b8a1,0x0121075,0x0268859,0x219962f,0x03213f2,0x3022adc,
0x18de488,0x3dcdeb9,0x008d2e0 },
{ 0x06cfee6,0x26f2552,0x3c579b7,0x31fa796,0x2036a26,0x362ba5e,
0x103601c,0x012506b,0x387ff3a,0x101a41f,0x2c7eb58,0x23d2efc,
0x10a5a07,0x2fd5fa3,0x00e3731 } },
/* 73 */
{ { 0x1cd0abe,0x08a0af8,0x2fa272f,0x17a1fbf,0x1d4f901,0x30e0d2f,
0x1898066,0x273b674,0x0c1b8a2,0x3272337,0x3ee82eb,0x006e7d3,
0x2a75606,0x0af1c81,0x0037105 },
{ 0x2f32562,0x2842491,0x1bb476f,0x1305cd4,0x1daad53,0x0d8daed,
0x164c37b,0x138030f,0x05145d5,0x300e2a3,0x32c09e7,0x0798600,
0x3515130,0x2b9e55c,0x009764e } },
/* 74 */
{ { 0x3d5256a,0x06c67f2,0x3a3b879,0x3c9b284,0x04007e0,0x33c1a41,
0x3794604,0x1d6240e,0x022b6c1,0x22c62a7,0x01d4590,0x32df5f6,
0x368f1a1,0x2a7486e,0x006e13f },
{ 0x31e6e16,0x20f18a9,0x09ed471,0x23b861d,0x15cf0ef,0x397b502,
0x1c7f9b2,0x05f84b2,0x2cce6e1,0x3c10bba,0x13fb5a7,0x1b52058,
0x1feb1b8,0x03b7279,0x00ea1cf } },
/* 75 */
{ { 0x2a4cc9b,0x15cf273,0x08f36e6,0x076bf3b,0x2541796,0x10e2dbd,
0x0bf02aa,0x3aa2201,0x03cdcd4,0x3ee252c,0x3799571,0x3e01fa4,
0x156e8d0,0x1fd6188,0x003466a },
{ 0x2515664,0x166b355,0x2b0b51e,0x0f28f17,0x355b0f9,0x2909e76,
0x206b026,0x3823a12,0x179c5fa,0x0972141,0x2663a1a,0x01ee36e,
0x3fc8dcf,0x2ef3d1b,0x0049a36 } },
/* 76 */
{ { 0x2d93106,0x3d6b311,0x3c9ce47,0x382aa25,0x265b7ad,0x0b5f92f,
0x0f4c941,0x32aa4df,0x380d4b2,0x0e8aba6,0x260357a,0x1f38273,
0x0d5f95e,0x199f23b,0x0029f77 },
{ 0x0a0b1c5,0x21a3d6a,0x0ad8df6,0x33d8a5e,0x1240858,0x30000a8,
0x3ac101d,0x2a8143d,0x1d7ffe9,0x1c74a2a,0x1b962c9,0x1261359,
0x0c8b274,0x002cf4a,0x00a8a7c } },
/* 77 */
{ { 0x211a338,0x22a14ab,0x16e77c5,0x3c746be,0x3a78613,0x0d5731c,
0x1767d25,0x0b799fa,0x009792a,0x09ae8dc,0x124386b,0x183d860,
0x176747d,0x14c4445,0x00ab09b },
{ 0x0eb9dd0,0x0121066,0x032895a,0x330541c,0x1e6c17a,0x2271b92,
0x06da454,0x054c2bf,0x20abb21,0x0ead169,0x3d7ea93,0x2359649,
0x242c6c5,0x3194255,0x00a3ef3 } },
/* 78 */
{ { 0x3010879,0x1083a77,0x217989d,0x174e55d,0x29d2525,0x0e544ed,
0x1efd50e,0x30c4e73,0x05bd5d1,0x0793bf9,0x3f7af77,0x052779c,
0x2b06bc0,0x13d0d02,0x0055a6b },
{ 0x3eaf771,0x094947a,0x0288f13,0x0a21e35,0x22ab441,0x23816bf,
0x15832e1,0x2d8aff3,0x348cc1f,0x2bbd4a8,0x01c4792,0x34209d3,
0x06dc72b,0x211a1df,0x00345c5 } },
/* 79 */
{ { 0x2a65e90,0x173ac2f,0x199cde1,0x0ac905b,0x00987f7,0x3618f7b,
0x1b578df,0x0d5e113,0x34bac6a,0x27d85ed,0x1b48e99,0x18af5eb,
0x1a1be9e,0x3987aac,0x00877ca },
{ 0x2358610,0x3776a8e,0x2b0723a,0x344c978,0x22fc4d6,0x1615d53,
0x3198f51,0x2d61225,0x12cb392,0x07dd061,0x355f7de,0x09e0132,
0x0efae99,0x13b46aa,0x00e9e6c } },
/* 80 */
{ { 0x0683186,0x36d8e66,0x0ea9867,0x0937731,0x1fb5cf4,0x13c39ef,
0x1a7ffed,0x27dfb32,0x31c7a77,0x09f15fd,0x16b25ef,0x1dd01e7,
0x0168090,0x240ed02,0x0090eae },
{ 0x2e1fceb,0x2ab9783,0x1a1fdf2,0x093a1b0,0x33ff1da,0x2864fb7,
0x3587d6c,0x275aa03,0x123dc9b,0x0e95a55,0x0592030,0x2102402,
0x1bdef7b,0x37f2e9b,0x001efa4 } },
/* 81 */
{ { 0x0540015,0x20e3e78,0x37dcfbd,0x11b0e41,0x02c3239,0x3586449,
0x1fb9e6a,0x0baa22c,0x00c0ca6,0x3e58491,0x2dbe00f,0x366d4b0,
0x176439a,0x2a86b86,0x00f52ab },
{ 0x0ac32ad,0x226250b,0x0f91d0e,0x1098aa6,0x3dfb79e,0x1dbd572,
0x052ecf2,0x0f84995,0x0d27ad2,0x036c6b0,0x1e4986f,0x2317dab,
0x2327df6,0x0dee0b3,0x00389ac } },
/* 82 */
{ { 0x0e60f5b,0x0622d3e,0x2ada511,0x05522a8,0x27fe670,0x206af28,
0x333cb83,0x3f25f6c,0x19ddaf3,0x0ec579b,0x36aabc0,0x093dbac,
0x348b44b,0x277dca9,0x00c5978 },
{ 0x1cf5279,0x32e294a,0x1a6c26f,0x3f006b6,0x37a3c6b,0x2e2eb26,
0x2cf88d4,0x3410619,0x1899c80,0x23d3226,0x30add14,0x2810905,
0x01a41f0,0x11e5176,0x005a02f } },
/* 83 */
{ { 0x1c90202,0x321df30,0x3570fa5,0x103e2b1,0x3d099d4,0x05e207d,
0x0a5b1bd,0x0075d0a,0x3db5b25,0x2d87899,0x32e4465,0x226fc13,
0x24cb8f8,0x3821daa,0x004da3a },
{ 0x3e66861,0x03f89b8,0x386d3ef,0x14ccc62,0x35e7729,0x11ce5b7,
0x035fbc7,0x3f4df0f,0x29c439f,0x1144568,0x32d7037,0x312f65e,
0x06b9dbf,0x03a9589,0x0008863 } },
/* 84 */
{ { 0x0a9e8c9,0x1a19b6e,0x091ecd9,0x2e16ee0,0x2a11963,0x116cf34,
0x390d530,0x194131f,0x2b580f3,0x31d569c,0x21d3751,0x3e2ce64,
0x193de46,0x32454f0,0x004bffd },
{ 0x09554e7,0x170126e,0x2be6cd1,0x153de89,0x0353c67,0x350765c,
0x202370b,0x1db01e5,0x30b12b1,0x3778591,0x00c8809,0x2e845d5,
0x1fb1e56,0x170f90d,0x00e2db3 } },
/* 85 */
{ { 0x328e33f,0x392aad8,0x36d1d71,0x0aebe04,0x1548678,0x1b55c8c,
0x24995f8,0x2a5a01e,0x1bd1651,0x37c7c29,0x36803b6,0x3716c91,
0x1a935a5,0x32f10b7,0x005c587 },
{ 0x2e8b4c0,0x336ccae,0x11382b6,0x22ec4cc,0x066d159,0x35fa585,
0x23b2d25,0x3017528,0x2a674a8,0x3a4f900,0x1a7ce82,0x2b2539b,
0x3d46545,0x0a07918,0x00eb9f8 } },
/* 86 */
{ { 0x2cf5b9b,0x03e747f,0x166a34e,0x0afc81a,0x0a115b1,0x3aa814d,
0x11cf3b1,0x163e556,0x3cbfb15,0x157c0a4,0x1bc703a,0x2141e90,
0x01f811c,0x207218b,0x0092e6b },
{ 0x1af24e3,0x3af19b3,0x3c70cc9,0x335cbf3,0x068917e,0x055ee92,
0x09a9308,0x2cac9b7,0x008b06a,0x1175097,0x36e929c,0x0be339c,
0x0932436,0x15f18ba,0x0009f6f } },
/* 87 */
{ { 0x29375fb,0x35ade34,0x11571c7,0x07b8d74,0x3fabd85,0x090fa91,
0x362dcd4,0x02c3fdb,0x0608fe3,0x2477649,0x3fc6e70,0x059b7eb,
0x1e6a708,0x1a4c220,0x00c6c4c },
{ 0x2a53fb0,0x1a3e1f5,0x11f9203,0x27e7ad3,0x038718e,0x3f5f9e4,
0x308acda,0x0a8700f,0x34472fe,0x3420d7a,0x08076e5,0x014240e,
0x0e7317e,0x197a98e,0x00538f7 } },
/* 88 */
{ { 0x2663b4b,0x0927670,0x38dd0e0,0x16d1f34,0x3e700ab,0x3119567,
0x12559d2,0x399b6c6,0x0a84bcd,0x163e7dd,0x3e2aced,0x058548c,
0x03a5bad,0x011cf74,0x00c155c },
{ 0x3e454eb,0x2a1e64e,0x1ccd346,0x36e0edf,0x266ee94,0x2e74aaf,
0x2d8378a,0x3cd547d,0x1d27733,0x0928e5b,0x353553c,0x26f502b,
0x1d94341,0x2635cc7,0x00d0ead } },
/* 89 */
{ { 0x0142408,0x382c3bb,0x3310908,0x2e50452,0x398943c,0x1d0ac75,
0x1bf7d81,0x04bd00f,0x36b6934,0x3349c37,0x0f69e20,0x0195252,
0x243a1c5,0x030da5f,0x00a76a9 },
{ 0x224825a,0x28ce111,0x34c2e0f,0x02e2b30,0x382e48c,0x26853ca,
0x24bd14e,0x0200dec,0x1e24db3,0x0d3d775,0x132da0a,0x1dea79e,
0x253dc0c,0x03c9d31,0x0020db9 } },
/* 90 */
{ { 0x26c5fd9,0x05e6dc3,0x2eea261,0x08db260,0x2f8bec1,0x1255edf,
0x283338d,0x3d9a91d,0x2640a72,0x03311f9,0x1bad935,0x152fda8,
0x0e95abd,0x31abd15,0x00dfbf4 },
{ 0x107f4fa,0x29ebe9a,0x27353f7,0x3821972,0x27311fa,0x2925ab6,
0x337ab82,0x2de6c91,0x1f115fe,0x044f909,0x21b93c2,0x3a5f142,
0x13eb5e9,0x3ab1377,0x00b26b6 } },
/* 91 */
{ { 0x22e5f2b,0x2ae7d4a,0x1ac481c,0x0a6fce1,0x2f93caf,0x242658e,
0x3f35c3c,0x050f3d2,0x30074c9,0x142079c,0x0281b4c,0x295fea3,
0x007413e,0x01726cd,0x00e4979 },
{ 0x1ab3cfb,0x1b76295,0x36adf55,0x1ad4636,0x1d444b9,0x3bd2e55,
0x35425a5,0x1aa8cd3,0x3acecd2,0x1f769e8,0x1a655e9,0x1f6846f,
0x24c70b5,0x3bff080,0x0002da3 } },
/* 92 */
{ { 0x081d0d9,0x2c00d99,0x1fe2e24,0x396063f,0x03740db,0x243f680,
0x3c1f451,0x1ff7b07,0x2803cf2,0x38ca724,0x2934f43,0x0d72d4d,
0x0e8fe74,0x2975e21,0x002b505 },
{ 0x11adcc9,0x331a99c,0x21e16cf,0x1714c78,0x1f03432,0x2caa2a6,
0x34a9679,0x2f7fe8b,0x0423c21,0x1a757ce,0x31b57d6,0x171e044,
0x093b9b2,0x13602e0,0x00db534 } },
/* 93 */
{ { 0x250a2f5,0x0b999eb,0x21d10d7,0x22b92a1,0x39b7f8d,0x0c37c72,
0x29f70f3,0x3bf0e84,0x1d7e04f,0x07a42a9,0x272c3ae,0x1587b2f,
0x155faff,0x10a336e,0x000d8fb },
{ 0x3663784,0x0d7dcf5,0x056ad22,0x319f8b1,0x0c05bae,0x2b6ff33,
0x0292e42,0x0435797,0x188efb1,0x0d3f45e,0x119d49f,0x395dcd3,
0x279fe27,0x133a13d,0x00188ac } },
/* 94 */
{ { 0x396c53e,0x0d133e9,0x009b7ee,0x13421a0,0x1bbf607,0x1d284a5,
0x1594f74,0x18cb47c,0x2dcac11,0x2999ddb,0x04e2fa5,0x1889e2c,
0x0a89a18,0x33cb215,0x0052665 },
{ 0x104ab58,0x1d91920,0x3d6d7e3,0x04dc813,0x1167759,0x13a8466,
0x0a06a54,0x103761b,0x25b1c92,0x26a8fdd,0x2474614,0x21406a4,
0x251d75f,0x38c3734,0x007b982 } },
/* 95 */
{ { 0x15f3060,0x3a7bf30,0x3be6e44,0x0baa1fa,0x05ad62f,0x1e54035,
0x099d41c,0x2a744d9,0x1c0336f,0x3e99b5b,0x1afd3b1,0x2bf1255,
0x1822bf8,0x2c93972,0x001d8cc },
{ 0x1d7584b,0x0508ade,0x20dd403,0x203a8fc,0x1c54a05,0x1611a31,
0x037c8f9,0x1dcd4fe,0x110fbea,0x30f60bc,0x3dffe2f,0x26a1de1,
0x0480367,0x18ec81c,0x0048eba } },
/* 96 */
{ { 0x346e2f6,0x0435077,0x036789b,0x3e06545,0x313ab57,0x351a721,
0x3372b91,0x15e6019,0x2fa4f6c,0x3c30656,0x272c9ac,0x10e84a8,
0x2bdacea,0x232d9e2,0x009dadd },
{ 0x182579a,0x15b1af8,0x02d8cce,0x36cb49b,0x086feba,0x2911d17,
0x268ee12,0x011e871,0x18698dc,0x35602b3,0x11b9ec2,0x0ade731,
0x0f6a05a,0x1821015,0x00007da } },
/* 97 */
{ { 0x3b00dd0,0x328d485,0x27a69e3,0x32c3a06,0x1046779,0x120b61c,
0x19fef3d,0x0fef2e6,0x134d923,0x039bce0,0x348cd0e,0x0b0c007,
0x066ae11,0x15d8f1b,0x00934e7 },
{ 0x33234dc,0x353f0f5,0x2fc1b44,0x18a193a,0x2fcae20,0x1afbc86,
0x3afe252,0x17f7e10,0x107f3b7,0x2d84d54,0x394c2e6,0x19e96a9,
0x0a37283,0x26c6152,0x003d262 } },
/* 98 */
{ { 0x37cfaf8,0x01863d0,0x0299623,0x32c80cb,0x25b8742,0x0a4d90e,
0x1f72472,0x13de652,0x31a0946,0x0ee0103,0x0f25414,0x2518b49,
0x07e7604,0x1488d9b,0x00abd6b },
{ 0x1338f55,0x2ce4af5,0x1a0c119,0x3380525,0x21a80a9,0x235d4df,
0x118ca7f,0x2dd8bcc,0x1c26bf4,0x32dc56b,0x28482b6,0x1418596,
0x3c84d24,0x1f1a5a9,0x00d958d } },
/* 99 */
{ { 0x1c21f31,0x22aa1ef,0x258c9ad,0x2d2018f,0x0adb3ca,0x01f75ee,
0x186283b,0x31ad3bf,0x3621be7,0x3b1ee6d,0x015582d,0x3d61d04,
0x2ddf32e,0x14b8a66,0x00c970c },
{ 0x2f24d66,0x00b8a88,0x100a78f,0x041d330,0x2efec1d,0x24c5b86,
0x2a6a390,0x37526bc,0x2055849,0x3339f08,0x16bffc4,0x07f9d72,
0x06ec09c,0x3f49ee8,0x00cad98 } },
/* 100 */
{ { 0x248b73e,0x1b8b42d,0x285eed7,0x39473f4,0x1a9f92c,0x3b44f78,
0x086c062,0x06a4ea3,0x34ea519,0x3c74e95,0x1ad1b8b,0x1737e2c,
0x2cfe338,0x0a291f4,0x00bbecc },
{ 0x1cec548,0x0c9b01a,0x20b298d,0x377c902,0x24f5bc1,0x2415c8d,
0x1a70622,0x2529090,0x1c5c682,0x283f1ba,0x2319f17,0x0120e2e,
0x01c6f4d,0x33c67ff,0x008b612 } },
/* 101 */
{ { 0x03830eb,0x02d4053,0x10c59bb,0x0f23b83,0x13d08f8,0x26ea4e2,
0x2626427,0x0a45292,0x0449cbc,0x0175750,0x074c46f,0x27ae0f8,
0x2d7d6ae,0x163dd3a,0x0063bb7 },
{ 0x2bb29e0,0x034bab1,0x341e1c4,0x21d2c0b,0x295aa2d,0x0f2c666,
0x1891755,0x13db64a,0x2fe5158,0x337646e,0x31a1aae,0x057bee4,
0x00f9e37,0x396d19e,0x00c1b6a } },
/* 102 */
{ { 0x2772f41,0x34f92d0,0x39d1cde,0x174ef2d,0x03a700d,0x03fbb98,
0x30d50e8,0x352ed10,0x1fcf5e5,0x3d113bc,0x26e358f,0x180653f,
0x1b43cc6,0x3cc9aa4,0x00e68a2 },
{ 0x37fe4d2,0x09dd725,0x01eb584,0x171f8a9,0x278fdef,0x3e37c03,
0x3bec02f,0x149757c,0x0cd5852,0x37d2e10,0x0e6988b,0x1c120e9,
0x0b83708,0x38e7319,0x0039499 } },
/* 103 */
{ { 0x08df5fe,0x177a02c,0x0362fc0,0x1f18ee8,0x00c1295,0x173c50a,
0x379414d,0x1885ba8,0x32a54ef,0x2315644,0x39e65cf,0x357c4be,
0x1d66333,0x09e05a5,0x0009c60 },
{ 0x1f7a2fb,0x073b518,0x2eb83ac,0x11353d7,0x1dd8384,0x0c63f2b,
0x238c6c8,0x2a1920a,0x2e5e9f1,0x1cc56f8,0x042daf4,0x1ed5dc5,
0x25f9e31,0x012a56a,0x0081b59 } },
/* 104 */
{ { 0x321d232,0x2c71422,0x3a756b6,0x30230b2,0x387f3db,0x3a7c3eb,
0x274b46a,0x201e69f,0x185bb7b,0x140da82,0x0d974a2,0x0616e42,
0x35ec94f,0x3bc366b,0x005aa7c },
{ 0x3dcfffc,0x19a9c15,0x3225e05,0x36ae114,0x16ea311,0x0cda2aa,
0x2a1a8d2,0x154b5cb,0x08348cd,0x17b66c8,0x080ea43,0x21e59f3,
0x04173b9,0x31d5b04,0x00ad735 } },
/* 105 */
{ { 0x2e76ef4,0x216acf3,0x2b93aea,0x112bc74,0x3449974,0x2b2e48f,
0x11929be,0x2f03021,0x19051e3,0x0ac202d,0x19be68a,0x3b87619,
0x26cdac4,0x086592c,0x00f00de },
{ 0x2e90d4d,0x3ed703c,0x2c648d7,0x29ddf67,0x000e219,0x3471247,
0x26febd5,0x1161713,0x3541a8f,0x302038d,0x08d2af9,0x26e1b21,
0x398514a,0x36dad99,0x002ed70 } },
/* 106 */
{ { 0x06f25cb,0x1104596,0x370faee,0x07e83f3,0x0f7b686,0x228d43a,
0x12cd201,0x0a1bd57,0x3e592dc,0x1e186fc,0x2226aba,0x2c63fe9,
0x17b039a,0x1efaa61,0x00d1582 },
{ 0x2e6acef,0x07d51e4,0x3ac326c,0x322b07e,0x1422c63,0x32ff5c7,
0x18760df,0x048928b,0x139b251,0x04d7da9,0x048d1a2,0x2a23e84,
0x199dbba,0x2fa7afe,0x0049f1a } },
/* 107 */
{ { 0x3492b73,0x27d3d3d,0x2b1a16f,0x07b2ce4,0x0cf28ec,0x2729bff,
0x3130d46,0x3e96116,0x140b72e,0x14a2ea3,0x1ca066f,0x3a61f1d,
0x022ebac,0x09192b4,0x003e399 },
{ 0x12555bb,0x0b6139d,0x239463a,0x12a70ab,0x2aaa93b,0x2254e72,
0x00424ec,0x26a6736,0x26daa11,0x25b5ad6,0x379f262,0x140cd30,
0x0c7d3bd,0x097bbcf,0x00899e9 } },
/* 108 */
{ { 0x3825dc4,0x3cd946f,0x0462b7f,0x31102e7,0x30f741c,0x3313ed6,
0x1ff5a95,0x15bf9dc,0x09b47fd,0x0f2e7a7,0x1626c0d,0x3c14f6d,
0x14098bd,0x19d7df8,0x00a97ce },
{ 0x0934f5e,0x3f968db,0x046f68a,0x12333bf,0x26cd5e1,0x1ea2161,
0x358570d,0x235031d,0x35edd55,0x05265e3,0x24ae00c,0x3542229,
0x25bb2a1,0x1c83c75,0x0058f2a } },
/* 109 */
{ { 0x24daedb,0x376928f,0x305266f,0x0499746,0x038318c,0x312efd7,
0x1910a24,0x33450a3,0x1c478a9,0x39d8bf9,0x12cc0ae,0x397aeab,
0x0654c08,0x095f283,0x00d2cdf },
{ 0x0b717d2,0x1f162c2,0x107a48f,0x128e1b3,0x2380718,0x39f4044,
0x00f626a,0x05ec0c9,0x21bc439,0x200fa4d,0x20aea01,0x186a1d8,
0x26372f2,0x1a91f87,0x0053f55 } },
/* 110 */
{ { 0x3512a90,0x33b958b,0x29f1c84,0x0106c3a,0x224b3c0,0x09b307a,
0x215d2de,0x3bdf43b,0x22cf0c9,0x176121d,0x1534143,0x09ba717,
0x16b3110,0x0f73f6c,0x008f5b7 },
{ 0x2c75d95,0x26fbcb4,0x0dda1f6,0x206f819,0x28d33d5,0x1fb4d79,
0x024c125,0x30a0630,0x1f9c309,0x0fe350d,0x1696019,0x0a54187,
0x09541fd,0x35e3a79,0x0066618 } },
/* 111 */
{ { 0x0e382de,0x33f5163,0x0dde571,0x3bb7a40,0x1175806,0x12ae8ed,
0x0499653,0x3b25586,0x38ade7a,0x3fa265d,0x3f4aa97,0x3c03dbb,
0x30c6de8,0x32d4042,0x00ae971 },
{ 0x2f788f1,0x1fbaf0e,0x3e2d182,0x3ff904f,0x0d46229,0x1d0726d,
0x15455b4,0x093ae28,0x290f8e4,0x097c0b9,0x1ae8771,0x28480bb,
0x04f6d40,0x3689925,0x0049b3b } },
/* 112 */
{ { 0x35b2d69,0x31819c0,0x11b0d63,0x035afb6,0x2b50715,0x2bece6c,
0x35f82f7,0x0ad987c,0x0011601,0x02e6f67,0x2d0a5f5,0x365e583,
0x2f7c900,0x11449c5,0x00ed705 },
{ 0x27abdb4,0x1bbfd04,0x301c157,0x263c079,0x36850d6,0x3f21f8b,
0x27d7493,0x0f9227e,0x06fb0ce,0x002daf3,0x37d8c1c,0x3ef87d7,
0x19cc6f4,0x0c3809c,0x00cf752 } },
/* 113 */
{ { 0x22d94ed,0x075b09c,0x020e676,0x084dc62,0x2d1ec3f,0x17439f1,
0x240b702,0x33cc596,0x30ebaf3,0x0359fe0,0x393ea43,0x0ece01e,
0x16c6963,0x03a82f2,0x0017faa },
{ 0x3866b98,0x3cd20b7,0x12d4e6b,0x3a6a76d,0x1205c1e,0x3e6ae1a,
0x2f9bbdf,0x2e61547,0x2d175ee,0x28e18f6,0x13cf442,0x085b0ef,
0x0e321ef,0x238fe72,0x003fb22 } },
/* 114 */
{ { 0x360ac07,0x26dc301,0x3f4d94f,0x2ba75e6,0x1f3c9cc,0x17ff20f,
0x0ea084c,0x30e39cf,0x143dc49,0x03bd43e,0x3c9e733,0x19e8aba,
0x27fbaf4,0x12d913a,0x005ee53 },
{ 0x3609e7f,0x2d89c80,0x09f020c,0x1558bf7,0x3098443,0x3c515fd,
0x1c8e580,0x16506bd,0x26cb4b2,0x1747d42,0x2ec8239,0x32c91f0,
0x1ca3377,0x079768f,0x00a5f3e } },
/* 115 */
{ { 0x185fa94,0x122759f,0x0e47023,0x0dcb6e7,0x10ba405,0x3b5eab4,
0x1f7a1fa,0x32d003f,0x1739a4c,0x3295ec3,0x1b18967,0x3f3b265,
0x34d2448,0x2dbadc9,0x00f30b5 },
{ 0x01c5338,0x2d1dcf2,0x2bd07cc,0x39a8fb5,0x2b85639,0x355bab6,
0x1df95f1,0x01eb5f6,0x17f0a16,0x1b895b5,0x157574d,0x29fff72,
0x3a8c46d,0x0118071,0x0065f84 } },
/* 116 */
{ { 0x3a1e7f1,0x17432f2,0x1f648d4,0x3000ad5,0x2ef0a08,0x1f86624,
0x1ca31b1,0x241f9dc,0x2cb4885,0x2b8610f,0x364ce16,0x1e5faf0,
0x0b33867,0x2cb637d,0x00816d2 },
{ 0x1aa8671,0x02c394e,0x35f5e87,0x393040a,0x39f0db3,0x1c831a5,
0x2966591,0x034a8d0,0x09e613c,0x042b532,0x018ddd6,0x3e402c9,
0x2e20e1a,0x29cb4cd,0x00e087c } },
/* 117 */
{ { 0x3a10079,0x20c7fea,0x3ff2222,0x1edb593,0x00dc5f8,0x3a32ccc,
0x1479073,0x0cfed11,0x2a2702a,0x17a056a,0x1fba321,0x235acb9,
0x149c833,0x172de7d,0x000f753 },
{ 0x2e95923,0x3b365cb,0x009f471,0x0df1b47,0x21e868b,0x199bbd3,
0x07b8ecc,0x12ff0af,0x189808a,0x3bd5059,0x3fbc4d2,0x0fa7b88,
0x1125bf2,0x0db0b5d,0x0043572 } },
/* 118 */
{ { 0x29cdb1b,0x1db656e,0x391efe1,0x004be09,0x245a1ca,0x3793328,
0x254af24,0x2f2e65d,0x10e5cc4,0x2af6fe7,0x2d97ac0,0x29f7d42,
0x19fd6f6,0x0ac184d,0x00c5211 },
{ 0x305eae3,0x36738d3,0x2c2b696,0x00ba50e,0x3903adc,0x2122f85,
0x0753470,0x1cf96a4,0x1702a39,0x247883c,0x2feb67e,0x2ab3071,
0x3c6b9e1,0x30cb85a,0x002ca0a } },
/* 119 */
{ { 0x3871eb5,0x284b93b,0x0a7affe,0x176a2fc,0x294c2f2,0x204d3aa,
0x1e4c2a7,0x3ec4134,0x2fb0360,0x3847b45,0x05fc11b,0x0a6db6e,
0x390fa40,0x2adfd34,0x005e9f7 },
{ 0x0646612,0x1b5cbcc,0x10d8507,0x0777687,0x3a0afed,0x1687440,
0x0222578,0x1af34a4,0x2174e27,0x372d267,0x11246c3,0x34769c5,
0x2044316,0x1b4d626,0x00c72d5 } },
/* 120 */
{ { 0x2e5bb45,0x3ff1d36,0x16dcdf5,0x128986f,0x399068c,0x2a63b1e,
0x0afa7aa,0x3a5b770,0x200f121,0x33b74bb,0x1414045,0x0f31ef8,
0x2f50e16,0x2f38cd6,0x00b0b1b },
{ 0x1a06293,0x035e140,0x2644d44,0x1f1954b,0x2cdebab,0x31d5f91,
0x0b8dbc8,0x38f2d23,0x3783cab,0x2a07e73,0x3123f59,0x3409846,
0x3784ddd,0x223bbac,0x003dc7b } },
/* 121 */
{ { 0x0741456,0x234e631,0x2121e1b,0x00980ca,0x3a9dfa9,0x098c916,
0x3fc86d1,0x1c63072,0x3625244,0x13d0471,0x05b0fc5,0x1487550,
0x2498596,0x11bb6ea,0x001afab },
{ 0x274b4ad,0x240aea1,0x3d12a75,0x2b56b61,0x1486b43,0x1b83426,
0x31c7363,0x35b59ca,0x207bb6c,0x38e6243,0x19bace4,0x0a26671,
0x35e3381,0x0c2ded4,0x00d8da4 } },
/* 122 */
{ { 0x2b75791,0x19590b1,0x2bfb39f,0x2988601,0x0050947,0x0d8bbe1,
0x23e3701,0x08e4432,0x2ed8c3d,0x326f182,0x332e1dd,0x12219c5,
0x2e0779b,0x367aa63,0x0012d10 },
{ 0x251b7dc,0x0a08b4d,0x1138b6f,0x2ea02af,0x06345a5,0x1cb4f21,
0x0332624,0x1d49d88,0x140acc5,0x2f55287,0x024447c,0x291ace9,
0x1a4966e,0x015cbec,0x005bc41 } },
/* 123 */
{ { 0x351cd0e,0x315e8e9,0x07d6e70,0x067ae8f,0x2190d84,0x351f556,
0x03bee79,0x31b62c7,0x266f912,0x1b6a504,0x007a6ad,0x3a6ab31,
0x3891112,0x3c45ba0,0x00d6ce5 },
{ 0x0e1f2ce,0x32a5edc,0x1434063,0x1ca084f,0x2a3e47c,0x137e042,
0x16e2418,0x2069280,0x3b0dfd8,0x35a22b5,0x289bf0a,0x1f667f2,
0x02d23a3,0x0ce688f,0x00d8e3f } },
/* 124 */
{ { 0x10bed6f,0x14c58dd,0x0b0abdf,0x0ca0f9a,0x3808abc,0x2ec228c,
0x2366275,0x12afa16,0x20f6b0e,0x37dca8e,0x3af0c6a,0x1c5b467,
0x1b25ff7,0x00814de,0x0022dcc },
{ 0x1a56e11,0x02fe37e,0x3f21740,0x35d5a91,0x06cb8ba,0x29bad91,
0x17176f7,0x2d919f2,0x0f7d1f5,0x13a3f61,0x04ddb05,0x0c82a51,
0x286f598,0x2e8c777,0x0007071 } },
/* 125 */
{ { 0x0f8fcb9,0x3e83966,0x170c6fd,0x3825343,0x089cec8,0x01b482a,
0x0993971,0x3327282,0x39aba8a,0x32456fe,0x1507e01,0x1c3252d,
0x21ffb13,0x29822a0,0x0083246 },
{ 0x23c378f,0x1cea7ef,0x1be9a82,0x224d689,0x37e5447,0x3764a75,
0x3a49724,0x361e1b3,0x19d365b,0x3a61ffb,0x1c29a7a,0x20ab251,
0x17ec549,0x175d777,0x004589a } },
/* 126 */
{ { 0x15540a9,0x2ec5d2a,0x05b09fa,0x1bc058b,0x07cfb88,0x28f7b86,
0x3e766be,0x189305e,0x01fe88e,0x23fdf69,0x0b919c3,0x02dc7ae,
0x3f9a9ad,0x0b83cc7,0x0086a52 },
{ 0x28bc259,0x39bdca1,0x39e4bc8,0x0e0f33b,0x16130c6,0x2919955,
0x31f4549,0x2fed027,0x30919b2,0x0a39b03,0x0ca7bb2,0x1711b24,
0x3b67b94,0x05a136b,0x00acd87 } },
/* 127 */
{ { 0x0c53841,0x31cb284,0x3ced090,0x06d5693,0x1c20ae0,0x0408d2b,
0x37ebd5e,0x081900f,0x26a8589,0x0acfd0a,0x34a1472,0x2f0c302,
0x124ccbd,0x10de328,0x00971bc },
{ 0x17ff2ff,0x27d1b54,0x147b6f7,0x38bb2ea,0x26a9c96,0x0a49448,
0x39f2f46,0x247c579,0x3b16a4e,0x28c2a5a,0x2d4c72d,0x11f248c,
0x1e4df11,0x047d604,0x0065bc3 } },
/* 128 */
{ { 0x39b3239,0x1f75f44,0x3bae87c,0x139360c,0x18b5782,0x3ffc005,
0x3c48789,0x2bc6af2,0x38b909e,0x223ff3b,0x31443a7,0x017d3bb,
0x0bfed99,0x128b857,0x00020dd },
{ 0x306d695,0x25a7b28,0x2f60ca2,0x2b6e4f2,0x1df940c,0x1fa9b8e,
0x37fab78,0x13f959f,0x10ff98c,0x38343b8,0x019cb91,0x11a1e6b,
0x17ab4c6,0x1431f47,0x004b4ea } },
/* 129 */
{ { 0x20db57e,0x102515e,0x170219e,0x2b66a32,0x1e6017c,0x2f973fe,
0x3739e51,0x0e28b6f,0x3cda7a9,0x30d91ac,0x28350df,0x1444215,
0x098b504,0x1bcd5b8,0x00ad3bd },
{ 0x22e3e3e,0x3aeaffb,0x26cb935,0x0091ce4,0x2fbd017,0x3a7ed6a,
0x335b029,0x3bfc1f1,0x3852e3f,0x2b14a86,0x046b405,0x266af4c,
0x3997191,0x33b0e40,0x00e306f } },
/* 130 */
{ { 0x3e4712c,0x26bb208,0x18eed6d,0x1b30f06,0x27ca837,0x06faf62,
0x1831873,0x3fbcf9b,0x3f3d88b,0x1fb55eb,0x0f44edc,0x29917bb,
0x3151772,0x342d72e,0x00d4e63 },
{ 0x2ee0ecf,0x39e8733,0x2e8e98c,0x0cd4e0f,0x08f0126,0x1ad157a,
0x079078a,0x23018ee,0x196c765,0x2b2f34f,0x0783336,0x075bf9c,
0x3713672,0x098d699,0x00f21a7 } },
/* 131 */
{ { 0x186ba11,0x22cf365,0x048019d,0x2ca2970,0x0d9e0ae,0x08c3bd7,
0x261dbf2,0x2fc2790,0x1ee02e6,0x10256a7,0x00dc778,0x18dc8f2,
0x157b189,0x2ebc514,0x005c97d },
{ 0x3c4503e,0x1d10d12,0x337097e,0x0c6169a,0x30fb1cb,0x3481752,
0x0df2bec,0x19768fa,0x1bcf8f7,0x2925f74,0x2c988a1,0x3be571d,
0x04cfa92,0x2ea9937,0x003f924 } },
/* 132 */
{ { 0x268b448,0x06e375c,0x1b946bf,0x287bf5e,0x3d4c28b,0x138d547,
0x21f8c8e,0x21ea4be,0x2d45c91,0x35da78e,0x00326c0,0x210ed35,
0x1d66928,0x0251435,0x00fefc8 },
{ 0x0339366,0x216ff64,0x2c3a30c,0x3c5733d,0x04eeb56,0x2333477,
0x32b1492,0x25e3839,0x1b5f2ce,0x0dcfba1,0x3165bb2,0x3acafcc,
0x10abfcd,0x248d390,0x008106c } },
/* 133 */
{ { 0x102f4ee,0x3c0585f,0x1225c8d,0x11c6388,0x08a7815,0x2b3e790,
0x2895eb6,0x18cf53a,0x0b56e5a,0x2e2c003,0x3e981ff,0x0761b55,
0x1bc32f3,0x0a7111d,0x00f5c80 },
{ 0x3568973,0x1587386,0x16ec764,0x20698a6,0x02f809b,0x2821502,
0x113d64d,0x38c2679,0x15de61c,0x0309f60,0x272999e,0x29bfe64,
0x173f70d,0x1de7fab,0x00bd284 } },
/* 134 */
{ { 0x31cdf2b,0x0f0be66,0x2151603,0x01af17e,0x32a99cf,0x085dece,
0x27d2591,0x1520df4,0x273c448,0x1ec7c54,0x102e229,0x355f604,
0x2acb75f,0x005f1fd,0x003d43e },
{ 0x270eb28,0x22ec2ce,0x306b41a,0x238fa02,0x167de2d,0x030a379,
0x245a417,0x1808c24,0x0b1a7b2,0x3ab5f6f,0x2cbc6c1,0x2c228d4,
0x3041f70,0x2d9a6cc,0x00b504f } },
/* 135 */
{ { 0x17a27c2,0x216ad7e,0x011ba8e,0x22f0428,0x16ac5ec,0x3ef3c58,
0x345533f,0x0298155,0x2856579,0x0005e03,0x19ee75b,0x146fe16,
0x29881e4,0x18ece70,0x008907a },
{ 0x20189ed,0x119ce09,0x35cb76d,0x0d91ef4,0x2284a44,0x032ad87,
0x0e8c402,0x3c82b5d,0x38c416c,0x398992f,0x1fd820c,0x169b255,
0x3b5fcfa,0x1343c92,0x00fa715 } },
/* 136 */
{ { 0x33f5034,0x20b3b26,0x28fd184,0x16b3679,0x3962d44,0x15d1bc8,
0x2fb1d69,0x1292c99,0x25a58c9,0x1b19ab7,0x2d68a5b,0x2f6a09b,
0x0d6aedb,0x2935eac,0x0005664 },
{ 0x25e32fc,0x13f9440,0x3252bcd,0x2fea5b7,0x161a5ae,0x0564a8c,
0x0a07e23,0x1545f62,0x0de9890,0x1d76765,0x1fd440e,0x2ed0041,
0x3db4c96,0x1e8ba01,0x001b0c4 } },
/* 137 */
{ { 0x0223878,0x29ab202,0x15585c2,0x1a79969,0x1ba08c2,0x2ef09ff,
0x2b1b9b9,0x181f748,0x1bf72b9,0x224645c,0x2588dc5,0x2d157e7,
0x22d939a,0x05b88d9,0x006d549 },
{ 0x31de0c1,0x23a4e0e,0x278f8da,0x1aa013c,0x1a84d18,0x0d185a5,
0x0988ccd,0x2c32efd,0x3bee10e,0x37d7ab8,0x3f2a66e,0x3e2da3e,
0x1b5701f,0x3d9f0c1,0x00a68da } },
/* 138 */
{ { 0x0b2e045,0x0133fd1,0x05d4c10,0x0d92c70,0x391b5e1,0x2292281,
0x2e40908,0x2ec694e,0x195ea11,0x29cfeca,0x3d93a4e,0x01215c0,
0x08a5f32,0x37a0eff,0x00cce45 },
{ 0x2b3106e,0x12a5fb0,0x0b4faff,0x0c2da12,0x09069c6,0x35d8907,
0x2837a6e,0x3db3fb6,0x3136cc3,0x222836b,0x3da018a,0x2741274,
0x13ba319,0x1ac7642,0x00f867c } },
/* 139 */
{ { 0x2527296,0x10a9595,0x178de4d,0x0f739c4,0x0ae26c7,0x3094599,
0x20adac6,0x2b875c2,0x3ae5dc0,0x3e04d20,0x1aab2da,0x1d3ab37,
0x15f4f75,0x0b730b5,0x00c56b5 },
{ 0x1f32923,0x2f059e5,0x2a89872,0x2056f74,0x04be175,0x1da67c0,
0x17f1e7a,0x3780a6d,0x0723ac2,0x257f367,0x1237773,0x2bcee86,
0x0b97f83,0x38aff14,0x00a64d4 } },
/* 140 */
{ { 0x2552b40,0x0b6b883,0x12e8217,0x0974d35,0x062f497,0x1e563e6,
0x30ee400,0x375d1e4,0x290751f,0x0d5b68a,0x353e48c,0x064a0d3,
0x3c343f1,0x309a394,0x0034d2a },
{ 0x3111286,0x0f08604,0x1827107,0x0536a76,0x0201dac,0x3a574de,
0x2c29dbe,0x382c7b0,0x1191f3e,0x324c5bc,0x144ce71,0x24327c1,
0x1212778,0x22bc9d8,0x00d7713 } },
/* 141 */
{ { 0x34ad1cd,0x1179b4e,0x1bc1780,0x1392a92,0x2cd86b9,0x359de85,
0x251f1df,0x0da5d5f,0x135fa61,0x0f64a42,0x34f4d89,0x0fe564c,
0x3cf9b7a,0x122d757,0x008c9c2 },
{ 0x370d4e9,0x0e9209b,0x0ae99f2,0x1518c64,0x0172734,0x2c20692,
0x1d7c135,0x149c52f,0x38928d6,0x3c78b78,0x25841d1,0x2eaa897,
0x372e50b,0x29e5d19,0x00c4c18 } },
/* 142 */
{ { 0x13375ac,0x389a056,0x211310e,0x2f9f757,0x04f3288,0x103cd4e,
0x17b2fb2,0x2c78a6a,0x09f1de6,0x23e8442,0x1351bc5,0x1b69588,
0x285b551,0x0464b7e,0x00573b6 },
{ 0x0ba7df5,0x259a0db,0x2b4089e,0x05630a2,0x3f299be,0x350ff2f,
0x1c9348a,0x3becfa4,0x3cc9a1c,0x17a6ef1,0x338b277,0x2b761d9,
0x2aa01c8,0x3cb9dd7,0x006e3b1 } },
/* 143 */
{ { 0x277788b,0x16a222d,0x173c036,0x310ff58,0x2634ae8,0x392636f,
0x0987619,0x1e6acc1,0x26dc8f7,0x242310f,0x0c09aca,0x22b8e11,
0x0d17006,0x1c2c806,0x002380c },
{ 0x297c5ec,0x1fef0e8,0x3948cf7,0x14f2915,0x2dacbc8,0x0dafb1f,
0x10de043,0x31184da,0x06414ee,0x3c9aeeb,0x1f713ab,0x308f1f8,
0x1569ed1,0x3f379bf,0x00f08bb } },
/* 144 */
{ { 0x0770ee3,0x058fd21,0x17065f8,0x251d128,0x10e0c7f,0x06cb51b,
0x0f05f7e,0x3666a72,0x3e7d01f,0x2d05fab,0x11440e5,0x28577d4,
0x2fbcf2b,0x14aa469,0x00dc5c5 },
{ 0x270f721,0x1c75d28,0x085b862,0x1d68011,0x132c0a0,0x37be81d,
0x1a87e38,0x083fa74,0x3acbf0d,0x16d6429,0x0feda1f,0x031070a,
0x2ec2443,0x21e563d,0x00454d2 } },
/* 145 */
{ { 0x0525435,0x1e98d5f,0x3dbc52b,0x1fcdf12,0x13d9ef5,0x3ff311d,
0x393e9ed,0x3cef8ae,0x2987710,0x3bdee2e,0x21b727d,0x3ba1b68,
0x10d0142,0x3c64b92,0x0055ac3 },
{ 0x0c1c390,0x38e9bb0,0x1e7b487,0x11511b3,0x1036fb3,0x25aba54,
0x1eb2764,0x048d022,0x0d971ed,0x1bb7fb5,0x100f0b4,0x06c3756,
0x2f0d366,0x3c6e160,0x0011bd6 } },
/* 146 */
{ { 0x36bc9d1,0x24d43c1,0x12c35cf,0x2fb3cf3,0x015d903,0x16bc0c7,
0x0fc8c22,0x3195c87,0x2488b1c,0x1f82b4c,0x30014e8,0x27ee58d,
0x31658dd,0x1684a5f,0x00f0f3a },
{ 0x1f703aa,0x023eebc,0x20babb9,0x080bd9d,0x12f9cc4,0x1a8e2d4,
0x0eec666,0x1176803,0x33005d6,0x1137b68,0x37de339,0x33d71cb,
0x0c906b9,0x14086b5,0x00aeef6 } },
/* 147 */
{ { 0x219045d,0x0f22c5e,0x024c058,0x00b414a,0x0ae7c31,0x3db3e96,
0x234979f,0x0cf00a8,0x3c962c7,0x27fa77f,0x1c0c4b0,0x1fe8942,
0x218053a,0x1eed3f8,0x0051643 },
{ 0x2a23ddb,0x138f570,0x104e945,0x21ca270,0x30726d8,0x3f45490,
0x37d9184,0x242ea25,0x33f6d77,0x3f15679,0x065af85,0x34fa1f5,
0x2e46b8f,0x31d17fb,0x00a2615 } },
/* 148 */
{ { 0x335167d,0x181ea10,0x0887c8d,0x01383d7,0x18b42d8,0x263447e,
0x1f13df3,0x0319d7e,0x0872074,0x2d6aa94,0x23d9234,0x36a69aa,
0x0bad183,0x3138a95,0x00bd3a5 },
{ 0x1b0f658,0x0e4530b,0x373add1,0x1b968fc,0x329dcb6,0x09169ca,
0x162df55,0x0211eff,0x02391e4,0x3867460,0x3136b1a,0x37dd36e,
0x3bc5bd9,0x2dacfe4,0x0072a06 } },
/* 149 */
{ { 0x119d96f,0x067b0eb,0x00996da,0x293eca9,0x2b342da,0x1889c7a,
0x21633a6,0x0152c39,0x281ce8c,0x18ef3b3,0x0bd62dc,0x3238186,
0x38d8b7c,0x3867b95,0x00ae189 },
{ 0x0ed1eed,0x1e89777,0x13ab73e,0x029e1d7,0x2c1257f,0x33fbc09,
0x32d5a21,0x3d870b2,0x39bb1fd,0x33663bc,0x24e83e6,0x239bda4,
0x3088bcd,0x01db1ed,0x00d71e7 } },
/* 150 */
{ { 0x14245bf,0x0da0c27,0x153b339,0x05cab0a,0x122d962,0x1b0f0f3,
0x3f5a825,0x267a2ce,0x2910d06,0x254326f,0x0f36645,0x025118e,
0x37c35ec,0x36e944e,0x006c056 },
{ 0x05ab0e3,0x29aa0c1,0x1295687,0x1fd1172,0x08d40b5,0x05bd655,
0x345048a,0x02a1c3c,0x2393d8f,0x0992d71,0x1f71c5e,0x18d4e8a,
0x30dd410,0x11d61d3,0x00dd58b } },
/* 151 */
{ { 0x2230c72,0x30213d8,0x05e367e,0x329204e,0x0f14f6c,0x3369ddd,
0x0bb4074,0x2edafd6,0x1b1aa2d,0x0785404,0x0c035ab,0x220da74,
0x1f2fdd4,0x092a091,0x00ef83c },
{ 0x3dc2538,0x1cca3e7,0x246afb5,0x24c647f,0x0798082,0x0bb7952,
0x0f5c443,0x008b38a,0x299ea1a,0x3c6cf36,0x3df2ec7,0x398e6dc,
0x29a1839,0x1cadd83,0x0077b62 } },
/* 152 */
{ { 0x25d56d5,0x3546f69,0x16e02b1,0x3e5fa9a,0x03a9b71,0x2413d31,
0x250ecc9,0x1d2de54,0x2ebe757,0x2a2f135,0x2aeeb9a,0x0d0fe2b,
0x204cb0e,0x07464c3,0x00c473c },
{ 0x24cd8ae,0x0c86c41,0x221c282,0x0795588,0x1f4b437,0x06fc488,
0x0c81ecd,0x020bf07,0x3a9e2c8,0x2294a81,0x3a64a95,0x0363966,
0x32c9a35,0x0f79bec,0x0029e4f } },
/* 153 */
{ { 0x289aaa5,0x2755b2e,0x059e0aa,0x3031318,0x0f0208a,0x35b7729,
0x00d9c6b,0x3dd29d0,0x075f2c2,0x0ece139,0x31562dd,0x04187f2,
0x13b8d4c,0x0920b85,0x003924e },
{ 0x09808ab,0x2e36621,0x2a36f38,0x1829246,0x229bf32,0x20883b7,
0x159ada8,0x3108a14,0x15bbe5b,0x1e2d1e4,0x1730096,0x0d35cbb,
0x15d0da9,0x0e60b94,0x00c4f30 } },
/* 154 */
{ { 0x31de38b,0x27b9086,0x2760e3e,0x169098d,0x2a124e2,0x00596c6,
0x3f73c09,0x0d31642,0x2341464,0x248600a,0x2e1fa10,0x2aa0fc8,
0x051e954,0x00f3b67,0x001d4bd },
{ 0x18751e6,0x25a8e1e,0x07f5c2d,0x17e30d4,0x0ed2723,0x23093e2,
0x3b80e2c,0x13de2d7,0x2fad37f,0x1be1cfb,0x3224ba9,0x0a7f5d3,
0x1714972,0x06667b7,0x009dcd9 } },
/* 155 */
{ { 0x294f22a,0x3e06993,0x0341ee9,0x24bdc7b,0x2e56098,0x2660a13,
0x018ddda,0x2c261b2,0x2953b54,0x267f51c,0x0e8a7cc,0x29ab00c,
0x3a38247,0x397ac81,0x00de684 },
{ 0x36b956b,0x347b34a,0x35834bd,0x053c06c,0x0090844,0x148cec5,
0x380b325,0x2f17b8b,0x054ef5e,0x09683fb,0x3f8b29a,0x33c979a,
0x1e01474,0x3e81fca,0x001c757 } },
/* 156 */
{ { 0x30fdfe4,0x2d712ba,0x13671bc,0x2cfc226,0x3d7c649,0x16f020e,
0x368e3f0,0x2981ebb,0x246a78a,0x115e81b,0x21223a4,0x04dbb30,
0x1a50ba2,0x12114bd,0x0089bd6 },
{ 0x055f15a,0x1046e51,0x00fd724,0x1c022a7,0x323dfa9,0x36d8efb,
0x0da4d16,0x0910dec,0x2c1fb16,0x2dbe29f,0x298284f,0x2b273bb,
0x26022c1,0x20accd5,0x00085a5 } },
/* 157 */
{ { 0x01f138a,0x2d87e7b,0x0c2815c,0x0c19a3c,0x311c9a2,0x3e4fce3,
0x029729d,0x21236b2,0x2984048,0x3f3bc95,0x2bba8fb,0x1a1b680,
0x0619a3f,0x29e0447,0x00ed5fe },
{ 0x2d1c833,0x3dcef35,0x3f809b4,0x01a1b9e,0x1509516,0x10ac754,
0x2735080,0x27b0a8a,0x2495fb8,0x0a7bdba,0x1ef8b89,0x00233a5,
0x0568bf1,0x1a126ba,0x0078a7e } },
/* 158 */
{ { 0x0470cd8,0x20e9f04,0x30003fe,0x20be1b7,0x1927346,0x2a5026d,
0x1ac06bd,0x2717ed7,0x2609493,0x3079ea5,0x1cc116d,0x31b0541,
0x2c8ccde,0x10219ae,0x001a52b },
{ 0x2864045,0x0e8d95b,0x2fc1530,0x0aa44e7,0x345eae7,0x3cc7553,
0x3ec6466,0x229b60e,0x06f6e95,0x00bed2a,0x0ff4403,0x181c639,
0x2e0df67,0x1f8fa46,0x0000811 } },
/* 159 */
{ { 0x04310a2,0x20cee8e,0x09fc5d5,0x3707f5b,0x0bdfb4e,0x12713ee,
0x24f1028,0x0787ee6,0x39a581c,0x3797ec8,0x10a9746,0x112cb9f,
0x142b9ba,0x1da0ef6,0x0078f7b },
{ 0x07607ae,0x3232872,0x2a7e076,0x0bb572a,0x182b23c,0x1d8f918,
0x181f392,0x37c45a9,0x24a3886,0x0b2a297,0x264e7f2,0x1fa433c,
0x0fcfcc8,0x21c0857,0x0004f74 } },
/* 160 */
{ { 0x01d161c,0x1744585,0x2d17528,0x03a4f13,0x267cd2e,0x30d861f,
0x062a647,0x213284b,0x139ed25,0x27d4ca5,0x02fbbd6,0x31ddf11,
0x3c50ac4,0x1dd86f7,0x00107de },
{ 0x16beebd,0x1b7317a,0x2151997,0x256a196,0x3be2aff,0x3621cab,
0x0a9da19,0x05f3038,0x23da63c,0x3178d5e,0x215cc67,0x07f7f63,
0x0c6d8d3,0x3bf5e5c,0x00c44bb } },
/* 161 */
{ { 0x00c62f1,0x3e0f893,0x1572703,0x3b93865,0x19b1e28,0x389b33b,
0x02858bf,0x0e3e9aa,0x04bc436,0x234e072,0x25ba43d,0x3dca19e,
0x0274394,0x20f442e,0x003b4a7 },
{ 0x176451e,0x2b5ed5d,0x35c8ee1,0x25c52da,0x0c3d0b5,0x32b306e,
0x030954f,0x275ecf7,0x10e472c,0x21577c4,0x02f8a32,0x321bb5c,
0x0098f97,0x104e237,0x00d0433 } },
/* 162 */
{ { 0x0a8f2fe,0x034548b,0x141f1a6,0x121246f,0x1616409,0x237f80d,
0x2e29a55,0x1218db6,0x3ea278e,0x1669856,0x1ad7c8e,0x36d11de,
0x2c2fcbb,0x18c0b3a,0x001c706 },
{ 0x1699b4b,0x2d531a6,0x17e85e2,0x1b48e78,0x2b509ca,0x2818ea0,
0x0165fee,0x0b809ca,0x09db6a2,0x3dad798,0x326ee1d,0x204e416,
0x091fa12,0x1c890e5,0x0007b9f } },
/* 163 */
{ { 0x0ff4e49,0x0bb0512,0x0129159,0x05db591,0x03e4e9f,0x055ab30,
0x0f82881,0x0ac2deb,0x3a8bb09,0x356a8d2,0x3d38393,0x03e4089,
0x38187cd,0x1377a93,0x0041672 },
{ 0x0139e73,0x3990730,0x187d3c4,0x33e4793,0x2e0fe46,0x2ad87e2,
0x33c792c,0x21d4fb6,0x1e4d386,0x2932d1b,0x20f1098,0x1270874,
0x0ea6ee4,0x0167d6e,0x005e5fd } },
/* 164 */
{ { 0x1856031,0x2b7519d,0x3bd07fc,0x337abcb,0x089c7a4,0x2a1f120,
0x3523ce7,0x2ba406b,0x09561d9,0x1797f04,0x3cdb95f,0x2d6193e,
0x32c7d3f,0x223aed6,0x00beb51 },
{ 0x2e65825,0x158f0ce,0x16413d1,0x310395f,0x3116854,0x250baf4,
0x373d341,0x156cc47,0x104c069,0x0893716,0x195a0a6,0x035320e,
0x37b7d8a,0x21b5755,0x00fb26b } },
/* 165 */
{ { 0x286ae17,0x04239f1,0x1a56c53,0x0e74707,0x29090d7,0x2bb142b,
0x03b0139,0x1aac916,0x08ba49a,0x0376682,0x3382f85,0x064bbab,
0x2910e28,0x1d5bd7f,0x00cc8df },
{ 0x0ab7630,0x208e8e7,0x3fc1877,0x26bee39,0x264984a,0x192ff05,
0x08ef9c3,0x0aa6951,0x071c44e,0x26eed3e,0x035c95e,0x06906ad,
0x10a0690,0x397eaa9,0x00c6c23 } },
/* 166 */
{ { 0x034d8dd,0x005b064,0x279bb78,0x12c2c4f,0x1856bb4,0x0c90681,
0x06409ab,0x3b48617,0x19a2d78,0x0a34bf8,0x326eddf,0x31f09b5,
0x04f04dc,0x3d7c944,0x003ccaf },
{ 0x321f843,0x35fb71a,0x1e4c397,0x377a5d7,0x2da88e4,0x3d6ada7,
0x33d3964,0x1b30149,0x0e39aae,0x054dda0,0x3e6f946,0x1273394,
0x3ffd3f7,0x2f6655e,0x00021dd } },
/* 167 */
{ { 0x37233cf,0x11617dd,0x26f07b6,0x3d8250a,0x0fe6771,0x3f9bbbc,
0x2aba7ad,0x200a58d,0x3568603,0x198eefa,0x1e8fcf3,0x3b9610b,
0x20524ac,0x2a67528,0x0048d9a },
{ 0x1a5e57a,0x1e9d303,0x16c9cff,0x0f39527,0x3c23259,0x03c8a1e,
0x104bccf,0x182d5a1,0x18dbc83,0x05b5f42,0x1b402f4,0x317c525,
0x11bf1ea,0x3c46e1f,0x0061936 } },
/* 168 */
{ { 0x0153a9d,0x36859ee,0x2cf0aa9,0x2b27a0f,0x0a49fe3,0x2d984e1,
0x018f8e1,0x1378453,0x1ab3843,0x1987093,0x283dae9,0x25cf0e8,
0x14fc93d,0x280609d,0x00c99ba },
{ 0x026b1e3,0x34663d3,0x2202477,0x21a9d45,0x212e8e1,0x18ab77e,
0x2e52f63,0x0a14ce1,0x295c396,0x00c7a3d,0x2aaedb6,0x30abc4d,
0x374acde,0x1318a73,0x00fcfdb } },
/* 169 */
{ { 0x0a40298,0x3ba5633,0x11956b3,0x14fcbd7,0x3c38781,0x34bab96,
0x165630e,0x1f3c831,0x37e3a69,0x2b4226c,0x2d5029e,0x3b4ab1e,
0x1da6ac2,0x3eb43c3,0x007e5cd },
{ 0x1b86202,0x109b7f6,0x2054f98,0x2c50cd7,0x2ed1960,0x3c518e7,
0x1b02463,0x319c07f,0x1c30db6,0x045fdc2,0x373421e,0x31a1eb9,
0x1a8acbf,0x31289b0,0x0013fef } },
/* 170 */
{ { 0x3fa0a5f,0x068661f,0x2109e36,0x00b18ff,0x1f4b261,0x31d3844,
0x0acbc56,0x3aebc99,0x1fa77ab,0x152bd11,0x24cddb7,0x2313f74,
0x06eea44,0x15f5114,0x000b131 },
{ 0x2e9993d,0x1ac565c,0x2cbe22a,0x3921797,0x12c3c57,0x360f868,
0x33560bf,0x320ee99,0x382c3b8,0x39af88f,0x00bbe38,0x2c4ea59,
0x3399b40,0x00ceb45,0x0066eea } },
/* 171 */
{ { 0x0c6c693,0x31ba56d,0x3d3849f,0x378dabd,0x0efc735,0x17f90bf,
0x13343d3,0x2df0f81,0x27c6a9a,0x13c2a90,0x0a0fcb2,0x27c10d9,
0x3bc50c7,0x090e4fa,0x0016287 },
{ 0x2927e1e,0x35af405,0x184c5c3,0x3499cee,0x240158e,0x33522e6,
0x386fc84,0x0a0b69f,0x1a660ea,0x34590fb,0x22a1bee,0x2ce4fab,
0x31a9445,0x0e78655,0x00664c8 } },
/* 172 */
{ { 0x3eeaf94,0x115d409,0x21e7577,0x097aa67,0x22875c9,0x021ab7a,
0x27e7ba5,0x1093f04,0x2a086fe,0x05d9494,0x2b6c028,0x10f31b0,
0x1312d11,0x262759c,0x00c9bb2 },
{ 0x1acb0a5,0x30cdf14,0x0f78880,0x0574f18,0x1a37109,0x098adbb,
0x2113c09,0x2060925,0x1f89ce4,0x1974976,0x3381358,0x2dab5ca,
0x2159c53,0x3af1303,0x000ea3b } },
/* 173 */
{ { 0x1e49bea,0x29142b1,0x1a59cab,0x055f017,0x0684e54,0x39eb0db,
0x29cab9d,0x255ee8b,0x35f2e6f,0x05329e6,0x09b817b,0x1ec091c,
0x1df0fef,0x2641f62,0x00eb304 },
{ 0x2fe5096,0x3dcc1d1,0x2aaf508,0x3a0b813,0x0695810,0x144bddb,
0x2f1bd93,0x281ae23,0x3513ebc,0x1ddd984,0x0cf158b,0x35218eb,
0x257daf7,0x391253b,0x00b2a81 } },
/* 174 */
{ { 0x153e6ba,0x22396db,0x0ea2ff2,0x2a45121,0x0a90de1,0x34cf23b,
0x2db60ce,0x1a900be,0x2f328b6,0x355e75b,0x2c24372,0x0b75b77,
0x2ec7d4f,0x3f24759,0x00e9e33 },
{ 0x39eab6e,0x2267480,0x3b5e110,0x1e8fa5e,0x2a31a66,0x3f739a3,
0x00166dc,0x3552d88,0x3ae5137,0x3efa0fa,0x0800acd,0x17df61d,
0x38c8608,0x04cc31b,0x00cf4ab } },
/* 175 */
{ { 0x31e08fb,0x1961164,0x22c003f,0x078541b,0x3643855,0x30da587,
0x11f0dc9,0x324595e,0x329e3dc,0x29a041e,0x3495d2c,0x0908dd3,
0x1895b83,0x198dbb9,0x00d8cfb },
{ 0x0349b1b,0x383c5a8,0x2b86525,0x1b1283e,0x133cd2c,0x2be376a,
0x012ee82,0x1eb4d1b,0x0ba71e9,0x01f3109,0x37621eb,0x1d9b77c,
0x0d39069,0x3d5a97c,0x0095565 } },
/* 176 */
{ { 0x20f5e94,0x1eefc86,0x1327e0e,0x054760b,0x2f771e1,0x3ac447e,
0x033e3dc,0x198e040,0x04dd342,0x1b49a5d,0x00d01ef,0x3cb6768,
0x1ceafbd,0x31c6812,0x001cb80 },
{ 0x221c677,0x060ca27,0x398b17f,0x0146723,0x36452af,0x02d9e65,
0x39c5f78,0x3cf50d6,0x0be40f8,0x2970b87,0x26d667c,0x3e45959,
0x16e7943,0x01673e7,0x009faaa } },
/* 177 */
{ { 0x2078fe6,0x0918602,0x11dd8ad,0x399193f,0x0f6cc73,0x0f8dd12,
0x2ce34dc,0x06d7d34,0x0c5e327,0x0989254,0x2fc5af7,0x2443d7b,
0x32bc662,0x2fe2a84,0x008b585 },
{ 0x039327f,0x08e616a,0x252f117,0x1f52ab0,0x234e2d2,0x0a5b313,
0x2f59ef6,0x0f7a500,0x15c4705,0x2c02b81,0x28b4f09,0x08aa5c8,
0x0180efc,0x0993e83,0x00a9e86 } },
/* 178 */
{ { 0x0310ecc,0x2d8892f,0x14ed0b7,0x3c59fe8,0x08a1a74,0x0850e57,
0x1d09607,0x044a21f,0x109f5c9,0x237c6cf,0x06b264a,0x3fc8f1a,
0x0d4c539,0x2740f96,0x00dc2d4 },
{ 0x1d6f501,0x0adf4ea,0x14f7215,0x0930102,0x3f4c32e,0x24e2643,
0x366596d,0x081ff18,0x38f94fb,0x2c21341,0x328594c,0x267c75c,
0x196b3fd,0x29932cb,0x0036def } },
/* 179 */
{ { 0x3ed7cbe,0x26de044,0x3d0e461,0x0565e12,0x295e500,0x31dc17f,
0x32251c2,0x3420ca8,0x3995f0d,0x2e8ddab,0x0361a45,0x10971b0,
0x11e7b55,0x33bc7ca,0x00812d2 },
{ 0x3d94972,0x1606817,0x0383ccf,0x0e795b7,0x026e20e,0x0f6fefc,
0x13685d6,0x315d402,0x0cc36b8,0x1c7f059,0x390ef5e,0x316ae04,
0x08c66b9,0x2fac9a4,0x0040086 } },
/* 180 */
{ { 0x3e3c115,0x153de4d,0x1a8ae5e,0x2330511,0x169b8ee,0x1d965c2,
0x2edff2b,0x3ef99e6,0x1631b46,0x1f8a238,0x118d7bb,0x12113c3,
0x26424db,0x0f4122a,0x00e0ea2 },
{ 0x3d80a73,0x30393bc,0x0f98714,0x278ef59,0x087a0aa,0x3b18c20,
0x04b8a82,0x2068e21,0x030255d,0x3382b27,0x055397f,0x05448dd,
0x2015586,0x1190be0,0x000b979 } },
/* 181 */
{ { 0x2e03080,0x2895692,0x09fb127,0x2d1602a,0x1232306,0x105bd4e,
0x28cd6a6,0x0a83813,0x1ee13b0,0x2abadc3,0x0c09684,0x00e33e1,
0x033eea3,0x30f0a39,0x00a710e },
{ 0x01b1f7d,0x1c959da,0x017077a,0x254bf0a,0x086fbce,0x15cd6b2,
0x008683f,0x23a4f4d,0x22a6bd6,0x14e8c93,0x0027d15,0x31d0d4f,
0x271777e,0x1533510,0x00ab603 } },
/* 182 */
{ { 0x34c209d,0x14d0abb,0x270432a,0x1d02358,0x22ba752,0x209757f,
0x34af6fc,0x1ffc52e,0x1ced28e,0x1870e46,0x1e0340f,0x3f0bf73,
0x33ba91d,0x2ebca7c,0x00c6580 },
{ 0x1d442cb,0x0879d50,0x24e4ae1,0x3f4e91c,0x04c7727,0x093cd1d,
0x16d6a45,0x10a8b95,0x0c77856,0x361f84f,0x217845f,0x0bbeec6,
0x0485718,0x33c5385,0x00dcec0 } },
/* 183 */
{ { 0x1539819,0x225507a,0x1bf11cb,0x13e7653,0x0c8cb3b,0x05f695e,
0x353f634,0x2827874,0x3fb8053,0x22de9a5,0x035d8b7,0x2105cc7,
0x2a7a98d,0x35bed95,0x0085748 },
{ 0x1859c5d,0x00e51f0,0x22a21fd,0x3054d74,0x06ce965,0x328eab7,
0x26a13e0,0x13bfc65,0x01d4fb1,0x36600b9,0x36dd3fc,0x01232ed,
0x15bbaa9,0x0ad7a51,0x0089b18 } },
/* 184 */
{ { 0x3360710,0x1eb5a90,0x136bd77,0x3bd57a6,0x0841287,0x12886c9,
0x35c6700,0x21bc6eb,0x25f35ad,0x3bcb01c,0x0707e72,0x23e9943,
0x03e5233,0x34bb622,0x002bf8e },
{ 0x16e0d6a,0x04b3d2d,0x290cb02,0x049a10c,0x350537e,0x22cf71b,
0x3184a19,0x2dc8b62,0x2350210,0x3b4afa6,0x159781e,0x1d01b6d,
0x1853440,0x16442f0,0x005a78d } },
/* 185 */
{ { 0x348b02c,0x1ea8ab5,0x3b954d5,0x14684ac,0x0be5b34,0x11c4496,
0x0a7a456,0x14f6eb7,0x11a3221,0x2d65f82,0x32eb1ea,0x09c4018,
0x3f301f3,0x32e8a1c,0x00bd9ad },
{ 0x0543f7f,0x31e744e,0x1fefd1d,0x24a486c,0x1000220,0x3977e3b,
0x1b3ef51,0x2512a1b,0x2049e6b,0x122232b,0x391a32b,0x2f4a7b1,
0x1c13e71,0x081a9b4,0x00d3516 } },
/* 186 */
{ { 0x1924f43,0x1ae5495,0x28d52ef,0x2b93e77,0x2d2f401,0x371a010,
0x33e8d7a,0x06ed3f1,0x30c0d9d,0x2589fa9,0x3bf3567,0x2ecf8fa,
0x2dee4c3,0x152b620,0x007e8a2 },
{ 0x1924407,0x01bd42d,0x044a089,0x18686b5,0x2f14a0e,0x17cdce3,
0x0efa216,0x3c586a8,0x1d6ae71,0x375831f,0x3175894,0x20e43eb,
0x34c009e,0x3480527,0x00d115c } },
/* 187 */
{ { 0x12abf77,0x38b0769,0x25682f2,0x295508c,0x0c2a0dc,0x1259b73,
0x023ea25,0x340e7b5,0x3c7cd0d,0x1f92324,0x176405c,0x1528894,
0x18f2e1e,0x2c59c35,0x001efb5 },
{ 0x0fb1471,0x07e7665,0x141da75,0x07d9f4a,0x0fdb31e,0x0dccda6,
0x074eb25,0x3d92a9b,0x11189a0,0x1b4c557,0x24b8d2b,0x0533f92,
0x0e9e344,0x2fa3dea,0x008d5a4 } },
/* 188 */
{ { 0x2669e98,0x1ad3514,0x2a035c9,0x08a3f50,0x24547f9,0x0a145d3,
0x1c1319d,0x3fe833d,0x1ae064b,0x1e01734,0x246d27e,0x3a2f13c,
0x01e1150,0x263f55e,0x00f89ef },
{ 0x2e0b63f,0x3e57db7,0x23a4b4f,0x11c8899,0x0ad8500,0x348f3a7,
0x2918604,0x27d6409,0x1ce5001,0x38f94c2,0x29a508a,0x39bdc89,
0x3a52c27,0x194899e,0x00e9376 } },
/* 189 */
{ { 0x0368708,0x34a2730,0x2e1da04,0x0bd78c1,0x2c45887,0x0c44bfa,
0x3a23de3,0x390b9db,0x1746efd,0x05c638e,0x1d20609,0x3263370,
0x31987f0,0x2988529,0x005fa3c },
{ 0x0aa9f2a,0x20622f7,0x060deee,0x0c9626a,0x3312cc7,0x18ebac7,
0x008dd6c,0x0ad4fe6,0x3db4ea6,0x1dc3f50,0x090b6e9,0x0aff8d2,
0x26aa62c,0x18f3e90,0x00105f8 } },
/* 190 */
{ { 0x38059ad,0x25e576c,0x3ea00b2,0x1fa4191,0x25686b7,0x2d1ce8f,
0x30470ed,0x3478bbf,0x340f9b6,0x1c9e348,0x3d594ec,0x2ffe56e,
0x3f23deb,0x0cd34e9,0x00f4b72 },
{ 0x1a83f0b,0x2166029,0x28b32a2,0x06a5c5a,0x20786c4,0x0944604,
0x0901bd2,0x379b84e,0x221e2fe,0x0346d54,0x1f4eb59,0x01b8993,
0x2462e08,0x25f9d8b,0x006c4c8 } },
/* 191 */
{ { 0x0b41d9d,0x2e417ed,0x265bd10,0x199148e,0x3826ca4,0x1a67e8d,
0x1bbd13b,0x23e414d,0x3d773bc,0x356e64c,0x0d2118a,0x0cb587f,
0x25fd093,0x24fb529,0x00158c6 },
{ 0x2806e63,0x3ecaa39,0x251b4dd,0x3b2d779,0x2e31ed3,0x066f1a6,
0x060e518,0x2c7e3e5,0x0d62c76,0x0d88a70,0x101970a,0x1e3c8c6,
0x272b8bb,0x083e73b,0x0031f38 } },
/* 192 */
{ { 0x09e1c72,0x072bcb0,0x0cf4e93,0x2604a64,0x00715f2,0x10c98b6,
0x2ad81d9,0x234fcce,0x37a7304,0x1974a4a,0x1c7415f,0x14aaa93,
0x19587b1,0x3f643f4,0x00c3d10 },
{ 0x1ddadd0,0x2cd715d,0x294cf76,0x14479ed,0x19f5f4a,0x0198c09,
0x1ab7ebc,0x182c0bc,0x0879202,0x1807273,0x05d39da,0x2c7d868,
0x29c4ec4,0x1b13ad2,0x006dcd7 } },
/* 193 */
{ { 0x1c83f01,0x0245bff,0x24f90ba,0x112554f,0x2354c8b,0x3f17988,
0x0c511af,0x39e1e9b,0x26ae95b,0x0ae551c,0x35b41a6,0x0120455,
0x1e989cb,0x1b37aff,0x00fa2ae },
{ 0x324659a,0x1aef1c3,0x1c43637,0x3f530a2,0x313a999,0x326af62,
0x134184e,0x2ac131c,0x3f6a789,0x30a300a,0x13e526e,0x2107af3,
0x093a8ff,0x2479902,0x00442b1 } },
/* 194 */
{ { 0x22b6e20,0x31b18be,0x18614ca,0x26fdb5a,0x197f29e,0x325b44b,
0x0ab1dbb,0x042348a,0x3275e8e,0x15bae44,0x0077124,0x2cf5345,
0x2803ad4,0x188f2a2,0x0061b20 },
{ 0x2a560b1,0x3ced069,0x3cf42c2,0x100e167,0x3879e1d,0x0936ff0,
0x1b51450,0x14c55f3,0x3153bfa,0x2957423,0x2a93823,0x15f5dce,
0x2c9a22f,0x16731a8,0x00a97f2 } },
/* 195 */
{ { 0x18edbbb,0x18c5ef9,0x1f13c30,0x071e77f,0x225ade5,0x1b60f75,
0x1beaf11,0x3e495ad,0x2441dd8,0x2fa00e2,0x32a87b6,0x00050f2,
0x038de7f,0x0037d6d,0x00a885d },
{ 0x39e48bd,0x1d9e433,0x2768e9f,0x3c29458,0x3f0bdf9,0x35ed5f2,
0x36709fa,0x176dc10,0x012f7c1,0x2df8547,0x1d90ee3,0x053c089,
0x21a8d35,0x200cb0d,0x002e84e } },
/* 196 */
{ { 0x23ec8d8,0x1d81f55,0x0cb7227,0x07f8e4d,0x2a66181,0x163f577,
0x272e7af,0x131a8f2,0x2046229,0x25e6276,0x36bbefe,0x2cdc22f,
0x17c8288,0x33dd4fb,0x000d524 },
{ 0x330c073,0x1a6728b,0x1cf369f,0x12e7707,0x2f0fa26,0x17c2abd,
0x0a45680,0x26ebd13,0x3c7d19b,0x1c3d6c8,0x2abd110,0x064fd07,
0x09b8339,0x02b4a9f,0x009e3e1 } },
/* 197 */
{ { 0x0ae972f,0x2093c35,0x06e7a90,0x0af1ba1,0x243eef0,0x2748582,
0x0606122,0x13a45f9,0x0acfe60,0x08a685e,0x0eb184b,0x015bc11,
0x0cdf423,0x157fad5,0x004fcad },
{ 0x2728d15,0x3e5bceb,0x0331a0f,0x31b1a80,0x28a2680,0x3b94955,
0x04cae07,0x176b57e,0x03ac5a6,0x3d7918b,0x22d23f4,0x0ae077f,
0x1eb075d,0x006f16c,0x006e473 } },
/* 198 */
{ { 0x38219b9,0x0475a2b,0x107a774,0x39946c6,0x1cb883c,0x004e0ed,
0x087e571,0x25c3497,0x059982f,0x0a71f66,0x118305d,0x1aaf294,
0x3a5dbaa,0x34be404,0x00725fe },
{ 0x3abd109,0x336ebea,0x2528487,0x15a1d61,0x0c0f8cf,0x2b56095,
0x2591e68,0x3549a80,0x1d1debb,0x0701c6c,0x161e7e3,0x1f7fa2e,
0x3dfe192,0x17e6498,0x0055f89 } },
/* 199 */
{ { 0x175645b,0x26c036c,0x0b92f89,0x09ed96d,0x351f3a6,0x19ce67b,
0x33ac8db,0x2f0828b,0x27fe400,0x0b9c5e1,0x1967b95,0x3324080,
0x11de142,0x1d44fb3,0x003d596 },
{ 0x3979775,0x3af37b6,0x3e88d41,0x2f1a8b9,0x299ba61,0x085413c,
0x1149a53,0x0beb40e,0x31427ba,0x239f708,0x357d836,0x1558c22,
0x280a79f,0x1b255f6,0x002b6d1 } },
/* 200 */
{ { 0x39ad982,0x3d79d89,0x01a684a,0x0b6722e,0x39bb4c9,0x39a6399,
0x1ad44e0,0x3059f5e,0x048265f,0x33a2fa4,0x0c3a4cc,0x0d7df98,
0x23a33f1,0x34e2e21,0x00a0a10 },
{ 0x386efd9,0x1c91f34,0x06c2e19,0x3e6d48d,0x00eefd3,0x2181ef2,
0x2415f97,0x1d33b08,0x0625086,0x1e8aa3e,0x08c9d60,0x0ab427b,
0x2764fa7,0x3b7943e,0x00cd9f0 } },
/* 201 */
{ { 0x1a46d4d,0x0e471f4,0x1693063,0x0467ac0,0x22df51c,0x127a0f7,
0x0498008,0x20e0b16,0x1aa8ad0,0x1923f42,0x2a74273,0x01761ce,
0x1600ca4,0x187b87e,0x00ee49e },
{ 0x0c76f73,0x19daf92,0x0b2ad76,0x3d8049d,0x1d9c100,0x0fe1c63,
0x0bb67c8,0x035cc44,0x02002fc,0x37b2169,0x344656a,0x1127879,
0x1939bc0,0x0dd8df6,0x0028ce7 } },
/* 202 */
{ { 0x0544ac7,0x26bdc91,0x042697e,0x356e804,0x1f2c658,0x2ceb7ef,
0x2dec39f,0x02c1dcc,0x391a2df,0x2344beb,0x2171e20,0x3099c94,
0x0fa548a,0x37216c9,0x00f820c },
{ 0x0f4cf77,0x29bbaa5,0x33c6307,0x34a5128,0x118c783,0x2dd06b1,
0x139d4c0,0x2db912e,0x1153ffb,0x1075eb3,0x3a255e4,0x2892161,
0x36d5006,0x125338c,0x0014fbc } },
/* 203 */
{ { 0x1584e3c,0x0830314,0x00279b9,0x167df95,0x2c7733c,0x2108aef,
0x0ce1398,0x35aaf89,0x012523b,0x3c46b6a,0x388e6de,0x01a2002,
0x0582dde,0x19c7fa3,0x007b872 },
{ 0x1e53510,0x11bca1f,0x19684e7,0x267de5c,0x2492f8b,0x364a2b0,
0x080bc77,0x2c6d47b,0x248432e,0x3ace44f,0x32028f6,0x0212198,
0x2f38bad,0x20d63f0,0x00122bb } },
/* 204 */
{ { 0x30b29c3,0x3cec78e,0x01510a9,0x0c93e91,0x3837b64,0x1eca3a9,
0x105c921,0x05d42e6,0x1379845,0x07ce6f2,0x0e8b6da,0x0e0f093,
0x220b2cd,0x1f6c041,0x00299f5 },
{ 0x0afdce3,0x2b0e596,0x2f477b6,0x2ccf417,0x3a15206,0x26ec0bf,
0x2e37e2b,0x2593282,0x0ab9db3,0x2841dd8,0x27954be,0x277a681,
0x03f82e2,0x2b610c7,0x00446a1 } },
/* 205 */
{ { 0x06b8195,0x3b3a817,0x31b9c6f,0x317d279,0x3d744a7,0x1de9eb9,
0x296acc1,0x1ce9ea3,0x06c3587,0x246815d,0x3756736,0x0588518,
0x1c971a4,0x1fde1f4,0x00aa021 },
{ 0x3fd3226,0x274561d,0x00be61e,0x01393d8,0x30f6f23,0x29b7fc1,
0x04cebc7,0x0a892a7,0x20109f1,0x27456be,0x0c863ee,0x2eb6c8a,
0x38c782b,0x039397a,0x00a2829 } },
/* 206 */
{ { 0x29de330,0x21fe80f,0x145b55b,0x1986570,0x012b260,0x2482fbc,
0x0536e0a,0x16b7382,0x32c4d19,0x1deffdb,0x145f418,0x0c67a76,
0x2ce477f,0x218fe24,0x00f9848 },
{ 0x3e37657,0x3f074d3,0x245ad0e,0x20973c3,0x23c58de,0x2c332ef,
0x2ad21a8,0x0bf1589,0x208af95,0x1f4a8c4,0x2b43735,0x1e46657,
0x15d4f81,0x0c3e63a,0x005f19d } },
/* 207 */
{ { 0x26865bb,0x20f6683,0x16a672e,0x0efd8d1,0x222f5af,0x18f2367,
0x1e9c734,0x25c3902,0x178dfe6,0x2903a79,0x311b91c,0x1adbbe9,
0x225a387,0x0b3e509,0x0089551 },
{ 0x34e462b,0x23b6a32,0x27c884c,0x129104b,0x384c015,0x3adedc7,
0x325db1c,0x021dc10,0x1e366f7,0x3054df7,0x1992b9a,0x2824e64,
0x0ae77f3,0x181b526,0x00a7316 } },
/* 208 */
{ { 0x2d260f5,0x2434bf2,0x28c0139,0x0a7bb03,0x176c3be,0x3def5f5,
0x05bee00,0x3692df7,0x3d2efeb,0x3a6f859,0x1122b87,0x38f779a,
0x1415ccc,0x2c260ad,0x0075a28 },
{ 0x04607a6,0x042f37a,0x3f0df68,0x0a1bd36,0x3c6d581,0x2d36bfa,
0x2d577d1,0x0a3affa,0x0b2066b,0x2e6f110,0x0b17e84,0x3c76a5e,
0x1a57553,0x012f36a,0x0004595 } },
/* 209 */
{ { 0x29e5836,0x0e6808c,0x269d13e,0x147dc5c,0x32c9e7d,0x09b258e,
0x2c58d6f,0x1efd716,0x0437996,0x34ec31b,0x15908d9,0x2efa8fd,
0x09ad160,0x079fc1f,0x00d8481 },
{ 0x3d20e4a,0x18269d6,0x3aa8fe7,0x34829c2,0x2e4325d,0x0d800e1,
0x11f370b,0x10c08dc,0x22fd092,0x1a5fe55,0x0acc443,0x037030d,
0x1cdd404,0x097379e,0x00fd6d7 } },
/* 210 */
{ { 0x313eafb,0x3f438f3,0x2e5fb3e,0x2ed6a82,0x121009c,0x240889e,
0x00c5537,0x269b792,0x334b2fc,0x1dd573c,0x07096ae,0x19296fc,
0x3813985,0x2742f48,0x00ddd64 },
{ 0x2045041,0x3842c62,0x1572d0d,0x04f255f,0x06e05b4,0x383ec97,
0x1ff8064,0x18bed71,0x39b6411,0x2764cc5,0x257439f,0x3521217,
0x172aa42,0x342a2a3,0x0070c5b } },
/* 211 */
{ { 0x3bdf646,0x1c5ce25,0x1f7ca76,0x2d2acca,0x3aa1485,0x23c97f7,
0x3e11d6f,0x0609338,0x07ec622,0x01da8ff,0x3392474,0x17ca07f,
0x13a9a04,0x353a5b4,0x0024557 },
{ 0x14c27cd,0x32012f7,0x3fea875,0x3d03d71,0x211c5f0,0x3157fdf,
0x0c880bd,0x3c406b2,0x2c51103,0x24ab377,0x399faa8,0x0d06887,
0x16b5738,0x28b33a7,0x00c7b67 } },
/* 212 */
{ { 0x2357586,0x35c93e3,0x0da09a0,0x3d77d92,0x11d7f4f,0x37b98a9,
0x3e6c9bf,0x2cdca70,0x2f00389,0x2412673,0x18eab87,0x0101436,
0x11617e9,0x06d9b01,0x00e8eef },
{ 0x37e3ca9,0x16ffaf0,0x391debf,0x1b69382,0x07c5e94,0x312fa8a,
0x0973142,0x2cadde4,0x109ee67,0x3a07db0,0x1afc5ed,0x08df66f,
0x304c7af,0x0804aae,0x00d2e60 } },
/* 213 */
{ { 0x24f57bf,0x1818322,0x182a615,0x25bfc44,0x0f97586,0x0a5bbc0,
0x36773c6,0x1a2660c,0x3ceff66,0x3270152,0x319cd11,0x2845845,
0x1acfad6,0x19076f8,0x009824a },
{ 0x289fd01,0x2de97ee,0x39d80b7,0x026227d,0x0f8d3b8,0x15e0a17,
0x21ea08f,0x20a2317,0x136ae6d,0x3deb1d1,0x3521ef5,0x0de8801,
0x0a25d5d,0x0612c98,0x005ecc4 } },
/* 214 */
{ { 0x308c8d3,0x3aec669,0x01ecddc,0x13f18fe,0x1e63ed0,0x061cfe5,
0x05f5a01,0x1db5741,0x14479f2,0x0ced6b5,0x025ae5b,0x09ca8f5,
0x2160581,0x1404433,0x008bfeb },
{ 0x08228bf,0x0e02722,0x37df423,0x33ecabf,0x34bd82a,0x32f529f,
0x28f1800,0x0c8f671,0x1246b44,0x1ff35dc,0x091db95,0x303f3da,
0x28f7f60,0x3624136,0x00cfbb4 } },
/* 215 */
{ { 0x326139a,0x2977e4e,0x3eb89a6,0x20ecb31,0x13e076a,0x2a592f3,
0x28e82d5,0x235ad1e,0x239b927,0x262938a,0x2444354,0x141b263,
0x0d56693,0x2a3fc78,0x0006497 },
{ 0x31efa05,0x3a3664a,0x3e333de,0x2a114e4,0x12da63c,0x3c15e6b,
0x2f7277c,0x363aa92,0x2393236,0x16bd2d1,0x32b617f,0x32b656c,
0x3b1246c,0x22e2e22,0x00ce76d } },
/* 216 */
{ { 0x03843dc,0x094de82,0x13b463d,0x0507905,0x089eb35,0x2a6bf25,
0x35ebc4e,0x2bb5d45,0x1808ed1,0x1de9949,0x185e829,0x0a55847,
0x0b73d67,0x1a2ed61,0x008dd2d },
{ 0x133c3a4,0x04e7980,0x38ea237,0x2ad2f49,0x19de838,0x018bf36,
0x29b072c,0x21c1ba0,0x14f63ba,0x31c1cc3,0x13cd05e,0x20120ff,
0x1f84d60,0x16e0321,0x00872ab } },
/* 217 */
{ { 0x19d4d49,0x1ddb4e6,0x05e7fc0,0x37bb0fd,0x1a3eb59,0x36b87f0,
0x190e440,0x1c7fef2,0x31ea153,0x14cd65a,0x1bc7ab2,0x11f72ca,
0x39582d4,0x0fa4d65,0x00cd5b6 },
{ 0x3d1ff11,0x0d9be9d,0x2903ae3,0x017b7b9,0x259f28f,0x110cefc,
0x03fed1a,0x38039bd,0x09bdf9c,0x3055027,0x2ca9c5d,0x2d737b6,
0x3bdb421,0x16560b5,0x00f9f33 } },
/* 218 */
{ { 0x022c792,0x110de25,0x38bf959,0x08f2562,0x1239ea9,0x3c1d950,
0x21a247d,0x315112d,0x285bb9f,0x2534a73,0x0b42455,0x1a4a99c,
0x069009a,0x1680392,0x006e0ca },
{ 0x1b3bece,0x269e0a1,0x18926b7,0x0e7187e,0x241f35e,0x39d1fe0,
0x02099aa,0x1675bfe,0x23fd0ca,0x3d6322b,0x19406b5,0x324c38a,
0x242434a,0x3ae677c,0x002ce04 } },
/* 219 */
{ { 0x2c37b82,0x1ae6506,0x0d83436,0x23496c1,0x0ff0c72,0x2711edf,
0x1513611,0x04f9c7d,0x1edbeff,0x376fcb5,0x212a683,0x23bf547,
0x0f9c4f7,0x16e6627,0x0082cd8 },
{ 0x0cb5d37,0x31b6db8,0x1a15e23,0x2f5cbb8,0x0818aee,0x21dc6c5,
0x12aafd2,0x205f608,0x1d91def,0x3def088,0x1445c51,0x3100e8a,
0x3746bda,0x145c4b0,0x00711b0 } },
/* 220 */
{ { 0x2a99ecc,0x27b5217,0x35e10ed,0x036e32a,0x0f79950,0x15c32f7,
0x2c87dcb,0x3ebb2a3,0x2c2d35d,0x114b3ec,0x2e4d80a,0x0c7eb89,
0x2abe58d,0x3727737,0x00e6a37 },
{ 0x1eca452,0x1968d07,0x344e5d3,0x29435a2,0x109a5f8,0x181d12c,
0x238ea5a,0x127a564,0x00dbb42,0x0fcbfb7,0x2909b2e,0x2571d3a,
0x08250e3,0x0694e4e,0x00e156d } },
/* 221 */
{ { 0x3181ae9,0x1acf411,0x3808d79,0x2a11065,0x0baf44b,0x133cfeb,
0x1330943,0x1711b9a,0x2dec3bd,0x1906a9a,0x2ed947c,0x369d763,
0x1a5254f,0x104a7a9,0x00acd9d },
{ 0x030301b,0x31568f5,0x2a4965c,0x33ded4b,0x03c9a5b,0x16541fc,
0x1319cf1,0x2a3748b,0x1b5de74,0x18bb82e,0x077ac2b,0x309a87a,
0x3c31420,0x0f6a4b9,0x00387d7 } },
/* 222 */
{ { 0x0d3fdac,0x120cfa3,0x1b8e13c,0x1ccccb9,0x376fcd4,0x0bf87f4,
0x271b4be,0x363b3fd,0x28b5d98,0x0535cd3,0x114bbc1,0x3ab4f19,
0x10494b1,0x2161ece,0x00d14ca },
{ 0x12d37e9,0x110ebd7,0x062295a,0x1cc0119,0x073c6ea,0x15d5411,
0x0aeb4b1,0x23fba91,0x175fab5,0x3ee8fe1,0x1c680a6,0x1e76f27,
0x3ddfc97,0x3d69ecd,0x00e1ee5 } },
/* 223 */
{ { 0x2d29f46,0x2d19204,0x3137cd0,0x02c3b54,0x193295b,0x02fbdb2,
0x2260948,0x22c02ff,0x3885424,0x1299595,0x00e7f9c,0x310ff2a,
0x01ea169,0x0deef85,0x0021908 },
{ 0x1b26cfb,0x38566a8,0x2852875,0x21debff,0x290ca9f,0x0b29663,
0x26550d9,0x2b44457,0x05d1938,0x1f8f825,0x366ef93,0x1d8daec,
0x069e5ef,0x342ece6,0x00b6034 } },
/* 224 */
{ { 0x2d8356e,0x1578c09,0x226f4d2,0x3b74c51,0x0f83666,0x0323b59,
0x1ddf61d,0x1ed8508,0x3c52667,0x0e5b91c,0x1e9b18b,0x352bdfa,
0x13f75da,0x352aa4e,0x00fceff },
{ 0x1c731d5,0x04e2844,0x01d9843,0x286cbc5,0x105bcb3,0x05edd9c,
0x21fa956,0x3b1ec83,0x01288cc,0x22fbf3a,0x10f1b56,0x081cf72,
0x15cb758,0x18687c1,0x00f5722 } },
/* 225 */
{ { 0x2973088,0x1209dcd,0x3980f31,0x0221aa7,0x1c008e7,0x011b098,
0x395947e,0x2f2806d,0x27dca76,0x037c79a,0x31acddf,0x2bf6219,
0x0d8f4ab,0x13644d9,0x00ff705 },
{ 0x2260594,0x18d51f8,0x277e2cf,0x1cb5cec,0x2468a53,0x3e6f4d7,
0x019e24e,0x0f30f1d,0x0202404,0x34ad287,0x090b39c,0x23c11ea,
0x1a2e3a2,0x3a851be,0x00dca2c } },
/* 226 */
{ { 0x3277538,0x221cd94,0x3738ab7,0x0973da5,0x1a734e2,0x2c8b8b0,
0x2e1d1e6,0x348499b,0x389ebe1,0x18b1854,0x02bb076,0x1b2b500,
0x0f207f3,0x170cf99,0x0012088 },
{ 0x0fbfec2,0x1df55a4,0x34ae59e,0x2ab5e95,0x3f9e781,0x3411794,
0x1410b05,0x17c3a00,0x0aaa91b,0x074ed7c,0x3fbb352,0x3477c01,
0x3ee9ab3,0x0cfb1ca,0x0011c4b } },
/* 227 */
{ { 0x3c3a7f3,0x2e60ca0,0x2354d32,0x33e2362,0x28083ab,0x03d3b16,
0x3164045,0x0a41f7a,0x3f0641e,0x38635d1,0x31bbf03,0x225e2bb,
0x0cd894e,0x1f72228,0x0093244 },
{ 0x33d5897,0x383faf3,0x0e6d561,0x0bc4d80,0x3fc3a68,0x05a9adc,
0x0b9d73d,0x3d6031e,0x2ded29b,0x339c4ff,0x08d69e5,0x089488c,
0x3fda40a,0x295c7fd,0x003a924 } },
/* 228 */
{ { 0x0093bee,0x115532d,0x2ec0fb6,0x0969631,0x3a6d65a,0x0f43b4d,
0x26994d4,0x0b51104,0x2515515,0x3695a26,0x284caa8,0x397aa30,
0x25538b8,0x353f47c,0x0033f05 },
{ 0x3615d6e,0x37f8246,0x07dae0f,0x23dc154,0x02ded7e,0x1eef320,
0x1631e51,0x3447f75,0x13e267f,0x353e1d1,0x3f89d62,0x369c8ff,
0x1a21dc6,0x2b8b8f3,0x0055cbc } },
/* 229 */
{ { 0x34e84f3,0x2f2539a,0x2c35336,0x0c53bdc,0x1728630,0x3ad5fe6,
0x05fdeee,0x3386db6,0x272a42e,0x29fd38c,0x36f0320,0x21b2ed4,
0x331e67f,0x28ae48c,0x00f09b6 },
{ 0x2778435,0x0fb3c55,0x32d221d,0x2660c8e,0x32977ba,0x1c12f03,
0x1b57fb1,0x01229a8,0x38b389f,0x375ddf3,0x2c6b42c,0x3885d3e,
0x2c55a9c,0x2ffc279,0x00404e2 } },
/* 230 */
{ { 0x04c5ddb,0x2c4d788,0x150e9b9,0x110fbfd,0x29dbfe0,0x30ef83d,
0x2ab4bfe,0x395bcd7,0x30d0a43,0x0e2d30f,0x0e73f9b,0x07199cc,
0x0c9054c,0x22f4b1e,0x0092ed3 },
{ 0x386e27c,0x00fdaa8,0x0507c70,0x1beb3b6,0x0b9c4f4,0x277d519,
0x024ec85,0x1cbaba8,0x1524295,0x112be58,0x21fc119,0x273578b,
0x2358c27,0x280ca07,0x00aa376 } },
/* 231 */
{ { 0x0dbc95c,0x16488cf,0x337a078,0x1abbcb8,0x0aae1aa,0x1caa151,
0x00108d4,0x1edf701,0x3e68d03,0x1203214,0x0c7eee2,0x084c572,
0x07752d2,0x215a3b9,0x00195d3 },
{ 0x2cd7fbe,0x06e80f6,0x052bd4b,0x07b4f83,0x24b5ac6,0x2aaded4,
0x13c0526,0x0ffa9a3,0x08c660e,0x13c35c9,0x3145efb,0x36cfe24,
0x0936daf,0x268e3d0,0x00a73fd } },
/* 232 */
{ { 0x31b17ce,0x2e7bcee,0x3f31891,0x19f1849,0x1140236,0x015487f,
0x32e58d3,0x202204a,0x049e350,0x1ce91f9,0x3f75150,0x27f212f,
0x0d16ee4,0x1c894c4,0x004023f },
{ 0x33399fa,0x2397b6d,0x2a3ea60,0x36354ca,0x1f12632,0x117a105,
0x22758e8,0x361844e,0x3851fc2,0x0ab92db,0x339d02f,0x1e7d6c4,
0x19ebd38,0x0a9a036,0x00446d2 } },
/* 233 */
{ { 0x3e164f1,0x008c092,0x19200f5,0x35a22e0,0x38d09d2,0x212b3bf,
0x0056f19,0x3a03545,0x1f075e9,0x0e97137,0x1f496a9,0x32d1f9b,
0x36bf738,0x35ace37,0x00899e1 },
{ 0x19eb2a6,0x21fa22d,0x338b69e,0x18e6d1f,0x1280d9d,0x1953a55,
0x1411ea3,0x2960566,0x0fd969a,0x1f3e375,0x130742a,0x170aebd,
0x33085ff,0x14d868d,0x00a4391 } },
/* 234 */
{ { 0x0a4bdd2,0x39ca8ea,0x37026ac,0x346da3b,0x0c656cd,0x03136b6,
0x233e7e9,0x0714352,0x08a9d95,0x192bb38,0x085d68e,0x20016b8,
0x102b8ea,0x1f5dbdd,0x00fdd7a },
{ 0x0d6fa45,0x3ec29a6,0x2b8cce6,0x1c84413,0x0228f86,0x28275f7,
0x3d8787d,0x0c19748,0x28b2ae9,0x1954850,0x2a56c36,0x3eae8f7,
0x0aca595,0x00e42a2,0x00edbe5 } },
/* 235 */
{ { 0x3b26c82,0x3682b6f,0x2f9cd64,0x0f254b0,0x0e5d70b,0x1f9dfda,
0x28f365f,0x35a57d7,0x00208f2,0x19c8d38,0x112e7be,0x3e403bb,
0x3734efa,0x24d12b3,0x0027dc6 },
{ 0x260a46a,0x13fd7b0,0x1c2880e,0x338b70c,0x27da5eb,0x29a7d54,
0x1c5d73c,0x2130921,0x32969cc,0x2b37eda,0x2d6d4ec,0x0716bfb,
0x0763703,0x1320889,0x00c7bbf } },
/* 236 */
{ { 0x1fe01b2,0x2dcb1d2,0x11b89d5,0x219e4ea,0x0347851,0x3d1810e,
0x3a3c54c,0x06dbe8e,0x03d3ab2,0x2dcfa39,0x3e57b8a,0x337a382,
0x0426450,0x0e9f748,0x006488b },
{ 0x1dc4582,0x0e62cf7,0x06fea9e,0x2a56fb1,0x31698c1,0x15b4e10,
0x1446ef1,0x0a689fc,0x1d87703,0x20ff497,0x2c71066,0x2c48868,
0x2e6cf05,0x30aa9cb,0x0065b2d } },
/* 237 */
{ { 0x1021d63,0x2217df3,0x1f0821a,0x057fa98,0x23f344b,0x173dcf9,
0x1ba6ddc,0x22c8eb5,0x18f227a,0x0455343,0x1c55931,0x1d0dcf3,
0x20fa19b,0x1c56618,0x004feab },
{ 0x19ec924,0x224e39f,0x2550509,0x179b51f,0x284d54a,0x2d85d41,
0x2d1bdc1,0x1a29068,0x3826158,0x1267f85,0x3005a92,0x0769e00,
0x379b617,0x17b5f63,0x00a70bf } },
/* 238 */
{ { 0x22216c5,0x049437f,0x33510bc,0x141d806,0x22c37e2,0x1bc1adf,
0x300175d,0x2e6ded8,0x0a18bfe,0x35377a3,0x382f843,0x08410ca,
0x00afd4f,0x0be6c6b,0x008d70e },
{ 0x2e91abb,0x1cede2a,0x28f225c,0x28e18c0,0x30230dc,0x173cc2d,
0x123ecfe,0x3c9962e,0x2c25506,0x27b5d53,0x329a5e3,0x106e231,
0x3889b8e,0x3b0aeaf,0x00ee67c } },
/* 239 */
{ { 0x3e46c65,0x0eb3d46,0x1d7ae18,0x23f9d59,0x2978953,0x2589ed3,
0x073391d,0x2461e1e,0x0c19f1d,0x22fd2b1,0x0691f5c,0x2e67d8d,
0x1fb985d,0x200dd28,0x00a68df },
{ 0x392b5fa,0x123b46f,0x1c323c4,0x104f82f,0x0a098c8,0x26fc05b,
0x34cd557,0x0913639,0x09c115e,0x3977c34,0x3410b66,0x062b404,
0x0213094,0x132c5e8,0x008b612 } },
/* 240 */
{ { 0x26e3392,0x3b0ebf0,0x2e00425,0x1c285c8,0x3c07f84,0x08d5ad0,
0x028190e,0x1669b73,0x1ffb1ef,0x053b65f,0x063028c,0x0aceb47,
0x18988c2,0x0f09a30,0x0007072 },
{ 0x0f49e7d,0x28c0bd3,0x252270d,0x24cfc4a,0x0c5e87c,0x2165052,
0x2cdd1d1,0x04931d2,0x3abca74,0x22b57dc,0x169fd47,0x0b928fb,
0x17cc3e7,0x21a1ec4,0x0061593 } },
/* 241 */
{ { 0x1aa0486,0x2e55dea,0x15577b7,0x0d6818f,0x36e41fb,0x2a411f5,
0x17d5c7d,0x1eea6c0,0x28068a8,0x0e31d20,0x1f08ad9,0x117e973,
0x08a28ab,0x085d30a,0x00cd9fb },
{ 0x347843d,0x1119095,0x11e3595,0x1b29584,0x134d64c,0x2ff3a35,
0x247ea14,0x099fc4b,0x2056169,0x145dd03,0x2ed03fb,0x1250e3b,
0x3f5135c,0x2b753f0,0x009da30 } },
/* 242 */
{ { 0x0fa5200,0x214a0b3,0x313dc4e,0x23da866,0x3270760,0x15c9b8b,
0x39a53df,0x1f79772,0x3c9e942,0x2984901,0x154d582,0x1685f87,
0x2e1183e,0x1f79956,0x00b9987 },
{ 0x15254de,0x3a5cac0,0x37c56f0,0x2c7c29b,0x292a56d,0x195be2c,
0x17e4e1a,0x0660f4a,0x052ad98,0x1267f80,0x07cfed8,0x194b4bc,
0x01738d3,0x14ba10f,0x00c7843 } },
/* 243 */
{ { 0x29b2d8a,0x242bc1f,0x19646ee,0x0615f3c,0x0ac8d70,0x07ca3bf,
0x2d90317,0x2c83bdb,0x1a96812,0x39fdc35,0x31c61ee,0x2d55fd3,
0x2375827,0x355f189,0x00f1c9b },
{ 0x21a6194,0x1f4050a,0x2b845cf,0x02c6242,0x2dd614e,0x3a4f0a9,
0x39de100,0x24714fb,0x175e0cd,0x0be633d,0x14befc3,0x13b0318,
0x1d68c50,0x299989e,0x00d0513 } },
/* 244 */
{ { 0x059fb6a,0x2b6eb6a,0x3666a8e,0x39f6ca0,0x1cf8346,0x388b8d5,
0x35e61a3,0x271adec,0x22c9963,0x20a4fb3,0x16f241c,0x0058b89,
0x21ddafa,0x1ee6fde,0x00d2e6c },
{ 0x0075e63,0x39894d0,0x0286d0d,0x187e7b2,0x02405aa,0x3f91525,
0x37830a8,0x2723088,0x2c7364e,0x013f406,0x104ba75,0x270f486,
0x3520b4d,0x3852bc6,0x00d589b } },
/* 245 */
{ { 0x262e53b,0x1da93d1,0x3676135,0x147e41d,0x335ec2f,0x1f02be5,
0x297d139,0x22d6198,0x1fe9e59,0x13b4c80,0x1e70f60,0x2f1d4a9,
0x2d95149,0x14d6ec4,0x00b54af },
{ 0x12c1c76,0x2930ac8,0x0dfd36e,0x31fac94,0x218f5bb,0x2828691,
0x1466cc9,0x3645e83,0x1a4dac2,0x1549593,0x0e95fab,0x19567d2,
0x27a3320,0x0642729,0x007487c } },
/* 246 */
{ { 0x1e98e9c,0x2ff8df7,0x119975a,0x098a904,0x099b90b,0x336c7df,
0x010996d,0x159d46d,0x3118b3b,0x3aacd1b,0x31f8ae1,0x214864f,
0x398c104,0x089dae2,0x001ec4d },
{ 0x1452baa,0x2f24991,0x2572ba3,0x162b312,0x2387d18,0x147c5c7,
0x38eff6e,0x0700251,0x37d931e,0x23cd5c1,0x254c8ca,0x3b9df37,
0x1c9a4ff,0x0bfd547,0x00fb489 } },
/* 247 */
{ { 0x1b8dff8,0x2f6b40b,0x05a25b1,0x3f5688a,0x1d462f4,0x2802d18,
0x2aad8ed,0x1b46c75,0x3cf4130,0x250fefb,0x2a13fe1,0x23a1bcd,
0x0940442,0x04605fe,0x00c8b2f },
{ 0x0d51afb,0x14a2abc,0x1d06762,0x291526c,0x2a3e2fe,0x28f77d9,
0x3ad8f2e,0x3481a1b,0x04b4fbd,0x2836733,0x0189ff5,0x3a5f533,
0x319a6cd,0x0f58667,0x00c3679 } },
/* 248 */
{ { 0x1b85197,0x22426d4,0x2895ea3,0x342d324,0x3ffb17d,0x376cfcf,
0x30878b1,0x3c3c83a,0x0ffc57c,0x0ac174a,0x1abd57e,0x2f78b9c,
0x01b20d8,0x0a37103,0x007f2be },
{ 0x19a2d48,0x137288a,0x182d655,0x0ba0dde,0x25130ba,0x01c65c6,
0x23205f1,0x2097621,0x2827cf2,0x2c57b98,0x03748f2,0x2db15fc,
0x385a0d4,0x13690c0,0x00a9e3f } },
/* 249 */
{ { 0x3fbc9c6,0x2df3b20,0x377e33e,0x31d1505,0x024a311,0x3c1d9ff,
0x1377f74,0x00b6b20,0x2364ab7,0x184ab6b,0x2a77969,0x3f2db6c,
0x2a6adb7,0x0a10073,0x004a6fb },
{ 0x1fc73de,0x2c74ab3,0x3d325e8,0x2346c0b,0x1d0efae,0x2076146,
0x19c190d,0x225c4fe,0x3fafc80,0x2cf063d,0x11b7ae7,0x3dc4f9d,
0x3c3f841,0x10d7c1f,0x000a4b3 } },
/* 250 */
{ { 0x19b7d2e,0x28f1300,0x0b897dd,0x06b5371,0x0631c8d,0x336cc4f,
0x09cd6e1,0x2ec1952,0x1104c07,0x07512bb,0x35f000d,0x25f84e9,
0x1df4d8f,0x193f769,0x000e9ee },
{ 0x2346910,0x267cecf,0x0ad7eaa,0x087e8a5,0x1622f69,0x342cbfa,
0x2aa20d0,0x206e88a,0x3991e58,0x093fb4b,0x0157180,0x3cecb5b,
0x2e17c9a,0x1ea371f,0x00919e6 } },
/* 251 */
{ { 0x2250533,0x13f931d,0x3ef8c72,0x395f605,0x18a2080,0x1cb25d4,
0x2fb0f41,0x1c0ba8a,0x1eb17c0,0x266c433,0x09b7e3e,0x0e5d78f,
0x0cdc5bf,0x1f7c734,0x0020611 },
{ 0x205ebd5,0x127986f,0x02c0fb0,0x1705b1e,0x1eb0bb5,0x2dffb42,
0x2331b8a,0x18fc04e,0x31d6328,0x17db162,0x0d3b619,0x193bdb9,
0x3f11662,0x2d8e694,0x0092c51 } },
/* 252 */
{ { 0x08b364d,0x31ef20a,0x25c4a57,0x021ed07,0x14a562e,0x262a684,
0x1d21c66,0x126e5a6,0x181f3f8,0x2a93b65,0x1eb726b,0x08fbbce,
0x084f9a2,0x308f30a,0x0013159 },
{ 0x23f4963,0x0c7960e,0x2a81739,0x2242b69,0x3965003,0x2aca542,
0x28a1c65,0x2ad48fb,0x149775f,0x1bbb7d2,0x0f2671b,0x3594b85,
0x22f5563,0x2470f13,0x00fed44 } },
/* 253 */
{ { 0x0eb453e,0x3ab70fd,0x1a5b335,0x18f2b74,0x25ff74b,0x3612a46,
0x33d0d75,0x28cdda4,0x2b9b49b,0x22728fb,0x004c15b,0x1beb33b,
0x1a7e41f,0x0c9b702,0x004ef19 },
{ 0x1ca3233,0x0b4c90f,0x1d4b53d,0x2428896,0x20ee405,0x151bc00,
0x022edb5,0x1adc463,0x00109ea,0x06490a6,0x30e91e6,0x3682b76,
0x23c50aa,0x3bd2665,0x005fe53 } },
/* 254 */
{ { 0x0c28c65,0x3741ae4,0x247d372,0x0b04673,0x2176524,0x2c8bf20,
0x01fb806,0x3330701,0x307b0a7,0x3999fb7,0x1261bec,0x256679c,
0x3f22ac7,0x26e8673,0x00bc69d },
{ 0x3c06819,0x35df344,0x379d009,0x2bb8a0a,0x0635a66,0x096c6fa,
0x1ac4a62,0x023e53b,0x0e45240,0x115f53d,0x3056af8,0x0a66b16,
0x3c386ee,0x1130e82,0x00cc384 } },
/* 255 */
{ { 0x14c2356,0x190ec73,0x07be490,0x145d415,0x0740a48,0x1251301,
0x3eaf29d,0x2628190,0x079299a,0x26e95c9,0x2e05fdf,0x2ca7c5b,
0x32d7b48,0x3d84226,0x0033fb4 },
{ 0x150f955,0x01240aa,0x3ddf867,0x137fb70,0x297e103,0x17eeda8,
0x1320b60,0x266ec84,0x13f4322,0x0c8f5ee,0x0590e4a,0x386815e,
0x00ce61f,0x161bd63,0x008e1d0 } },
};
/* Multiply the base point of P384 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
static int sp_384_ecc_mulmod_base_15(sp_point_384* r, const sp_digit* k,
int map, void* heap)
{
return sp_384_ecc_mulmod_stripe_15(r, &p384_base, p384_table,
k, map, heap);
}
#endif
/* Multiply the base point of P384 by the scalar and return the result.
* If map is true then convert result to affine coordinates.
*
* km Scalar to multiply by.
* r Resulting point.
* map Indicates whether to convert result to affine.
* heap Heap to use for allocation.
* returns MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_mulmod_base_384(mp_int* km, ecc_point* r, int map, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 p;
sp_digit kd[15];
#endif
sp_point_384* point;
sp_digit* k = NULL;
int err = MP_OKAY;
err = sp_384_point_new_15(heap, p, point);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 15, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL) {
err = MEMORY_E;
}
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_384_from_mp(k, 15, km);
err = sp_384_ecc_mulmod_base_15(point, k, map, heap);
}
if (err == MP_OKAY) {
err = sp_384_point_to_ecc_point_15(point, r);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(point, 0, heap);
return err;
}
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* Returns 1 if the number of zero.
* Implementation is constant time.
*
* a Number to check.
* returns 1 if the number is zero and 0 otherwise.
*/
static int sp_384_iszero_15(const sp_digit* a)
{
return (a[0] | a[1] | a[2] | a[3] | a[4] | a[5] | a[6] | a[7] |
a[8] | a[9] | a[10] | a[11] | a[12] | a[13] | a[14]) == 0;
}
#endif /* WOLFSSL_VALIDATE_ECC_KEYGEN || HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
/* Add 1 to a. (a = a + 1)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_384_add_one_15(sp_digit* a)
{
a[0]++;
sp_384_norm_15(a);
}
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a Byte array.
* n Number of bytes in array to read.
*/
static void sp_384_from_bin(sp_digit* r, int size, const byte* a, int n)
{
int i, j = 0;
word32 s = 0;
r[0] = 0;
for (i = n-1; i >= 0; i--) {
r[j] |= (((sp_digit)a[i]) << s);
if (s >= 18U) {
r[j] &= 0x3ffffff;
s = 26U - s;
if (j + 1 >= size) {
break;
}
r[++j] = (sp_digit)a[i] >> s;
s = 8U - s;
}
else {
s += 8U;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
}
/* Generates a scalar that is in the range 1..order-1.
*
* rng Random number generator.
* k Scalar value.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
static int sp_384_ecc_gen_k_15(WC_RNG* rng, sp_digit* k)
{
int err;
byte buf[48];
do {
err = wc_RNG_GenerateBlock(rng, buf, sizeof(buf));
if (err == 0) {
sp_384_from_bin(k, 15, buf, (int)sizeof(buf));
if (sp_384_cmp_15(k, p384_order2) < 0) {
sp_384_add_one_15(k);
break;
}
}
}
while (err == 0);
return err;
}
/* Makes a random EC key pair.
*
* rng Random number generator.
* priv Generated private value.
* pub Generated public point.
* heap Heap to use for allocation.
* returns ECC_INF_E when the point does not have the correct order, RNG
* failures, MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_make_key_384(WC_RNG* rng, mp_int* priv, ecc_point* pub, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 p;
sp_digit kd[15];
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_point_384 inf;
#endif
#endif
sp_point_384* point;
sp_digit* k = NULL;
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_point_384* infinity;
#endif
int err;
(void)heap;
err = sp_384_point_new_15(heap, p, point);
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, inf, infinity);
}
#endif
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 15, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL) {
err = MEMORY_E;
}
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
err = sp_384_ecc_gen_k_15(rng, k);
}
if (err == MP_OKAY) {
err = sp_384_ecc_mulmod_base_15(point, k, 1, NULL);
}
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
if (err == MP_OKAY) {
err = sp_384_ecc_mulmod_15(infinity, point, p384_order, 1, NULL);
}
if (err == MP_OKAY) {
if ((sp_384_iszero_15(point->x) == 0) || (sp_384_iszero_15(point->y) == 0)) {
err = ECC_INF_E;
}
}
#endif
if (err == MP_OKAY) {
err = sp_384_to_mp(k, priv);
}
if (err == MP_OKAY) {
err = sp_384_point_to_ecc_point_15(point, pub);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
sp_384_point_free_15(infinity, 1, heap);
#endif
sp_384_point_free_15(point, 1, heap);
return err;
}
#ifdef HAVE_ECC_DHE
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 48
*
* r A single precision integer.
* a Byte array.
*/
static void sp_384_to_bin(sp_digit* r, byte* a)
{
int i, j, s = 0, b;
for (i=0; i<14; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
j = 384 / 8 - 1;
a[j] = 0;
for (i=0; i<15 && j>=0; i++) {
b = 0;
/* lint allow cast of mismatch sp_digit and int */
a[j--] |= (byte)(r[i] << s); /*lint !e9033*/
b += 8 - s;
if (j < 0) {
break;
}
while (b < 26) {
a[j--] = (byte)(r[i] >> b);
b += 8;
if (j < 0) {
break;
}
}
s = 8 - (b - 26);
if (j >= 0) {
a[j] = 0;
}
if (s != 0) {
j++;
}
}
}
/* Multiply the point by the scalar and serialize the X ordinate.
* The number is 0 padded to maximum size on output.
*
* priv Scalar to multiply the point by.
* pub Point to multiply.
* out Buffer to hold X ordinate.
* outLen On entry, size of the buffer in bytes.
* On exit, length of data in buffer in bytes.
* heap Heap to use for allocation.
* returns BUFFER_E if the buffer is to small for output size,
* MEMORY_E when memory allocation fails and MP_OKAY on success.
*/
int sp_ecc_secret_gen_384(mp_int* priv, ecc_point* pub, byte* out,
word32* outLen, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 p;
sp_digit kd[15];
#endif
sp_point_384* point = NULL;
sp_digit* k = NULL;
int err = MP_OKAY;
if (*outLen < 48U) {
err = BUFFER_E;
}
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, p, point);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
k = (sp_digit*)XMALLOC(sizeof(sp_digit) * 15, heap,
DYNAMIC_TYPE_ECC);
if (k == NULL)
err = MEMORY_E;
}
#else
k = kd;
#endif
if (err == MP_OKAY) {
sp_384_from_mp(k, 15, priv);
sp_384_point_from_ecc_point_15(point, pub);
err = sp_384_ecc_mulmod_15(point, point, k, 1, heap);
}
if (err == MP_OKAY) {
sp_384_to_bin(point->x, out);
*outLen = 48;
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (k != NULL) {
XFREE(k, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(point, 0, heap);
return err;
}
#endif /* HAVE_ECC_DHE */
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
/* Multiply a by scalar b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_384_mul_d_15(sp_digit* r, const sp_digit* a,
sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
int64_t tb = b;
int64_t t = 0;
int i;
for (i = 0; i < 15; i++) {
t += tb * a[i];
r[i] = t & 0x3ffffff;
t >>= 26;
}
r[15] = (sp_digit)t;
#else
int64_t tb = b;
int64_t t[15];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
t[ 5] = tb * a[ 5];
t[ 6] = tb * a[ 6];
t[ 7] = tb * a[ 7];
t[ 8] = tb * a[ 8];
t[ 9] = tb * a[ 9];
t[10] = tb * a[10];
t[11] = tb * a[11];
t[12] = tb * a[12];
t[13] = tb * a[13];
t[14] = tb * a[14];
r[ 0] = (t[ 0] & 0x3ffffff);
r[ 1] = (sp_digit)(t[ 0] >> 26) + (t[ 1] & 0x3ffffff);
r[ 2] = (sp_digit)(t[ 1] >> 26) + (t[ 2] & 0x3ffffff);
r[ 3] = (sp_digit)(t[ 2] >> 26) + (t[ 3] & 0x3ffffff);
r[ 4] = (sp_digit)(t[ 3] >> 26) + (t[ 4] & 0x3ffffff);
r[ 5] = (sp_digit)(t[ 4] >> 26) + (t[ 5] & 0x3ffffff);
r[ 6] = (sp_digit)(t[ 5] >> 26) + (t[ 6] & 0x3ffffff);
r[ 7] = (sp_digit)(t[ 6] >> 26) + (t[ 7] & 0x3ffffff);
r[ 8] = (sp_digit)(t[ 7] >> 26) + (t[ 8] & 0x3ffffff);
r[ 9] = (sp_digit)(t[ 8] >> 26) + (t[ 9] & 0x3ffffff);
r[10] = (sp_digit)(t[ 9] >> 26) + (t[10] & 0x3ffffff);
r[11] = (sp_digit)(t[10] >> 26) + (t[11] & 0x3ffffff);
r[12] = (sp_digit)(t[11] >> 26) + (t[12] & 0x3ffffff);
r[13] = (sp_digit)(t[12] >> 26) + (t[13] & 0x3ffffff);
r[14] = (sp_digit)(t[13] >> 26) + (t[14] & 0x3ffffff);
r[15] = (sp_digit)(t[14] >> 26);
#endif /* WOLFSSL_SP_SMALL */
}
#ifdef WOLFSSL_SP_DIV_32
static WC_INLINE sp_digit sp_384_div_word_15(sp_digit d1, sp_digit d0,
sp_digit dv)
{
sp_digit d, r, t;
/* All 26 bits from d1 and top 5 bits from d0. */
d = (d1 << 5) | (d0 >> 21);
r = d / dv;
d -= r * dv;
/* Up to 6 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 16) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 11 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 11) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 16 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 6) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 21 bits in r */
/* Next 5 bits from d0. */
r <<= 5;
d <<= 5;
d |= (d0 >> 1) & ((1 << 5) - 1);
t = d / dv;
d -= t * dv;
r += t;
/* Up to 26 bits in r */
/* Remaining 1 bits from d0. */
r <<= 1;
d <<= 1;
d |= d0 & ((1 << 1) - 1);
t = d / dv;
r += t;
return r;
}
#endif /* WOLFSSL_SP_DIV_32 */
/* Divide d in a and put remainder into r (m*d + r = a)
* m is not calculated as it is not needed at this time.
*
* a Number to be divided.
* d Number to divide with.
* m Multiplier result.
* r Remainder from the division.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_384_div_15(const sp_digit* a, const sp_digit* d, sp_digit* m,
sp_digit* r)
{
int i;
#ifndef WOLFSSL_SP_DIV_32
int64_t d1;
#endif
sp_digit dv, r1;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* td;
#else
sp_digit t1d[30], t2d[15 + 1];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
(void)m;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (3 * 15 + 1), NULL,
DYNAMIC_TYPE_TMP_BUFFER);
if (td == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = td;
t2 = td + 2 * 15;
#else
t1 = t1d;
t2 = t2d;
#endif
dv = d[14];
XMEMCPY(t1, a, sizeof(*t1) * 2U * 15U);
for (i=14; i>=0; i--) {
t1[15 + i] += t1[15 + i - 1] >> 26;
t1[15 + i - 1] &= 0x3ffffff;
#ifndef WOLFSSL_SP_DIV_32
d1 = t1[15 + i];
d1 <<= 26;
d1 += t1[15 + i - 1];
r1 = (sp_digit)(d1 / dv);
#else
r1 = sp_384_div_word_15(t1[15 + i], t1[15 + i - 1], dv);
#endif
sp_384_mul_d_15(t2, d, r1);
(void)sp_384_sub_15(&t1[i], &t1[i], t2);
t1[15 + i] -= t2[15];
t1[15 + i] += t1[15 + i - 1] >> 26;
t1[15 + i - 1] &= 0x3ffffff;
r1 = (((-t1[15 + i]) << 26) - t1[15 + i - 1]) / dv;
r1++;
sp_384_mul_d_15(t2, d, r1);
(void)sp_384_add_15(&t1[i], &t1[i], t2);
t1[15 + i] += t1[15 + i - 1] >> 26;
t1[15 + i - 1] &= 0x3ffffff;
}
t1[15 - 1] += t1[15 - 2] >> 26;
t1[15 - 2] &= 0x3ffffff;
r1 = t1[15 - 1] / dv;
sp_384_mul_d_15(t2, d, r1);
(void)sp_384_sub_15(t1, t1, t2);
XMEMCPY(r, t1, sizeof(*r) * 2U * 15U);
for (i=0; i<13; i++) {
r[i+1] += r[i] >> 26;
r[i] &= 0x3ffffff;
}
sp_384_cond_add_15(r, r, d, 0 - ((r[14] < 0) ?
(sp_digit)1 : (sp_digit)0));
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (td != NULL) {
XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
}
#endif
return err;
}
/* Reduce a modulo m into r. (r = a mod m)
*
* r A single precision number that is the reduced result.
* a A single precision number that is to be reduced.
* m A single precision number that is the modulus to reduce with.
* returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
*/
static int sp_384_mod_15(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
return sp_384_div_15(a, m, NULL, r);
}
#endif
#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
#ifdef WOLFSSL_SP_SMALL
/* Order-2 for the P384 curve. */
static const uint32_t p384_order_minus_2[12] = {
0xccc52971U,0xecec196aU,0x48b0a77aU,0x581a0db2U,0xf4372ddfU,0xc7634d81U,
0xffffffffU,0xffffffffU,0xffffffffU,0xffffffffU,0xffffffffU,0xffffffffU
};
#else
/* The low half of the order-2 of the P384 curve. */
static const uint32_t p384_order_low[6] = {
0xccc52971U,0xecec196aU,0x48b0a77aU,0x581a0db2U,0xf4372ddfU,0xc7634d81U
};
#endif /* WOLFSSL_SP_SMALL */
/* Multiply two number mod the order of P384 curve. (r = a * b mod order)
*
* r Result of the multiplication.
* a First operand of the multiplication.
* b Second operand of the multiplication.
*/
static void sp_384_mont_mul_order_15(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
sp_384_mul_15(r, a, b);
sp_384_mont_reduce_order_15(r, p384_order, p384_mp_order);
}
/* Square number mod the order of P384 curve. (r = a * a mod order)
*
* r Result of the squaring.
* a Number to square.
*/
static void sp_384_mont_sqr_order_15(sp_digit* r, const sp_digit* a)
{
sp_384_sqr_15(r, a);
sp_384_mont_reduce_order_15(r, p384_order, p384_mp_order);
}
#ifndef WOLFSSL_SP_SMALL
/* Square number mod the order of P384 curve a number of times.
* (r = a ^ n mod order)
*
* r Result of the squaring.
* a Number to square.
*/
static void sp_384_mont_sqr_n_order_15(sp_digit* r, const sp_digit* a, int n)
{
int i;
sp_384_mont_sqr_order_15(r, a);
for (i=1; i<n; i++) {
sp_384_mont_sqr_order_15(r, r);
}
}
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the order of the P384 curve.
* (r = 1 / a mod order)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_384_mont_inv_order_15(sp_digit* r, const sp_digit* a,
sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 15);
for (i=382; i>=0; i--) {
sp_384_mont_sqr_order_15(t, t);
if ((p384_order_minus_2[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_384_mont_mul_order_15(t, t, a);
}
}
XMEMCPY(r, t, sizeof(sp_digit) * 15U);
#else
sp_digit* t = td;
sp_digit* t2 = td + 2 * 15;
sp_digit* t3 = td + 4 * 15;
int i;
/* t = a^2 */
sp_384_mont_sqr_order_15(t, a);
/* t = a^3 = t * a */
sp_384_mont_mul_order_15(t, t, a);
/* t2= a^c = t ^ 2 ^ 2 */
sp_384_mont_sqr_n_order_15(t2, t, 2);
/* t = a^f = t2 * t */
sp_384_mont_mul_order_15(t, t2, t);
/* t2= a^f0 = t ^ 2 ^ 4 */
sp_384_mont_sqr_n_order_15(t2, t, 4);
/* t = a^ff = t2 * t */
sp_384_mont_mul_order_15(t, t2, t);
/* t2= a^ff00 = t ^ 2 ^ 8 */
sp_384_mont_sqr_n_order_15(t2, t, 8);
/* t3= a^ffff = t2 * t */
sp_384_mont_mul_order_15(t3, t2, t);
/* t2= a^ffff0000 = t3 ^ 2 ^ 16 */
sp_384_mont_sqr_n_order_15(t2, t3, 16);
/* t = a^ffffffff = t2 * t3 */
sp_384_mont_mul_order_15(t, t2, t3);
/* t2= a^ffffffff0000 = t ^ 2 ^ 16 */
sp_384_mont_sqr_n_order_15(t2, t, 16);
/* t = a^ffffffffffff = t2 * t3 */
sp_384_mont_mul_order_15(t, t2, t3);
/* t2= a^ffffffffffff000000000000 = t ^ 2 ^ 48 */
sp_384_mont_sqr_n_order_15(t2, t, 48);
/* t= a^fffffffffffffffffffffffff = t2 * t */
sp_384_mont_mul_order_15(t, t2, t);
/* t2= a^ffffffffffffffffffffffff000000000000000000000000 */
sp_384_mont_sqr_n_order_15(t2, t, 96);
/* t2= a^ffffffffffffffffffffffffffffffffffffffffffffffff = t2 * t */
sp_384_mont_mul_order_15(t2, t2, t);
for (i=191; i>=1; i--) {
sp_384_mont_sqr_order_15(t2, t2);
if (((sp_digit)p384_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
sp_384_mont_mul_order_15(t2, t2, a);
}
}
sp_384_mont_sqr_order_15(t2, t2);
sp_384_mont_mul_order_15(r, t2, a);
#endif /* WOLFSSL_SP_SMALL */
}
#endif /* HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_SIGN
#ifndef SP_ECC_MAX_SIG_GEN
#define SP_ECC_MAX_SIG_GEN 64
#endif
/* Sign the hash using the private key.
* e = [hash, 384 bits] from binary
* r = (k.G)->x mod order
* s = (r * x + e) / k mod order
* The hash is truncated to the first 384 bits.
*
* hash Hash to sign.
* hashLen Length of the hash data.
* rng Random number generator.
* priv Private part of key - scalar.
* rm First part of result as an mp_int.
* sm Sirst part of result as an mp_int.
* heap Heap to use for allocation.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
int sp_ecc_sign_384(const byte* hash, word32 hashLen, WC_RNG* rng, mp_int* priv,
mp_int* rm, mp_int* sm, mp_int* km, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d = NULL;
#else
sp_digit ed[2*15];
sp_digit xd[2*15];
sp_digit kd[2*15];
sp_digit rd[2*15];
sp_digit td[3 * 2*15];
sp_point_384 p;
#endif
sp_digit* e = NULL;
sp_digit* x = NULL;
sp_digit* k = NULL;
sp_digit* r = NULL;
sp_digit* tmp = NULL;
sp_point_384* point = NULL;
sp_digit carry;
sp_digit* s = NULL;
sp_digit* kInv = NULL;
int err = MP_OKAY;
int32_t c;
int i;
(void)heap;
err = sp_384_point_new_15(heap, p, point);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 7 * 2 * 15, heap,
DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
e = d + 0 * 15;
x = d + 2 * 15;
k = d + 4 * 15;
r = d + 6 * 15;
tmp = d + 8 * 15;
#else
e = ed;
x = xd;
k = kd;
r = rd;
tmp = td;
#endif
s = e;
kInv = k;
if (hashLen > 48U) {
hashLen = 48U;
}
sp_384_from_bin(e, 15, hash, (int)hashLen);
}
for (i = SP_ECC_MAX_SIG_GEN; err == MP_OKAY && i > 0; i--) {
sp_384_from_mp(x, 15, priv);
/* New random point. */
if (km == NULL || mp_iszero(km)) {
err = sp_384_ecc_gen_k_15(rng, k);
}
else {
sp_384_from_mp(k, 15, km);
mp_zero(km);
}
if (err == MP_OKAY) {
err = sp_384_ecc_mulmod_base_15(point, k, 1, NULL);
}
if (err == MP_OKAY) {
/* r = point->x mod order */
XMEMCPY(r, point->x, sizeof(sp_digit) * 15U);
sp_384_norm_15(r);
c = sp_384_cmp_15(r, p384_order);
sp_384_cond_sub_15(r, r, p384_order, 0L - (sp_digit)(c >= 0));
sp_384_norm_15(r);
/* Conv k to Montgomery form (mod order) */
sp_384_mul_15(k, k, p384_norm_order);
err = sp_384_mod_15(k, k, p384_order);
}
if (err == MP_OKAY) {
sp_384_norm_15(k);
/* kInv = 1/k mod order */
sp_384_mont_inv_order_15(kInv, k, tmp);
sp_384_norm_15(kInv);
/* s = r * x + e */
sp_384_mul_15(x, x, r);
err = sp_384_mod_15(x, x, p384_order);
}
if (err == MP_OKAY) {
sp_384_norm_15(x);
carry = sp_384_add_15(s, e, x);
sp_384_cond_sub_15(s, s, p384_order, 0 - carry);
sp_384_norm_15(s);
c = sp_384_cmp_15(s, p384_order);
sp_384_cond_sub_15(s, s, p384_order, 0L - (sp_digit)(c >= 0));
sp_384_norm_15(s);
/* s = s * k^-1 mod order */
sp_384_mont_mul_order_15(s, s, kInv);
sp_384_norm_15(s);
/* Check that signature is usable. */
if (sp_384_iszero_15(s) == 0) {
break;
}
}
}
if (i == 0) {
err = RNG_FAILURE_E;
}
if (err == MP_OKAY) {
err = sp_384_to_mp(r, rm);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(s, sm);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XMEMSET(d, 0, sizeof(sp_digit) * 8 * 15);
XFREE(d, heap, DYNAMIC_TYPE_ECC);
}
#else
XMEMSET(e, 0, sizeof(sp_digit) * 2U * 15U);
XMEMSET(x, 0, sizeof(sp_digit) * 2U * 15U);
XMEMSET(k, 0, sizeof(sp_digit) * 2U * 15U);
XMEMSET(r, 0, sizeof(sp_digit) * 2U * 15U);
XMEMSET(r, 0, sizeof(sp_digit) * 2U * 15U);
XMEMSET(tmp, 0, sizeof(sp_digit) * 3U * 2U * 15U);
#endif
sp_384_point_free_15(point, 1, heap);
return err;
}
#endif /* HAVE_ECC_SIGN */
#ifdef HAVE_ECC_VERIFY
/* Verify the signature values with the hash and public key.
* e = Truncate(hash, 384)
* u1 = e/s mod order
* u2 = r/s mod order
* r == (u1.G + u2.Q)->x mod order
* Optimization: Leave point in projective form.
* (x, y, 1) == (x' / z'*z', y' / z'*z'*z', z' / z')
* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x'
* The hash is truncated to the first 384 bits.
*
* hash Hash to sign.
* hashLen Length of the hash data.
* rng Random number generator.
* priv Private part of key - scalar.
* rm First part of result as an mp_int.
* sm Sirst part of result as an mp_int.
* heap Heap to use for allocation.
* returns RNG failures, MEMORY_E when memory allocation fails and
* MP_OKAY on success.
*/
int sp_ecc_verify_384(const byte* hash, word32 hashLen, mp_int* pX,
mp_int* pY, mp_int* pZ, mp_int* r, mp_int* sm, int* res, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d = NULL;
#else
sp_digit u1d[2*15];
sp_digit u2d[2*15];
sp_digit sd[2*15];
sp_digit tmpd[2*15 * 5];
sp_point_384 p1d;
sp_point_384 p2d;
#endif
sp_digit* u1 = NULL;
sp_digit* u2 = NULL;
sp_digit* s = NULL;
sp_digit* tmp = NULL;
sp_point_384* p1;
sp_point_384* p2 = NULL;
sp_digit carry;
int32_t c;
int err;
err = sp_384_point_new_15(heap, p1d, p1);
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, p2d, p2);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 16 * 15, heap,
DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
u1 = d + 0 * 15;
u2 = d + 2 * 15;
s = d + 4 * 15;
tmp = d + 6 * 15;
#else
u1 = u1d;
u2 = u2d;
s = sd;
tmp = tmpd;
#endif
if (hashLen > 48U) {
hashLen = 48U;
}
sp_384_from_bin(u1, 15, hash, (int)hashLen);
sp_384_from_mp(u2, 15, r);
sp_384_from_mp(s, 15, sm);
sp_384_from_mp(p2->x, 15, pX);
sp_384_from_mp(p2->y, 15, pY);
sp_384_from_mp(p2->z, 15, pZ);
{
sp_384_mul_15(s, s, p384_norm_order);
}
err = sp_384_mod_15(s, s, p384_order);
}
if (err == MP_OKAY) {
sp_384_norm_15(s);
{
sp_384_mont_inv_order_15(s, s, tmp);
sp_384_mont_mul_order_15(u1, u1, s);
sp_384_mont_mul_order_15(u2, u2, s);
}
err = sp_384_ecc_mulmod_base_15(p1, u1, 0, heap);
}
if (err == MP_OKAY) {
err = sp_384_ecc_mulmod_15(p2, p2, u2, 0, heap);
}
if (err == MP_OKAY) {
{
sp_384_proj_point_add_15(p1, p1, p2, tmp);
if (sp_384_iszero_15(p1->z)) {
if (sp_384_iszero_15(p1->x) && sp_384_iszero_15(p1->y)) {
sp_384_proj_point_dbl_15(p1, p2, tmp);
}
else {
/* Y ordinate is not used from here - don't set. */
p1->x[0] = 0;
p1->x[1] = 0;
p1->x[2] = 0;
p1->x[3] = 0;
p1->x[4] = 0;
p1->x[5] = 0;
p1->x[6] = 0;
p1->x[7] = 0;
p1->x[8] = 0;
p1->x[9] = 0;
p1->x[10] = 0;
p1->x[11] = 0;
p1->x[12] = 0;
p1->x[13] = 0;
p1->x[14] = 0;
XMEMCPY(p1->z, p384_norm_mod, sizeof(p384_norm_mod));
}
}
}
/* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x' */
/* Reload r and convert to Montgomery form. */
sp_384_from_mp(u2, 15, r);
err = sp_384_mod_mul_norm_15(u2, u2, p384_mod);
}
if (err == MP_OKAY) {
/* u1 = r.z'.z' mod prime */
sp_384_mont_sqr_15(p1->z, p1->z, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(u1, u2, p1->z, p384_mod, p384_mp_mod);
*res = (int)(sp_384_cmp_15(p1->x, u1) == 0);
if (*res == 0) {
/* Reload r and add order. */
sp_384_from_mp(u2, 15, r);
carry = sp_384_add_15(u2, u2, p384_order);
/* Carry means result is greater than mod and is not valid. */
if (carry == 0) {
sp_384_norm_15(u2);
/* Compare with mod and if greater or equal then not valid. */
c = sp_384_cmp_15(u2, p384_mod);
if (c < 0) {
/* Convert to Montogomery form */
err = sp_384_mod_mul_norm_15(u2, u2, p384_mod);
if (err == MP_OKAY) {
/* u1 = (r + 1*order).z'.z' mod prime */
sp_384_mont_mul_15(u1, u2, p1->z, p384_mod,
p384_mp_mod);
*res = (int)(sp_384_cmp_15(p1->x, u1) == 0);
}
}
}
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL)
XFREE(d, heap, DYNAMIC_TYPE_ECC);
#endif
sp_384_point_free_15(p1, 0, heap);
sp_384_point_free_15(p2, 0, heap);
return err;
}
#endif /* HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_CHECK_KEY
/* Check that the x and y oridinates are a valid point on the curve.
*
* point EC point.
* heap Heap to use if dynamically allocating.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve and MP_OKAY otherwise.
*/
static int sp_384_ecc_is_point_15(sp_point_384* point, void* heap)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d = NULL;
#else
sp_digit t1d[2*15];
sp_digit t2d[2*15];
#endif
sp_digit* t1;
sp_digit* t2;
int err = MP_OKAY;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 15 * 4, heap, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = d + 0 * 15;
t2 = d + 2 * 15;
#else
(void)heap;
t1 = t1d;
t2 = t2d;
#endif
sp_384_sqr_15(t1, point->y);
(void)sp_384_mod_15(t1, t1, p384_mod);
sp_384_sqr_15(t2, point->x);
(void)sp_384_mod_15(t2, t2, p384_mod);
sp_384_mul_15(t2, t2, point->x);
(void)sp_384_mod_15(t2, t2, p384_mod);
(void)sp_384_sub_15(t2, p384_mod, t2);
sp_384_mont_add_15(t1, t1, t2, p384_mod);
sp_384_mont_add_15(t1, t1, point->x, p384_mod);
sp_384_mont_add_15(t1, t1, point->x, p384_mod);
sp_384_mont_add_15(t1, t1, point->x, p384_mod);
if (sp_384_cmp_15(t1, p384_b) != 0) {
err = MP_VAL;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, heap, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Check that the x and y oridinates are a valid point on the curve.
*
* pX X ordinate of EC point.
* pY Y ordinate of EC point.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve and MP_OKAY otherwise.
*/
int sp_ecc_is_point_384(mp_int* pX, mp_int* pY)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_point_384 pubd;
#endif
sp_point_384* pub;
byte one[1] = { 1 };
int err;
err = sp_384_point_new_15(NULL, pubd, pub);
if (err == MP_OKAY) {
sp_384_from_mp(pub->x, 15, pX);
sp_384_from_mp(pub->y, 15, pY);
sp_384_from_bin(pub->z, 15, one, (int)sizeof(one));
err = sp_384_ecc_is_point_15(pub, NULL);
}
sp_384_point_free_15(pub, 0, NULL);
return err;
}
/* Check that the private scalar generates the EC point (px, py), the point is
* on the curve and the point has the correct order.
*
* pX X ordinate of EC point.
* pY Y ordinate of EC point.
* privm Private scalar that generates EC point.
* returns MEMORY_E if dynamic memory allocation fails, MP_VAL if the point is
* not on the curve, ECC_INF_E if the point does not have the correct order,
* ECC_PRIV_KEY_E when the private scalar doesn't generate the EC point and
* MP_OKAY otherwise.
*/
int sp_ecc_check_key_384(mp_int* pX, mp_int* pY, mp_int* privm, void* heap)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit privd[15];
sp_point_384 pubd;
sp_point_384 pd;
#endif
sp_digit* priv = NULL;
sp_point_384* pub;
sp_point_384* p = NULL;
byte one[1] = { 1 };
int err;
err = sp_384_point_new_15(heap, pubd, pub);
if (err == MP_OKAY) {
err = sp_384_point_new_15(heap, pd, p);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
priv = (sp_digit*)XMALLOC(sizeof(sp_digit) * 15, heap,
DYNAMIC_TYPE_ECC);
if (priv == NULL) {
err = MEMORY_E;
}
}
#endif
if (err == MP_OKAY) {
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
priv = privd;
#endif
sp_384_from_mp(pub->x, 15, pX);
sp_384_from_mp(pub->y, 15, pY);
sp_384_from_bin(pub->z, 15, one, (int)sizeof(one));
sp_384_from_mp(priv, 15, privm);
/* Check point at infinitiy. */
if ((sp_384_iszero_15(pub->x) != 0) &&
(sp_384_iszero_15(pub->y) != 0)) {
err = ECC_INF_E;
}
}
if (err == MP_OKAY) {
/* Check range of X and Y */
if (sp_384_cmp_15(pub->x, p384_mod) >= 0 ||
sp_384_cmp_15(pub->y, p384_mod) >= 0) {
err = ECC_OUT_OF_RANGE_E;
}
}
if (err == MP_OKAY) {
/* Check point is on curve */
err = sp_384_ecc_is_point_15(pub, heap);
}
if (err == MP_OKAY) {
/* Point * order = infinity */
err = sp_384_ecc_mulmod_15(p, pub, p384_order, 1, heap);
}
if (err == MP_OKAY) {
/* Check result is infinity */
if ((sp_384_iszero_15(p->x) == 0) ||
(sp_384_iszero_15(p->y) == 0)) {
err = ECC_INF_E;
}
}
if (err == MP_OKAY) {
/* Base * private = point */
err = sp_384_ecc_mulmod_base_15(p, priv, 1, heap);
}
if (err == MP_OKAY) {
/* Check result is public key */
if (sp_384_cmp_15(p->x, pub->x) != 0 ||
sp_384_cmp_15(p->y, pub->y) != 0) {
err = ECC_PRIV_KEY_E;
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (priv != NULL) {
XFREE(priv, heap, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(p, 0, heap);
sp_384_point_free_15(pub, 0, heap);
return err;
}
#endif
#ifdef WOLFSSL_PUBLIC_ECC_ADD_DBL
/* Add two projective EC points together.
* (pX, pY, pZ) + (qX, qY, qZ) = (rX, rY, rZ)
*
* pX First EC point's X ordinate.
* pY First EC point's Y ordinate.
* pZ First EC point's Z ordinate.
* qX Second EC point's X ordinate.
* qY Second EC point's Y ordinate.
* qZ Second EC point's Z ordinate.
* rX Resultant EC point's X ordinate.
* rY Resultant EC point's Y ordinate.
* rZ Resultant EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_proj_add_point_384(mp_int* pX, mp_int* pY, mp_int* pZ,
mp_int* qX, mp_int* qY, mp_int* qZ,
mp_int* rX, mp_int* rY, mp_int* rZ)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit tmpd[2 * 15 * 5];
sp_point_384 pd;
sp_point_384 qd;
#endif
sp_digit* tmp;
sp_point_384* p;
sp_point_384* q = NULL;
int err;
err = sp_384_point_new_15(NULL, pd, p);
if (err == MP_OKAY) {
err = sp_384_point_new_15(NULL, qd, q);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 5, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_384_from_mp(p->x, 15, pX);
sp_384_from_mp(p->y, 15, pY);
sp_384_from_mp(p->z, 15, pZ);
sp_384_from_mp(q->x, 15, qX);
sp_384_from_mp(q->y, 15, qY);
sp_384_from_mp(q->z, 15, qZ);
sp_384_proj_point_add_15(p, p, q, tmp);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->x, rX);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->y, rY);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->z, rZ);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(q, 0, NULL);
sp_384_point_free_15(p, 0, NULL);
return err;
}
/* Double a projective EC point.
* (pX, pY, pZ) + (pX, pY, pZ) = (rX, rY, rZ)
*
* pX EC point's X ordinate.
* pY EC point's Y ordinate.
* pZ EC point's Z ordinate.
* rX Resultant EC point's X ordinate.
* rY Resultant EC point's Y ordinate.
* rZ Resultant EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_proj_dbl_point_384(mp_int* pX, mp_int* pY, mp_int* pZ,
mp_int* rX, mp_int* rY, mp_int* rZ)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit tmpd[2 * 15 * 2];
sp_point_384 pd;
#endif
sp_digit* tmp;
sp_point_384* p;
int err;
err = sp_384_point_new_15(NULL, pd, p);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 2, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_384_from_mp(p->x, 15, pX);
sp_384_from_mp(p->y, 15, pY);
sp_384_from_mp(p->z, 15, pZ);
sp_384_proj_point_dbl_15(p, p, tmp);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->x, rX);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->y, rY);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->z, rZ);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(p, 0, NULL);
return err;
}
/* Map a projective EC point to affine in place.
* pZ will be one.
*
* pX EC point's X ordinate.
* pY EC point's Y ordinate.
* pZ EC point's Z ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_map_384(mp_int* pX, mp_int* pY, mp_int* pZ)
{
#if (!defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)) || defined(WOLFSSL_SP_NO_MALLOC)
sp_digit tmpd[2 * 15 * 6];
sp_point_384 pd;
#endif
sp_digit* tmp;
sp_point_384* p;
int err;
err = sp_384_point_new_15(NULL, pd, p);
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (err == MP_OKAY) {
tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 15 * 6, NULL,
DYNAMIC_TYPE_ECC);
if (tmp == NULL) {
err = MEMORY_E;
}
}
#else
tmp = tmpd;
#endif
if (err == MP_OKAY) {
sp_384_from_mp(p->x, 15, pX);
sp_384_from_mp(p->y, 15, pY);
sp_384_from_mp(p->z, 15, pZ);
sp_384_map_15(p, p, tmp);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->x, pX);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->y, pY);
}
if (err == MP_OKAY) {
err = sp_384_to_mp(p->z, pZ);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (tmp != NULL) {
XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
}
#endif
sp_384_point_free_15(p, 0, NULL);
return err;
}
#endif /* WOLFSSL_PUBLIC_ECC_ADD_DBL */
#ifdef HAVE_COMP_KEY
/* Find the square root of a number mod the prime of the curve.
*
* y The number to operate on and the result.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
static int sp_384_mont_sqrt_15(sp_digit* y)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d;
#else
sp_digit t1d[2 * 15];
sp_digit t2d[2 * 15];
sp_digit t3d[2 * 15];
sp_digit t4d[2 * 15];
sp_digit t5d[2 * 15];
#endif
sp_digit* t1;
sp_digit* t2;
sp_digit* t3;
sp_digit* t4;
sp_digit* t5;
int err = MP_OKAY;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 5 * 2 * 15, NULL, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
t1 = d + 0 * 15;
t2 = d + 2 * 15;
t3 = d + 4 * 15;
t4 = d + 6 * 15;
t5 = d + 8 * 15;
#else
t1 = t1d;
t2 = t2d;
t3 = t3d;
t4 = t4d;
t5 = t5d;
#endif
{
/* t2 = y ^ 0x2 */
sp_384_mont_sqr_15(t2, y, p384_mod, p384_mp_mod);
/* t1 = y ^ 0x3 */
sp_384_mont_mul_15(t1, t2, y, p384_mod, p384_mp_mod);
/* t5 = y ^ 0xc */
sp_384_mont_sqr_n_15(t5, t1, 2, p384_mod, p384_mp_mod);
/* t1 = y ^ 0xf */
sp_384_mont_mul_15(t1, t1, t5, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x1e */
sp_384_mont_sqr_15(t2, t1, p384_mod, p384_mp_mod);
/* t3 = y ^ 0x1f */
sp_384_mont_mul_15(t3, t2, y, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x3e0 */
sp_384_mont_sqr_n_15(t2, t3, 5, p384_mod, p384_mp_mod);
/* t1 = y ^ 0x3ff */
sp_384_mont_mul_15(t1, t3, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x7fe0 */
sp_384_mont_sqr_n_15(t2, t1, 5, p384_mod, p384_mp_mod);
/* t3 = y ^ 0x7fff */
sp_384_mont_mul_15(t3, t3, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x3fff800 */
sp_384_mont_sqr_n_15(t2, t3, 15, p384_mod, p384_mp_mod);
/* t4 = y ^ 0x3ffffff */
sp_384_mont_mul_15(t4, t3, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0xffffffc000000 */
sp_384_mont_sqr_n_15(t2, t4, 30, p384_mod, p384_mp_mod);
/* t1 = y ^ 0xfffffffffffff */
sp_384_mont_mul_15(t1, t4, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0xfffffffffffffff000000000000000 */
sp_384_mont_sqr_n_15(t2, t1, 60, p384_mod, p384_mp_mod);
/* t1 = y ^ 0xffffffffffffffffffffffffffffff */
sp_384_mont_mul_15(t1, t1, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0xffffffffffffffffffffffffffffff000000000000000000000000000000 */
sp_384_mont_sqr_n_15(t2, t1, 120, p384_mod, p384_mp_mod);
/* t1 = y ^ 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff */
sp_384_mont_mul_15(t1, t1, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8000 */
sp_384_mont_sqr_n_15(t2, t1, 15, p384_mod, p384_mp_mod);
/* t1 = y ^ 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff */
sp_384_mont_mul_15(t1, t3, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff80000000 */
sp_384_mont_sqr_n_15(t2, t1, 31, p384_mod, p384_mp_mod);
/* t1 = y ^ 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffff */
sp_384_mont_mul_15(t1, t4, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffff0 */
sp_384_mont_sqr_n_15(t2, t1, 4, p384_mod, p384_mp_mod);
/* t1 = y ^ 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffffc */
sp_384_mont_mul_15(t1, t5, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000 */
sp_384_mont_sqr_n_15(t2, t1, 62, p384_mod, p384_mp_mod);
/* t1 = y ^ 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000001 */
sp_384_mont_mul_15(t1, y, t2, p384_mod, p384_mp_mod);
/* t2 = y ^ 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffffc00000000000000040000000 */
sp_384_mont_sqr_n_15(y, t1, 30, p384_mod, p384_mp_mod);
}
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
/* Uncompress the point given the X ordinate.
*
* xm X ordinate.
* odd Whether the Y ordinate is odd.
* ym Calculated Y ordinate.
* returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
*/
int sp_ecc_uncompress_384(mp_int* xm, int odd, mp_int* ym)
{
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
sp_digit* d;
#else
sp_digit xd[2 * 15];
sp_digit yd[2 * 15];
#endif
sp_digit* x = NULL;
sp_digit* y = NULL;
int err = MP_OKAY;
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 15, NULL, DYNAMIC_TYPE_ECC);
if (d == NULL) {
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
x = d + 0 * 15;
y = d + 2 * 15;
#else
x = xd;
y = yd;
#endif
sp_384_from_mp(x, 15, xm);
err = sp_384_mod_mul_norm_15(x, x, p384_mod);
}
if (err == MP_OKAY) {
/* y = x^3 */
{
sp_384_mont_sqr_15(y, x, p384_mod, p384_mp_mod);
sp_384_mont_mul_15(y, y, x, p384_mod, p384_mp_mod);
}
/* y = x^3 - 3x */
sp_384_mont_sub_15(y, y, x, p384_mod);
sp_384_mont_sub_15(y, y, x, p384_mod);
sp_384_mont_sub_15(y, y, x, p384_mod);
/* y = x^3 - 3x + b */
err = sp_384_mod_mul_norm_15(x, p384_b, p384_mod);
}
if (err == MP_OKAY) {
sp_384_mont_add_15(y, y, x, p384_mod);
/* y = sqrt(x^3 - 3x + b) */
err = sp_384_mont_sqrt_15(y);
}
if (err == MP_OKAY) {
XMEMSET(y + 15, 0, 15U * sizeof(sp_digit));
sp_384_mont_reduce_15(y, p384_mod, p384_mp_mod);
if ((((word32)y[0] ^ (word32)odd) & 1U) != 0U) {
sp_384_mont_sub_15(y, p384_mod, y, p384_mod);
}
err = sp_384_to_mp(y, ym);
}
#if (defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)) && !defined(WOLFSSL_SP_NO_MALLOC)
if (d != NULL) {
XFREE(d, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
}
#endif
#endif /* WOLFSSL_SP_384 */
#endif /* WOLFSSL_HAVE_SP_ECC */
#endif /* SP_WORD_SIZE == 32 */
#endif /* !WOLFSSL_SP_ASM */
#endif /* WOLFSSL_HAVE_SP_RSA || WOLFSSL_HAVE_SP_DH || WOLFSSL_HAVE_SP_ECC */