wolf SSL
wolfSSL SSL/TLS library, support up to TLS1.3
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wolfcrypt/src/ge_operations.c
- Committer:
- wolfSSL
- Date:
- 2020-06-05
- Revision:
- 17:a5f916481144
- Parent:
- 16:8e0d178b1d1e
File content as of revision 17:a5f916481144:
/* ge_operations.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
*/
/* Based On Daniel J Bernstein's ed25519 Public Domain ref10 work. */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <wolfssl/wolfcrypt/settings.h>
#ifdef HAVE_ED25519
#ifndef ED25519_SMALL /* run when not defined to use small memory math */
#include <wolfssl/wolfcrypt/ge_operations.h>
#include <wolfssl/wolfcrypt/ed25519.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#ifdef NO_INLINE
#include <wolfssl/wolfcrypt/misc.h>
#else
#define WOLFSSL_MISC_INCLUDED
#include <wolfcrypt/src/misc.c>
#endif
#if defined(CURVED25519_X64)
#define CURVED25519_ASM_64BIT
#define CURVED25519_ASM
#endif
#if defined(WOLFSSL_ARMASM)
#if defined(__aarch64__)
#define CURVED25519_ASM_64BIT
#else
#define CURVED25519_ASM_32BIT
#endif
#define CURVED25519_ASM
#endif
static void ge_p2_0(ge_p2 *);
#ifndef CURVED25519_ASM
static void ge_precomp_0(ge_precomp *);
#endif
static void ge_p3_to_p2(ge_p2 *,const ge_p3 *);
static void ge_p3_to_cached(ge_cached *,const ge_p3 *);
static void ge_p1p1_to_p2(ge_p2 *,const ge_p1p1 *);
static void ge_p1p1_to_p3(ge_p3 *,const ge_p1p1 *);
static void ge_p2_dbl(ge_p1p1 *,const ge_p2 *);
static void ge_p3_dbl(ge_p1p1 *,const ge_p3 *);
static void ge_madd(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
static void ge_msub(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
static void ge_add(ge_p1p1 *,const ge_p3 *,const ge_cached *);
static void ge_sub(ge_p1p1 *,const ge_p3 *,const ge_cached *);
/*
ge means group element.
Here the group is the set of pairs (x,y) of field elements (see ge_operations.h)
satisfying -x^2 + y^2 = 1 + d x^2y^2
where d = -121665/121666.
Representations:
ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
ge_precomp (Duif): (y+x,y-x,2dxy)
*/
#if !defined(HAVE___UINT128_T) || defined(NO_CURVED25519_128BIT)
#define MASK_21 0x1fffff
#define ORDER_0 0x15d3ed
#define ORDER_1 0x18d2e7
#define ORDER_2 0x160498
#define ORDER_3 0xf39ac
#define ORDER_4 0x1dea2f
#define ORDER_5 0xa6f7c
#ifdef CURVED25519_ASM_32BIT
uint64_t load_3(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
result |= ((uint64_t) in[2]) << 16;
return result;
}
uint64_t load_4(const unsigned char *in)
{
uint64_t result;
result = (uint64_t) in[0];
result |= ((uint64_t) in[1]) << 8;
result |= ((uint64_t) in[2]) << 16;
result |= ((uint64_t) in[3]) << 24;
return result;
}
#endif
/*
Input:
s[0]+256*s[1]+...+256^63*s[63] = s
Output:
s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.
Overwrites s in place.
*/
void sc_reduce(byte* s)
{
int64_t t[24];
int64_t carry;
t[ 0] = MASK_21 & (load_3(s + 0) >> 0);
t[ 1] = MASK_21 & (load_4(s + 2) >> 5);
t[ 2] = MASK_21 & (load_3(s + 5) >> 2);
t[ 3] = MASK_21 & (load_4(s + 7) >> 7);
t[ 4] = MASK_21 & (load_4(s + 10) >> 4);
t[ 5] = MASK_21 & (load_3(s + 13) >> 1);
t[ 6] = MASK_21 & (load_4(s + 15) >> 6);
t[ 7] = MASK_21 & (load_3(s + 18) >> 3);
t[ 8] = MASK_21 & (load_3(s + 21) >> 0);
t[ 9] = MASK_21 & (load_4(s + 23) >> 5);
t[10] = MASK_21 & (load_3(s + 26) >> 2);
t[11] = MASK_21 & (load_4(s + 28) >> 7);
t[12] = MASK_21 & (load_4(s + 31) >> 4);
t[13] = MASK_21 & (load_3(s + 34) >> 1);
t[14] = MASK_21 & (load_4(s + 36) >> 6);
t[15] = MASK_21 & (load_3(s + 39) >> 3);
t[16] = MASK_21 & (load_3(s + 42) >> 0);
t[17] = MASK_21 & (load_4(s + 44) >> 5);
t[18] = MASK_21 & (load_3(s + 47) >> 2);
t[19] = MASK_21 & (load_4(s + 49) >> 7);
t[20] = MASK_21 & (load_4(s + 52) >> 4);
t[21] = MASK_21 & (load_3(s + 55) >> 1);
t[22] = MASK_21 & (load_4(s + 57) >> 6);
t[23] = (load_4(s + 60) >> 3);
t[11] -= t[23] * ORDER_0;
t[12] -= t[23] * ORDER_1;
t[13] -= t[23] * ORDER_2;
t[14] -= t[23] * ORDER_3;
t[15] -= t[23] * ORDER_4;
t[16] -= t[23] * ORDER_5;
t[10] -= t[22] * ORDER_0;
t[11] -= t[22] * ORDER_1;
t[12] -= t[22] * ORDER_2;
t[13] -= t[22] * ORDER_3;
t[14] -= t[22] * ORDER_4;
t[15] -= t[22] * ORDER_5;
t[ 9] -= t[21] * ORDER_0;
t[10] -= t[21] * ORDER_1;
t[11] -= t[21] * ORDER_2;
t[12] -= t[21] * ORDER_3;
t[13] -= t[21] * ORDER_4;
t[14] -= t[21] * ORDER_5;
t[ 8] -= t[20] * ORDER_0;
t[ 9] -= t[20] * ORDER_1;
t[10] -= t[20] * ORDER_2;
t[11] -= t[20] * ORDER_3;
t[12] -= t[20] * ORDER_4;
t[13] -= t[20] * ORDER_5;
t[ 7] -= t[19] * ORDER_0;
t[ 8] -= t[19] * ORDER_1;
t[ 9] -= t[19] * ORDER_2;
t[10] -= t[19] * ORDER_3;
t[11] -= t[19] * ORDER_4;
t[12] -= t[19] * ORDER_5;
t[ 6] -= t[18] * ORDER_0;
t[ 7] -= t[18] * ORDER_1;
t[ 8] -= t[18] * ORDER_2;
t[ 9] -= t[18] * ORDER_3;
t[10] -= t[18] * ORDER_4;
t[11] -= t[18] * ORDER_5;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
carry = t[12] >> 21; t[13] += carry; t[12] &= MASK_21;
carry = t[14] >> 21; t[15] += carry; t[14] &= MASK_21;
carry = t[16] >> 21; t[17] += carry; t[16] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[11] >> 21; t[12] += carry; t[11] &= MASK_21;
carry = t[13] >> 21; t[14] += carry; t[13] &= MASK_21;
carry = t[15] >> 21; t[16] += carry; t[15] &= MASK_21;
t[ 5] -= t[17] * ORDER_0;
t[ 6] -= t[17] * ORDER_1;
t[ 7] -= t[17] * ORDER_2;
t[ 8] -= t[17] * ORDER_3;
t[ 9] -= t[17] * ORDER_4;
t[10] -= t[17] * ORDER_5;
t[ 4] -= t[16] * ORDER_0;
t[ 5] -= t[16] * ORDER_1;
t[ 6] -= t[16] * ORDER_2;
t[ 7] -= t[16] * ORDER_3;
t[ 8] -= t[16] * ORDER_4;
t[ 9] -= t[16] * ORDER_5;
t[ 3] -= t[15] * ORDER_0;
t[ 4] -= t[15] * ORDER_1;
t[ 5] -= t[15] * ORDER_2;
t[ 6] -= t[15] * ORDER_3;
t[ 7] -= t[15] * ORDER_4;
t[ 8] -= t[15] * ORDER_5;
t[ 2] -= t[14] * ORDER_0;
t[ 3] -= t[14] * ORDER_1;
t[ 4] -= t[14] * ORDER_2;
t[ 5] -= t[14] * ORDER_3;
t[ 6] -= t[14] * ORDER_4;
t[ 7] -= t[14] * ORDER_5;
t[ 1] -= t[13] * ORDER_0;
t[ 2] -= t[13] * ORDER_1;
t[ 3] -= t[13] * ORDER_2;
t[ 4] -= t[13] * ORDER_3;
t[ 5] -= t[13] * ORDER_4;
t[ 6] -= t[13] * ORDER_5;
t[ 0] -= t[12] * ORDER_0;
t[ 1] -= t[12] * ORDER_1;
t[ 2] -= t[12] * ORDER_2;
t[ 3] -= t[12] * ORDER_3;
t[ 4] -= t[12] * ORDER_4;
t[ 5] -= t[12] * ORDER_5;
t[12] = 0;
carry = t[ 0] >> 21; t[ 1] += carry; t[ 0] &= MASK_21;
carry = t[ 1] >> 21; t[ 2] += carry; t[ 1] &= MASK_21;
carry = t[ 2] >> 21; t[ 3] += carry; t[ 2] &= MASK_21;
carry = t[ 3] >> 21; t[ 4] += carry; t[ 3] &= MASK_21;
carry = t[ 4] >> 21; t[ 5] += carry; t[ 4] &= MASK_21;
carry = t[ 5] >> 21; t[ 6] += carry; t[ 5] &= MASK_21;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
carry = t[11] >> 21; t[12] += carry; t[11] &= MASK_21;
t[ 0] -= t[12] * ORDER_0;
t[ 1] -= t[12] * ORDER_1;
t[ 2] -= t[12] * ORDER_2;
t[ 3] -= t[12] * ORDER_3;
t[ 4] -= t[12] * ORDER_4;
t[ 5] -= t[12] * ORDER_5;
carry = t[ 0] >> 21; t[ 1] += carry; t[ 0] &= MASK_21;
carry = t[ 1] >> 21; t[ 2] += carry; t[ 1] &= MASK_21;
carry = t[ 2] >> 21; t[ 3] += carry; t[ 2] &= MASK_21;
carry = t[ 3] >> 21; t[ 4] += carry; t[ 3] &= MASK_21;
carry = t[ 4] >> 21; t[ 5] += carry; t[ 4] &= MASK_21;
carry = t[ 5] >> 21; t[ 6] += carry; t[ 5] &= MASK_21;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
s[ 0] = (byte)(t[ 0] >> 0);
s[ 1] = (byte)(t[ 0] >> 8);
s[ 2] = (byte)((t[ 0] >> 16) | (t[ 1] << 5));
s[ 3] = (byte)(t[ 1] >> 3);
s[ 4] = (byte)(t[ 1] >> 11);
s[ 5] = (byte)((t[ 1] >> 19) | (t[ 2] << 2));
s[ 6] = (byte)(t[ 2] >> 6);
s[ 7] = (byte)((t[ 2] >> 14) | (t[ 3] << 7));
s[ 8] = (byte)(t[ 3] >> 1);
s[ 9] = (byte)(t[ 3] >> 9);
s[10] = (byte)((t[ 3] >> 17) | (t[ 4] << 4));
s[11] = (byte)(t[ 4] >> 4);
s[12] = (byte)(t[ 4] >> 12);
s[13] = (byte)((t[ 4] >> 20) | (t[ 5] << 1));
s[14] = (byte)(t[ 5] >> 7);
s[15] = (byte)((t[ 5] >> 15) | (t[ 6] << 6));
s[16] = (byte)(t[ 6] >> 2);
s[17] = (byte)(t[ 6] >> 10);
s[18] = (byte)((t[ 6] >> 18) | (t[ 7] << 3));
s[19] = (byte)(t[ 7] >> 5);
s[20] = (byte)(t[ 7] >> 13);
s[21] = (byte)(t[ 8] >> 0);
s[22] = (byte)(t[ 8] >> 8);
s[23] = (byte)((t[ 8] >> 16) | (t[ 9] << 5));
s[24] = (byte)(t[ 9] >> 3);
s[25] = (byte)(t[ 9] >> 11);
s[26] = (byte)((t[ 9] >> 19) | (t[10] << 2));
s[27] = (byte)(t[10] >> 6);
s[28] = (byte)((t[10] >> 14) | (t[11] << 7));
s[29] = (byte)(t[11] >> 1);
s[30] = (byte)(t[11] >> 9);
s[31] = (byte)(t[11] >> 17);
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c
Output:
s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
void sc_muladd(byte* s, const byte* a, const byte* b, const byte* c)
{
uint32_t ad[12], bd[12], cd[12];
int64_t t[24];
int64_t carry;
ad[ 0] = MASK_21 & (load_3(a + 0) >> 0);
ad[ 1] = MASK_21 & (load_4(a + 2) >> 5);
ad[ 2] = MASK_21 & (load_3(a + 5) >> 2);
ad[ 3] = MASK_21 & (load_4(a + 7) >> 7);
ad[ 4] = MASK_21 & (load_4(a + 10) >> 4);
ad[ 5] = MASK_21 & (load_3(a + 13) >> 1);
ad[ 6] = MASK_21 & (load_4(a + 15) >> 6);
ad[ 7] = MASK_21 & (load_3(a + 18) >> 3);
ad[ 8] = MASK_21 & (load_3(a + 21) >> 0);
ad[ 9] = MASK_21 & (load_4(a + 23) >> 5);
ad[10] = MASK_21 & (load_3(a + 26) >> 2);
ad[11] = (uint32_t)(load_4(a + 28) >> 7);
bd[ 0] = MASK_21 & (load_3(b + 0) >> 0);
bd[ 1] = MASK_21 & (load_4(b + 2) >> 5);
bd[ 2] = MASK_21 & (load_3(b + 5) >> 2);
bd[ 3] = MASK_21 & (load_4(b + 7) >> 7);
bd[ 4] = MASK_21 & (load_4(b + 10) >> 4);
bd[ 5] = MASK_21 & (load_3(b + 13) >> 1);
bd[ 6] = MASK_21 & (load_4(b + 15) >> 6);
bd[ 7] = MASK_21 & (load_3(b + 18) >> 3);
bd[ 8] = MASK_21 & (load_3(b + 21) >> 0);
bd[ 9] = MASK_21 & (load_4(b + 23) >> 5);
bd[10] = MASK_21 & (load_3(b + 26) >> 2);
bd[11] = (uint32_t)(load_4(b + 28) >> 7);
cd[ 0] = MASK_21 & (load_3(c + 0) >> 0);
cd[ 1] = MASK_21 & (load_4(c + 2) >> 5);
cd[ 2] = MASK_21 & (load_3(c + 5) >> 2);
cd[ 3] = MASK_21 & (load_4(c + 7) >> 7);
cd[ 4] = MASK_21 & (load_4(c + 10) >> 4);
cd[ 5] = MASK_21 & (load_3(c + 13) >> 1);
cd[ 6] = MASK_21 & (load_4(c + 15) >> 6);
cd[ 7] = MASK_21 & (load_3(c + 18) >> 3);
cd[ 8] = MASK_21 & (load_3(c + 21) >> 0);
cd[ 9] = MASK_21 & (load_4(c + 23) >> 5);
cd[10] = MASK_21 & (load_3(c + 26) >> 2);
cd[11] = (uint32_t)(load_4(c + 28) >> 7);
t[ 0] = cd[ 0] + (int64_t)ad[ 0] * bd[ 0];
t[ 1] = cd[ 1] + (int64_t)ad[ 0] * bd[ 1] + (int64_t)ad[ 1] * bd[ 0];
t[ 2] = cd[ 2] + (int64_t)ad[ 0] * bd[ 2] + (int64_t)ad[ 1] * bd[ 1] +
(int64_t)ad[ 2] * bd[ 0];
t[ 3] = cd[ 3] + (int64_t)ad[ 0] * bd[ 3] + (int64_t)ad[ 1] * bd[ 2] +
(int64_t)ad[ 2] * bd[ 1] + (int64_t)ad[ 3] * bd[ 0];
t[ 4] = cd[ 4] + (int64_t)ad[ 0] * bd[ 4] + (int64_t)ad[ 1] * bd[ 3] +
(int64_t)ad[ 2] * bd[ 2] + (int64_t)ad[ 3] * bd[ 1] +
(int64_t)ad[ 4] * bd[ 0];
t[ 5] = cd[ 5] + (int64_t)ad[ 0] * bd[ 5] + (int64_t)ad[ 1] * bd[ 4] +
(int64_t)ad[ 2] * bd[ 3] + (int64_t)ad[ 3] * bd[ 2] +
(int64_t)ad[ 4] * bd[ 1] + (int64_t)ad[ 5] * bd[ 0];
t[ 6] = cd[ 6] + (int64_t)ad[ 0] * bd[ 6] + (int64_t)ad[ 1] * bd[ 5] +
(int64_t)ad[ 2] * bd[ 4] + (int64_t)ad[ 3] * bd[ 3] +
(int64_t)ad[ 4] * bd[ 2] + (int64_t)ad[ 5] * bd[ 1] +
(int64_t)ad[ 6] * bd[ 0];
t[ 7] = cd[ 7] + (int64_t)ad[ 0] * bd[ 7] + (int64_t)ad[ 1] * bd[ 6] +
(int64_t)ad[ 2] * bd[ 5] + (int64_t)ad[ 3] * bd[ 4] +
(int64_t)ad[ 4] * bd[ 3] + (int64_t)ad[ 5] * bd[ 2] +
(int64_t)ad[ 6] * bd[ 1] + (int64_t)ad[ 7] * bd[ 0];
t[ 8] = cd[ 8] + (int64_t)ad[ 0] * bd[ 8] + (int64_t)ad[ 1] * bd[ 7] +
(int64_t)ad[ 2] * bd[ 6] + (int64_t)ad[ 3] * bd[ 5] +
(int64_t)ad[ 4] * bd[ 4] + (int64_t)ad[ 5] * bd[ 3] +
(int64_t)ad[ 6] * bd[ 2] + (int64_t)ad[ 7] * bd[ 1] +
(int64_t)ad[ 8] * bd[ 0];
t[ 9] = cd[ 9] + (int64_t)ad[ 0] * bd[ 9] + (int64_t)ad[ 1] * bd[ 8] +
(int64_t)ad[ 2] * bd[ 7] + (int64_t)ad[ 3] * bd[ 6] +
(int64_t)ad[ 4] * bd[ 5] + (int64_t)ad[ 5] * bd[ 4] +
(int64_t)ad[ 6] * bd[ 3] + (int64_t)ad[ 7] * bd[ 2] +
(int64_t)ad[ 8] * bd[ 1] + (int64_t)ad[ 9] * bd[ 0];
t[10] = cd[10] + (int64_t)ad[ 0] * bd[10] + (int64_t)ad[ 1] * bd[ 9] +
(int64_t)ad[ 2] * bd[ 8] + (int64_t)ad[ 3] * bd[ 7] +
(int64_t)ad[ 4] * bd[ 6] + (int64_t)ad[ 5] * bd[ 5] +
(int64_t)ad[ 6] * bd[ 4] + (int64_t)ad[ 7] * bd[ 3] +
(int64_t)ad[ 8] * bd[ 2] + (int64_t)ad[ 9] * bd[ 1] +
(int64_t)ad[10] * bd[ 0];
t[11] = cd[11] + (int64_t)ad[ 0] * bd[11] + (int64_t)ad[ 1] * bd[10] +
(int64_t)ad[ 2] * bd[ 9] + (int64_t)ad[ 3] * bd[ 8] +
(int64_t)ad[ 4] * bd[ 7] + (int64_t)ad[ 5] * bd[ 6] +
(int64_t)ad[ 6] * bd[ 5] + (int64_t)ad[ 7] * bd[ 4] +
(int64_t)ad[ 8] * bd[ 3] + (int64_t)ad[ 9] * bd[ 2] +
(int64_t)ad[10] * bd[ 1] + (int64_t)ad[11] * bd[ 0];
t[12] = (int64_t)ad[ 1] * bd[11] + (int64_t)ad[ 2] * bd[10] +
(int64_t)ad[ 3] * bd[ 9] + (int64_t)ad[ 4] * bd[ 8] +
(int64_t)ad[ 5] * bd[ 7] + (int64_t)ad[ 6] * bd[ 6] +
(int64_t)ad[ 7] * bd[ 5] + (int64_t)ad[ 8] * bd[ 4] +
(int64_t)ad[ 9] * bd[ 3] + (int64_t)ad[10] * bd[ 2] +
(int64_t)ad[11] * bd[ 1];
t[13] = (int64_t)ad[ 2] * bd[11] + (int64_t)ad[ 3] * bd[10] +
(int64_t)ad[ 4] * bd[ 9] + (int64_t)ad[ 5] * bd[ 8] +
(int64_t)ad[ 6] * bd[ 7] + (int64_t)ad[ 7] * bd[ 6] +
(int64_t)ad[ 8] * bd[ 5] + (int64_t)ad[ 9] * bd[ 4] +
(int64_t)ad[10] * bd[ 3] + (int64_t)ad[11] * bd[ 2];
t[14] = (int64_t)ad[ 3] * bd[11] + (int64_t)ad[ 4] * bd[10] +
(int64_t)ad[ 5] * bd[ 9] + (int64_t)ad[ 6] * bd[ 8] +
(int64_t)ad[ 7] * bd[ 7] + (int64_t)ad[ 8] * bd[ 6] +
(int64_t)ad[ 9] * bd[ 5] + (int64_t)ad[10] * bd[ 4] +
(int64_t)ad[11] * bd[ 3];
t[15] = (int64_t)ad[ 4] * bd[11] + (int64_t)ad[ 5] * bd[10] +
(int64_t)ad[ 6] * bd[ 9] + (int64_t)ad[ 7] * bd[ 8] +
(int64_t)ad[ 8] * bd[ 7] + (int64_t)ad[ 9] * bd[ 6] +
(int64_t)ad[10] * bd[ 5] + (int64_t)ad[11] * bd[ 4];
t[16] = (int64_t)ad[ 5] * bd[11] + (int64_t)ad[ 6] * bd[10] +
(int64_t)ad[ 7] * bd[ 9] + (int64_t)ad[ 8] * bd[ 8] +
(int64_t)ad[ 9] * bd[ 7] + (int64_t)ad[10] * bd[ 6] +
(int64_t)ad[11] * bd[ 5];
t[17] = (int64_t)ad[ 6] * bd[11] + (int64_t)ad[ 7] * bd[10] +
(int64_t)ad[ 8] * bd[ 9] + (int64_t)ad[ 9] * bd[ 8] +
(int64_t)ad[10] * bd[ 7] + (int64_t)ad[11] * bd[ 6];
t[18] = (int64_t)ad[ 7] * bd[11] + (int64_t)ad[ 8] * bd[10] +
(int64_t)ad[ 9] * bd[ 9] + (int64_t)ad[10] * bd[ 8] +
(int64_t)ad[11] * bd[ 7];
t[19] = (int64_t)ad[ 8] * bd[11] + (int64_t)ad[ 9] * bd[10] +
(int64_t)ad[10] * bd[ 9] + (int64_t)ad[11] * bd[ 8];
t[20] = (int64_t)ad[ 9] * bd[11] + (int64_t)ad[10] * bd[10] +
(int64_t)ad[11] * bd[ 9];
t[21] = (int64_t)ad[10] * bd[11] + (int64_t)ad[11] * bd[10];
t[22] = (int64_t)ad[11] * bd[11];
t[23] = 0;
carry = t[ 0] >> 21; t[ 1] += carry; t[ 0] &= MASK_21;
carry = t[ 2] >> 21; t[ 3] += carry; t[ 2] &= MASK_21;
carry = t[ 4] >> 21; t[ 5] += carry; t[ 4] &= MASK_21;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
carry = t[12] >> 21; t[13] += carry; t[12] &= MASK_21;
carry = t[14] >> 21; t[15] += carry; t[14] &= MASK_21;
carry = t[16] >> 21; t[17] += carry; t[16] &= MASK_21;
carry = t[18] >> 21; t[19] += carry; t[18] &= MASK_21;
carry = t[20] >> 21; t[21] += carry; t[20] &= MASK_21;
carry = t[22] >> 21; t[23] += carry; t[22] &= MASK_21;
carry = t[ 1] >> 21; t[ 2] += carry; t[ 1] &= MASK_21;
carry = t[ 3] >> 21; t[ 4] += carry; t[ 3] &= MASK_21;
carry = t[ 5] >> 21; t[ 6] += carry; t[ 5] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[11] >> 21; t[12] += carry; t[11] &= MASK_21;
carry = t[13] >> 21; t[14] += carry; t[13] &= MASK_21;
carry = t[15] >> 21; t[16] += carry; t[15] &= MASK_21;
carry = t[17] >> 21; t[18] += carry; t[17] &= MASK_21;
carry = t[19] >> 21; t[20] += carry; t[19] &= MASK_21;
carry = t[21] >> 21; t[22] += carry; t[21] &= MASK_21;
t[11] -= t[23] * ORDER_0;
t[12] -= t[23] * ORDER_1;
t[13] -= t[23] * ORDER_2;
t[14] -= t[23] * ORDER_3;
t[15] -= t[23] * ORDER_4;
t[16] -= t[23] * ORDER_5;
t[10] -= t[22] * ORDER_0;
t[11] -= t[22] * ORDER_1;
t[12] -= t[22] * ORDER_2;
t[13] -= t[22] * ORDER_3;
t[14] -= t[22] * ORDER_4;
t[15] -= t[22] * ORDER_5;
t[ 9] -= t[21] * ORDER_0;
t[10] -= t[21] * ORDER_1;
t[11] -= t[21] * ORDER_2;
t[12] -= t[21] * ORDER_3;
t[13] -= t[21] * ORDER_4;
t[14] -= t[21] * ORDER_5;
t[ 8] -= t[20] * ORDER_0;
t[ 9] -= t[20] * ORDER_1;
t[10] -= t[20] * ORDER_2;
t[11] -= t[20] * ORDER_3;
t[12] -= t[20] * ORDER_4;
t[13] -= t[20] * ORDER_5;
t[ 7] -= t[19] * ORDER_0;
t[ 8] -= t[19] * ORDER_1;
t[ 9] -= t[19] * ORDER_2;
t[10] -= t[19] * ORDER_3;
t[11] -= t[19] * ORDER_4;
t[12] -= t[19] * ORDER_5;
t[ 6] -= t[18] * ORDER_0;
t[ 7] -= t[18] * ORDER_1;
t[ 8] -= t[18] * ORDER_2;
t[ 9] -= t[18] * ORDER_3;
t[10] -= t[18] * ORDER_4;
t[11] -= t[18] * ORDER_5;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
carry = t[12] >> 21; t[13] += carry; t[12] &= MASK_21;
carry = t[14] >> 21; t[15] += carry; t[14] &= MASK_21;
carry = t[16] >> 21; t[17] += carry; t[16] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[11] >> 21; t[12] += carry; t[11] &= MASK_21;
carry = t[13] >> 21; t[14] += carry; t[13] &= MASK_21;
carry = t[15] >> 21; t[16] += carry; t[15] &= MASK_21;
t[ 5] -= t[17] * ORDER_0;
t[ 6] -= t[17] * ORDER_1;
t[ 7] -= t[17] * ORDER_2;
t[ 8] -= t[17] * ORDER_3;
t[ 9] -= t[17] * ORDER_4;
t[10] -= t[17] * ORDER_5;
t[ 4] -= t[16] * ORDER_0;
t[ 5] -= t[16] * ORDER_1;
t[ 6] -= t[16] * ORDER_2;
t[ 7] -= t[16] * ORDER_3;
t[ 8] -= t[16] * ORDER_4;
t[ 9] -= t[16] * ORDER_5;
t[ 3] -= t[15] * ORDER_0;
t[ 4] -= t[15] * ORDER_1;
t[ 5] -= t[15] * ORDER_2;
t[ 6] -= t[15] * ORDER_3;
t[ 7] -= t[15] * ORDER_4;
t[ 8] -= t[15] * ORDER_5;
t[ 2] -= t[14] * ORDER_0;
t[ 3] -= t[14] * ORDER_1;
t[ 4] -= t[14] * ORDER_2;
t[ 5] -= t[14] * ORDER_3;
t[ 6] -= t[14] * ORDER_4;
t[ 7] -= t[14] * ORDER_5;
t[ 1] -= t[13] * ORDER_0;
t[ 2] -= t[13] * ORDER_1;
t[ 3] -= t[13] * ORDER_2;
t[ 4] -= t[13] * ORDER_3;
t[ 5] -= t[13] * ORDER_4;
t[ 6] -= t[13] * ORDER_5;
t[ 0] -= t[12] * ORDER_0;
t[ 1] -= t[12] * ORDER_1;
t[ 2] -= t[12] * ORDER_2;
t[ 3] -= t[12] * ORDER_3;
t[ 4] -= t[12] * ORDER_4;
t[ 5] -= t[12] * ORDER_5;
t[12] = 0;
carry = t[ 0] >> 21; t[ 1] += carry; t[ 0] &= MASK_21;
carry = t[ 1] >> 21; t[ 2] += carry; t[ 1] &= MASK_21;
carry = t[ 2] >> 21; t[ 3] += carry; t[ 2] &= MASK_21;
carry = t[ 3] >> 21; t[ 4] += carry; t[ 3] &= MASK_21;
carry = t[ 4] >> 21; t[ 5] += carry; t[ 4] &= MASK_21;
carry = t[ 5] >> 21; t[ 6] += carry; t[ 5] &= MASK_21;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
carry = t[11] >> 21; t[12] += carry; t[11] &= MASK_21;
t[ 0] -= t[12] * ORDER_0;
t[ 1] -= t[12] * ORDER_1;
t[ 2] -= t[12] * ORDER_2;
t[ 3] -= t[12] * ORDER_3;
t[ 4] -= t[12] * ORDER_4;
t[ 5] -= t[12] * ORDER_5;
carry = t[ 0] >> 21; t[ 1] += carry; t[ 0] &= MASK_21;
carry = t[ 1] >> 21; t[ 2] += carry; t[ 1] &= MASK_21;
carry = t[ 2] >> 21; t[ 3] += carry; t[ 2] &= MASK_21;
carry = t[ 3] >> 21; t[ 4] += carry; t[ 3] &= MASK_21;
carry = t[ 4] >> 21; t[ 5] += carry; t[ 4] &= MASK_21;
carry = t[ 5] >> 21; t[ 6] += carry; t[ 5] &= MASK_21;
carry = t[ 6] >> 21; t[ 7] += carry; t[ 6] &= MASK_21;
carry = t[ 7] >> 21; t[ 8] += carry; t[ 7] &= MASK_21;
carry = t[ 8] >> 21; t[ 9] += carry; t[ 8] &= MASK_21;
carry = t[ 9] >> 21; t[10] += carry; t[ 9] &= MASK_21;
carry = t[10] >> 21; t[11] += carry; t[10] &= MASK_21;
s[ 0] = (byte)(t[ 0] >> 0);
s[ 1] = (byte)(t[ 0] >> 8);
s[ 2] = (byte)((t[ 0] >> 16) | (t[ 1] << 5));
s[ 3] = (byte)(t[ 1] >> 3);
s[ 4] = (byte)(t[ 1] >> 11);
s[ 5] = (byte)((t[ 1] >> 19) | (t[ 2] << 2));
s[ 6] = (byte)(t[ 2] >> 6);
s[ 7] = (byte)((t[ 2] >> 14) | (t[ 3] << 7));
s[ 8] = (byte)(t[ 3] >> 1);
s[ 9] = (byte)(t[ 3] >> 9);
s[10] = (byte)((t[ 3] >> 17) | (t[ 4] << 4));
s[11] = (byte)(t[ 4] >> 4);
s[12] = (byte)(t[ 4] >> 12);
s[13] = (byte)((t[ 4] >> 20) | (t[ 5] << 1));
s[14] = (byte)(t[ 5] >> 7);
s[15] = (byte)((t[ 5] >> 15) | (t[ 6] << 6));
s[16] = (byte)(t[ 6] >> 2);
s[17] = (byte)(t[ 6] >> 10);
s[18] = (byte)((t[ 6] >> 18) | (t[ 7] << 3));
s[19] = (byte)(t[ 7] >> 5);
s[20] = (byte)(t[ 7] >> 13);
s[21] = (byte)(t[ 8] >> 0);
s[22] = (byte)(t[ 8] >> 8);
s[23] = (byte)((t[ 8] >> 16) | (t[ 9] << 5));
s[24] = (byte)(t[ 9] >> 3);
s[25] = (byte)(t[ 9] >> 11);
s[26] = (byte)((t[ 9] >> 19) | (t[10] << 2));
s[27] = (byte)(t[10] >> 6);
s[28] = (byte)((t[10] >> 14) | (t[11] << 7));
s[29] = (byte)(t[11] >> 1);
s[30] = (byte)(t[11] >> 9);
s[31] = (byte)(t[11] >> 17);
}
#else
static uint64_t load_6(const byte* a)
{
uint64_t n;
n = ((uint64_t)a[0] << 0) |
((uint64_t)a[1] << 8) |
((uint64_t)a[2] << 16) |
((uint64_t)a[3] << 24) |
((uint64_t)a[4] << 32) |
((uint64_t)a[5] << 40);
return n;
}
static uint64_t load_7(const byte* a)
{
uint64_t n;
n = ((uint64_t)a[0] << 0) |
((uint64_t)a[1] << 8) |
((uint64_t)a[2] << 16) |
((uint64_t)a[3] << 24) |
((uint64_t)a[4] << 32) |
((uint64_t)a[5] << 40) |
((uint64_t)a[6] << 48);
return n;
}
#define MASK_42 0x3ffffffffffl
#define ORDER_0 0x31a5cf5d3edl
#define ORDER_1 0x1e735960498l
#define ORDER_2 0x14def9dea2fl
/*
Input:
s[0]+256*s[1]+...+256^63*s[63] = s
Output:
s[0]+256*s[1]+...+256^31*s[31] = s mod l
where l = 2^252 + 27742317777372353535851937790883648493.
Overwrites s in place.
*/
void sc_reduce(byte* s)
{
__int128_t t[12];
__int128_t carry;
t[ 0] = MASK_42 & (load_6(s + 0) >> 0);
t[ 1] = MASK_42 & (load_6(s + 5) >> 2);
t[ 2] = MASK_42 & (load_6(s + 10) >> 4);
t[ 3] = MASK_42 & (load_6(s + 15) >> 6);
t[ 4] = MASK_42 & (load_6(s + 21) >> 0);
t[ 5] = MASK_42 & (load_6(s + 26) >> 2);
t[ 6] = MASK_42 & (load_6(s + 31) >> 4);
t[ 7] = MASK_42 & (load_6(s + 36) >> 6);
t[ 8] = MASK_42 & (load_6(s + 42) >> 0);
t[ 9] = MASK_42 & (load_6(s + 47) >> 2);
t[10] = MASK_42 & (load_6(s + 52) >> 4);
t[11] = (load_7(s + 57) >> 6);
t[ 5] -= t[11] * ORDER_0;
t[ 6] -= t[11] * ORDER_1;
t[ 7] -= t[11] * ORDER_2;
t[ 4] -= t[10] * ORDER_0;
t[ 5] -= t[10] * ORDER_1;
t[ 6] -= t[10] * ORDER_2;
t[ 3] -= t[ 9] * ORDER_0;
t[ 4] -= t[ 9] * ORDER_1;
t[ 5] -= t[ 9] * ORDER_2;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 5] >> 42; t[ 6] += carry; t[ 5] &= MASK_42;
carry = t[ 7] >> 42; t[ 8] += carry; t[ 7] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
carry = t[ 6] >> 42; t[ 7] += carry; t[ 6] &= MASK_42;
t[ 2] -= t[ 8] * ORDER_0;
t[ 3] -= t[ 8] * ORDER_1;
t[ 4] -= t[ 8] * ORDER_2;
t[ 1] -= t[ 7] * ORDER_0;
t[ 2] -= t[ 7] * ORDER_1;
t[ 3] -= t[ 7] * ORDER_2;
t[ 0] -= t[ 6] * ORDER_0;
t[ 1] -= t[ 6] * ORDER_1;
t[ 2] -= t[ 6] * ORDER_2;
t[ 6] = 0;
carry = t[ 0] >> 42; t[ 1] += carry; t[ 0] &= MASK_42;
carry = t[ 1] >> 42; t[ 2] += carry; t[ 1] &= MASK_42;
carry = t[ 2] >> 42; t[ 3] += carry; t[ 2] &= MASK_42;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
carry = t[ 5] >> 42; t[ 6] += carry; t[ 5] &= MASK_42;
t[ 0] -= t[ 6] * ORDER_0;
t[ 1] -= t[ 6] * ORDER_1;
t[ 2] -= t[ 6] * ORDER_2;
carry = t[ 0] >> 42; t[ 1] += carry; t[ 0] &= MASK_42;
carry = t[ 1] >> 42; t[ 2] += carry; t[ 1] &= MASK_42;
carry = t[ 2] >> 42; t[ 3] += carry; t[ 2] &= MASK_42;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
s[ 0] = (t[ 0] >> 0);
s[ 1] = (t[ 0] >> 8);
s[ 2] = (t[ 0] >> 16);
s[ 3] = (t[ 0] >> 24);
s[ 4] = (t[ 0] >> 32);
s[ 5] = (t[ 0] >> 40) | (t[ 1] << 2);
s[ 6] = (t[ 1] >> 6);
s[ 7] = (t[ 1] >> 14);
s[ 8] = (t[ 1] >> 22);
s[ 9] = (t[ 1] >> 30);
s[10] = (t[ 1] >> 38) | (t[ 2] << 4);
s[11] = (t[ 2] >> 4);
s[12] = (t[ 2] >> 12);
s[13] = (t[ 2] >> 20);
s[14] = (t[ 2] >> 28);
s[15] = (t[ 2] >> 36) | (t[ 3] << 6);
s[16] = (t[ 3] >> 2);
s[17] = (t[ 3] >> 10);
s[18] = (t[ 3] >> 18);
s[19] = (t[ 3] >> 26);
s[20] = (t[ 3] >> 34);
s[21] = (t[ 4] >> 0);
s[22] = (t[ 4] >> 8);
s[23] = (t[ 4] >> 16);
s[24] = (t[ 4] >> 24);
s[25] = (t[ 4] >> 32);
s[26] = (t[ 4] >> 40) | (t[ 5] << 2);
s[27] = (t[ 5] >> 6);
s[28] = (t[ 5] >> 14);
s[29] = (t[ 5] >> 22);
s[30] = (t[ 5] >> 30);
s[31] = (t[ 5] >> 38);
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
c[0]+256*c[1]+...+256^31*c[31] = c
Output:
s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
void sc_muladd(byte* s, const byte* a, const byte* b, const byte* c)
{
uint64_t ad[6], bd[6], cd[6];
__int128_t t[12];
__int128_t carry;
ad[ 0] = MASK_42 & (load_6(a + 0) >> 0);
ad[ 1] = MASK_42 & (load_6(a + 5) >> 2);
ad[ 2] = MASK_42 & (load_6(a + 10) >> 4);
ad[ 3] = MASK_42 & (load_6(a + 15) >> 6);
ad[ 4] = MASK_42 & (load_6(a + 21) >> 0);
ad[ 5] = (load_6(a + 26) >> 2);
bd[ 0] = MASK_42 & (load_6(b + 0) >> 0);
bd[ 1] = MASK_42 & (load_6(b + 5) >> 2);
bd[ 2] = MASK_42 & (load_6(b + 10) >> 4);
bd[ 3] = MASK_42 & (load_6(b + 15) >> 6);
bd[ 4] = MASK_42 & (load_6(b + 21) >> 0);
bd[ 5] = (load_6(b + 26) >> 2);
cd[ 0] = MASK_42 & (load_6(c + 0) >> 0);
cd[ 1] = MASK_42 & (load_6(c + 5) >> 2);
cd[ 2] = MASK_42 & (load_6(c + 10) >> 4);
cd[ 3] = MASK_42 & (load_6(c + 15) >> 6);
cd[ 4] = MASK_42 & (load_6(c + 21) >> 0);
cd[ 5] = (load_6(c + 26) >> 2);
t[ 0] = cd[ 0] + (__int128_t)ad[ 0] * bd[ 0];
t[ 1] = cd[ 1] + (__int128_t)ad[ 0] * bd[ 1] + (__int128_t)ad[ 1] * bd[ 0];
t[ 2] = cd[ 2] + (__int128_t)ad[ 0] * bd[ 2] + (__int128_t)ad[ 1] * bd[ 1] +
(__int128_t)ad[ 2] * bd[ 0];
t[ 3] = cd[ 3] + (__int128_t)ad[ 0] * bd[ 3] + (__int128_t)ad[ 1] * bd[ 2] +
(__int128_t)ad[ 2] * bd[ 1] + (__int128_t)ad[ 3] * bd[ 0];
t[ 4] = cd[ 4] + (__int128_t)ad[ 0] * bd[ 4] + (__int128_t)ad[ 1] * bd[ 3] +
(__int128_t)ad[ 2] * bd[ 2] + (__int128_t)ad[ 3] * bd[ 1] +
(__int128_t)ad[ 4] * bd[ 0];
t[ 5] = cd[ 5] + (__int128_t)ad[ 0] * bd[ 5] + (__int128_t)ad[ 1] * bd[ 4] +
(__int128_t)ad[ 2] * bd[ 3] + (__int128_t)ad[ 3] * bd[ 2] +
(__int128_t)ad[ 4] * bd[ 1] + (__int128_t)ad[ 5] * bd[ 0];
t[ 6] = (__int128_t)ad[ 1] * bd[ 5] + (__int128_t)ad[ 2] * bd[ 4] +
(__int128_t)ad[ 3] * bd[ 3] + (__int128_t)ad[ 4] * bd[ 2] +
(__int128_t)ad[ 5] * bd[ 1];
t[ 7] = (__int128_t)ad[ 2] * bd[ 5] + (__int128_t)ad[ 3] * bd[ 4] +
(__int128_t)ad[ 4] * bd[ 3] + (__int128_t)ad[ 5] * bd[ 2];
t[ 8] = (__int128_t)ad[ 3] * bd[ 5] + (__int128_t)ad[ 4] * bd[ 4] +
(__int128_t)ad[ 5] * bd[ 3];
t[ 9] = (__int128_t)ad[ 4] * bd[ 5] + (__int128_t)ad[ 5] * bd[ 4];
t[10] = (__int128_t)ad[ 5] * bd[ 5];
t[11] = 0;
carry = t[ 0] >> 42; t[ 1] += carry; t[ 0] &= MASK_42;
carry = t[ 2] >> 42; t[ 3] += carry; t[ 2] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
carry = t[ 6] >> 42; t[ 7] += carry; t[ 6] &= MASK_42;
carry = t[ 8] >> 42; t[ 9] += carry; t[ 8] &= MASK_42;
carry = t[10] >> 42; t[11] += carry; t[10] &= MASK_42;
carry = t[ 1] >> 42; t[ 2] += carry; t[ 1] &= MASK_42;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 5] >> 42; t[ 6] += carry; t[ 5] &= MASK_42;
carry = t[ 7] >> 42; t[ 8] += carry; t[ 7] &= MASK_42;
carry = t[ 9] >> 42; t[10] += carry; t[ 9] &= MASK_42;
t[ 5] -= t[11] * ORDER_0;
t[ 6] -= t[11] * ORDER_1;
t[ 7] -= t[11] * ORDER_2;
t[ 4] -= t[10] * ORDER_0;
t[ 5] -= t[10] * ORDER_1;
t[ 6] -= t[10] * ORDER_2;
t[ 3] -= t[ 9] * ORDER_0;
t[ 4] -= t[ 9] * ORDER_1;
t[ 5] -= t[ 9] * ORDER_2;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 5] >> 42; t[ 6] += carry; t[ 5] &= MASK_42;
carry = t[ 7] >> 42; t[ 8] += carry; t[ 7] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
carry = t[ 6] >> 42; t[ 7] += carry; t[ 6] &= MASK_42;
t[ 2] -= t[ 8] * ORDER_0;
t[ 3] -= t[ 8] * ORDER_1;
t[ 4] -= t[ 8] * ORDER_2;
t[ 1] -= t[ 7] * ORDER_0;
t[ 2] -= t[ 7] * ORDER_1;
t[ 3] -= t[ 7] * ORDER_2;
t[ 0] -= t[ 6] * ORDER_0;
t[ 1] -= t[ 6] * ORDER_1;
t[ 2] -= t[ 6] * ORDER_2;
t[ 6] = 0;
carry = t[ 0] >> 42; t[ 1] += carry; t[ 0] &= MASK_42;
carry = t[ 1] >> 42; t[ 2] += carry; t[ 1] &= MASK_42;
carry = t[ 2] >> 42; t[ 3] += carry; t[ 2] &= MASK_42;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
carry = t[ 5] >> 42; t[ 6] += carry; t[ 5] &= MASK_42;
t[ 0] -= t[ 6] * ORDER_0;
t[ 1] -= t[ 6] * ORDER_1;
t[ 2] -= t[ 6] * ORDER_2;
carry = t[ 0] >> 42; t[ 1] += carry; t[ 0] &= MASK_42;
carry = t[ 1] >> 42; t[ 2] += carry; t[ 1] &= MASK_42;
carry = t[ 2] >> 42; t[ 3] += carry; t[ 2] &= MASK_42;
carry = t[ 3] >> 42; t[ 4] += carry; t[ 3] &= MASK_42;
carry = t[ 4] >> 42; t[ 5] += carry; t[ 4] &= MASK_42;
s[ 0] = (t[ 0] >> 0);
s[ 1] = (t[ 0] >> 8);
s[ 2] = (t[ 0] >> 16);
s[ 3] = (t[ 0] >> 24);
s[ 4] = (t[ 0] >> 32);
s[ 5] = (t[ 0] >> 40) | (t[ 1] << 2);
s[ 6] = (t[ 1] >> 6);
s[ 7] = (t[ 1] >> 14);
s[ 8] = (t[ 1] >> 22);
s[ 9] = (t[ 1] >> 30);
s[10] = (t[ 1] >> 38) | (t[ 2] << 4);
s[11] = (t[ 2] >> 4);
s[12] = (t[ 2] >> 12);
s[13] = (t[ 2] >> 20);
s[14] = (t[ 2] >> 28);
s[15] = (t[ 2] >> 36) | (t[ 3] << 6);
s[16] = (t[ 3] >> 2);
s[17] = (t[ 3] >> 10);
s[18] = (t[ 3] >> 18);
s[19] = (t[ 3] >> 26);
s[20] = (t[ 3] >> 34);
s[21] = (t[ 4] >> 0);
s[22] = (t[ 4] >> 8);
s[23] = (t[ 4] >> 16);
s[24] = (t[ 4] >> 24);
s[25] = (t[ 4] >> 32);
s[26] = (t[ 4] >> 40) | (t[ 5] << 2);
s[27] = (t[ 5] >> 6);
s[28] = (t[ 5] >> 14);
s[29] = (t[ 5] >> 22);
s[30] = (t[ 5] >> 30);
s[31] = (t[ 5] >> 38);
}
#endif /* !HAVE___UINT128_T || NO_CURVED25519_128BIT */
int ge_compress_key(byte* out, const byte* xIn, const byte* yIn, word32 keySz)
{
ge x,y,z;
ge_p3 g;
byte bArray[ED25519_KEY_SIZE];
word32 i;
fe_0(x);
fe_0(y);
fe_1(z);
fe_frombytes(x, xIn);
fe_frombytes(y, yIn);
fe_copy(g.X, x);
fe_copy(g.Y, y);
fe_copy(g.Z, z);
ge_p3_tobytes(bArray, &g);
for (i = 0; i < keySz; i++) {
out[keySz - 1 - i] = bArray[i];
}
return 0;
}
/*
r = p + q
*/
static WC_INLINE void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
#ifndef CURVED25519_ASM
ge t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->YplusX);
fe_mul(r->Y,r->Y,q->YminusX);
fe_mul(r->T,q->T2d,p->T);
fe_mul(r->X,p->Z,q->Z);
fe_add(t0,r->X,r->X);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_add(r->Z,t0,r->T);
fe_sub(r->T,t0,r->T);
#else
fe_ge_add(r->X, r->Y, r->Z, r->T, p->X, p->Y, p->Z, p->T, q->Z, q->T2d,
q->YplusX, q->YminusX);
#endif
}
#ifndef CURVED25519_ASM
/* ge_scalar mult base */
static unsigned char equal(signed char b,signed char c)
{
unsigned char ub = b;
unsigned char uc = c;
unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
uint32_t y = x; /* 0: yes; 1..255: no */
y -= 1; /* 4294967295: yes; 0..254: no */
y >>= 31; /* 1: yes; 0: no */
return (unsigned char)y;
}
static unsigned char negative(signed char b)
{
return ((unsigned char)b) >> 7;
}
static WC_INLINE void cmov(ge_precomp *t,const ge_precomp *u,unsigned char b,
unsigned char n)
{
b = equal(b,n);
fe_cmov(t->yplusx,u->yplusx,b);
fe_cmov(t->yminusx,u->yminusx,b);
fe_cmov(t->xy2d,u->xy2d,b);
}
#endif
#ifdef CURVED25519_ASM_64BIT
static const ge_precomp base[64][8] = {
{
{
{ 0x2fbc93c6f58c3b85, -0x306cd2390473f1e7, 0x270b4898643d42c2, 0x07cf9d3a33d4ba65 },
{ -0x62efc6fa28bf6ec2, -0x02c660fa2ebf414d, -0x5a3e7bcb977075f7, 0x44fd2f9298f81267 },
{ -0x2442ea98b49044a7, 0x41e13f00eea2a5ea, -0x322b62e336a83906, 0x4f0ebe1faf16ecca }
},
{
{ -0x6ddb18036cc38e29, -0x60b9626985f00a4b, 0x5aa69a65e1d60702, 0x590c063fa87d2e2e },
{ -0x75665a9fbd4b2a58, -0x70d47ef3b19f530a, -0x1f61dc944e91c856, 0x6bb595a669c92555 },
{ 0x6e347eaadad36802, -0x450ca66c7c11b7fb, 0x3bcabe10e6076826, 0x49314f0a165ed1b8 }
},
{
{ -0x50da4f57b31168d0, 0x025a8430e8864b8a, -0x3ee4affd60fe98ce, 0x7a164e1b9a80f8f4 },
{ 0x56611fe8a4fcd265, 0x3bd353fde5c1ba7d, -0x7ece0ce5deb42943, 0x2ab91587555bda62 },
{ -0x640dee0b0e98b7cc, -0x47b194e809d2076b, -0x282190f8a48dd5b2, 0x549a04b963bb2a21 }
},
{
{ 0x287351b98efc099f, 0x6765c6f47dfd2538, -0x35cb72c204f56d9b, 0x680e910321e58727 },
{ -0x6a01faf5fa97e741, 0x327e89715660faa9, -0x3c171c32f95faf8d, 0x27933f4c7445a49a },
{ -0x40e1ba131aebd950, -0x1cd439c29245f06c, -0x1bd68b2a7307ad40, 0x44f079b1b0e64c18 }
},
{
{ -0x5ded43bbf75a44cd, -0x72afb73c38a112fe, -0x22e414f3a54013bc, 0x2945ccf146e206eb },
{ 0x7f9182c3a447d6ba, -0x2affeb2eb4d8d649, -0x1cc30ee3479b5f79, 0x154a7e73eb1b55f3 },
{ -0x37cd5e86182ffc4d, 0x5f729d0a00124d7e, 0x62c1d4a10e6d8ff3, 0x68b8ac5938b27a98 }
},
{
{ 0x3a0ceeeb77157131, -0x64d8ea76ff375078, -0x7f9a499725a658ca, 0x51e57bb6a2cc38bd },
{ 0x499806b67b7d8ca4, 0x575be28427d22739, -0x44f7a318dfbaac47, 0x38b64c41ae417884 },
{ -0x7062526e97621c5c, 0x175f2428f8fb9137, 0x050ab5329fcfb988, 0x7865dfa21354c09f }
},
{
{ 0x6b1a5cd0944ea3bf, 0x7470353ab39dc0d2, 0x71b2528228542e49, 0x461bea69283c927e },
{ -0x4590d36555cdde4f, 0x6ca021533bba23a7, -0x621589b06de6d3c6, 0x1d6edd5d2e5317e0 },
{ 0x217a8aacab0fda36, -0x5ad739abc2cab638, 0x37d05b8b13ab7568, 0x233cef623a2cbc37 }
},
{
{ 0x59b7596604dd3e8f, 0x6cb30377e288702c, -0x4ecc6399a1263cdd, 0x0915e76061bce52f },
{ -0x1d58a2120c6dcb27, -0x69c2897f1e4aa707, 0x2c2741ac6e3c23fb, 0x3a9024a1320e01c3 },
{ -0x208217ca57cb5c82, -0x741e63259767a816, 0x2c1185367167b326, 0x589eb3d9dbefd5c2 }
},
},
{
{
{ 0x322d04a52d9021f6, -0x463e60cc8a394064, 0x587a3a4342d20b09, 0x143b1cf8aa64fe61 },
{ 0x7ec851ca553e2df3, -0x58ed7b3459b7874d, -0x194a1be6cd772e19, 0x4cf210ec5a9a8883 },
{ -0x6079838269753555, 0x5f54258e27092729, -0x2f582cb415e7f68b, 0x21b546a3374126e1 }
},
{
{ 0x490a7a45d185218f, -0x65eac887b9fb6ccb, 0x0060ea09cc31e1f6, 0x7e041577f86ee965 },
{ -0x56b007a75d777cbd, -0x31f12ba9acec12c4, -0x0aa3c2304a40cb06, 0x0a653ca5c9eab371 },
{ 0x66b2a496ce5b67f3, -0x00ab6d2742a9686a, 0x503cec294a592cd0, 0x566943650813acb2 }
},
{
{ 0x5672f9eb1dabb69d, -0x458f4aca5017ac04, 0x47ac0f752796d66d, 0x32a5351794117275 },
{ -0x47e724f3d99df868, 0x5d5c31d9606e354a, 0x0982fa4f00a8cdc7, 0x17e12bcd4653e2d4 },
{ -0x2c59bb59209b7bc9, 0x703b6559880fbfdd, -0x347adabf52c5e55b, 0x0900b3f78e4c6468 }
},
{
{ -0x12d7f04137e952cf, 0x52d9595bd8e6efe3, 0x0fe71772f6c623f5, 0x4314030b051e293c },
{ 0x0a851b9f679d651b, -0x1ef7349efcccbd0e, -0x29fe0a801774cf5d, 0x371f3acaed2dd714 },
{ -0x2a9fffa1040f4353, -0x7148f0d12e78f3a2, 0x201f9033d084e6a0, 0x4c3a5ae1ce7b6670 }
},
{
{ -0x45078a1b36c25f23, -0x46cd7d588e46d6b3, -0x7f29c0480b393ba0, 0x6de9c73dea66c181 },
{ 0x4138a434dcb8fa95, -0x78f3098293697bf5, -0x21c77a8bd68417d4, 0x7c814db27262a55a },
{ 0x478904d5a04df8f2, -0x050451b54efebd2d, -0x0937539caaa2f668, 0x5aac4a412f90b104 }
},
{
{ 0x603a0d0abd7f5134, -0x7f7636cd1e2c51ba, -0x20da6ec67867429d, 0x1c145cd274ba0235 },
{ -0x39b0cd94c536d6f8, 0x5551b282e663e1e0, 0x476b35f54a1a4b83, 0x1b9da3fe189f68c2 },
{ 0x32e8386475f3d743, 0x365b8baf6ae5d9ef, -0x7dadc749c7a497e2, 0x234929c1167d65e1 }
},
{
{ 0x48145cc21d099fcf, 0x4535c192cc28d7e5, -0x7f183e1ab7db81ff, 0x4a5f28743b2973ee },
{ -0x67b213545f885218, 0x383f77ad19eb389d, -0x38139481d6ab286c, 0x59c77b3aeb7c3a7a },
{ -0x2c5228dadda3309e, -0x6ee5cc7e4dead3a3, -0x274c6052a4f70783, 0x6f05606b4799fe3b }
},
{
{ 0x5b433149f91b6483, -0x524a239aa5d3409e, -0x78057bed9cd7d84d, 0x60895e91ab49f8d8 },
{ -0x6001616de884569e, -0x675118e2f21a351f, 0x3ff4ae942d831044, 0x714de12e58533ac8 },
{ -0x16130d12f30793e8, -0x4b92f9edf8ca202c, -0x43625f67fb469419, 0x73e2e62fd96dc26b }
},
},
{
{
{ 0x2eccdd0e632f9c1d, 0x51d0b69676893115, 0x52dfb76ba8637a58, 0x6dd37d49a00eef39 },
{ -0x12a49cabb655aea2, -0x579a3b60f4397dc6, -0x7af3e016a4bd2e3c, 0x30d76d6f03d315b9 },
{ 0x6c4444172106e4c7, -0x04ac297f6d728097, -0x4b8c615b96b2c0da, 0x10c697112e864bb0 }
},
{
{ 0x0ca62aa08358c805, 0x6a3d4ae37a204247, 0x7464d3a63b11eddc, 0x03bf9baf550806ef },
{ 0x6493c4277dbe5fde, 0x265d4fad19ad7ea2, 0x0e00dfc846304590, 0x25e61cabed66fe09 },
{ 0x3f13e128cc586604, 0x6f5873ecb459747e, -0x5f49c21233ed970b, 0x566d78634586e22c }
},
{
{ -0x5efabd7a39a5d030, 0x6c64112af31667c3, 0x680ae240731aee58, 0x14fba5f34793b22a },
{ 0x1637a49f9cc10834, -0x4371a92a57643baf, 0x1cb5ec0f7f7fd2db, 0x33975bca5ecc35d9 },
{ 0x3cd746166985f7d4, 0x593e5e84c9c80057, 0x2fc3f2b67b61131e, 0x14829cea83fc526c }
},
{
{ 0x21e70b2f4e71ecb8, -0x19a92246bf5b881d, -0x409aa93131e2b080, 0x05fc3bc4535d7b7e },
{ -0x00bc847b68226a3e, 0x6c744e30aa4eb5a7, -0x61f3a29ec37a1775, 0x2fd9c71e5f758173 },
{ 0x24b8b3ae52afdedd, 0x3495638ced3b30cf, 0x33a4bc83a9be8195, 0x373767475c651f04 }
},
{
{ 0x634095cb14246590, -0x10edebbfe93eaacb, -0x61c7ebf376ef43a0, 0x6bf5905730907c8c },
{ 0x2fba99fd40d1add9, -0x4cf8e990690b2fd9, 0x4363f05215f03bae, 0x1fbea56c3b18f999 },
{ 0x0fa778f1e1415b8a, 0x06409ff7bac3a77e, 0x6f52d7b89aa29a50, 0x02521cf67a635a56 }
},
{
{ -0x4eeb98df88d0a11c, -0x17076b4e69f86532, 0x4af8224d00ac824a, 0x001753d9f7cd6cc4 },
{ 0x513fee0b0a9d5294, -0x706718a3f020a59a, -0x2b9e7977401ef832, 0x3fa00a7e71382ced },
{ 0x3c69232d963ddb34, 0x1dde87dab4973858, -0x55282e065f6e0d7b, 0x12b5fe2fa048edb6 }
},
{
{ -0x20d483d95290e16e, 0x4b66d323504b8913, -0x73bf623f8ae3743d, 0x6f7e93c20796c7b8 },
{ 0x71f0fbc496fce34d, 0x73b9826badf35bed, -0x2dfb8d9e00d73a9f, 0x749b76f96fb1206f },
{ 0x1f5af604aea6ae05, -0x3edcae0e411b6367, 0x61a808b5eeff6b66, 0x0fcec10f01e02151 }
},
{
{ 0x3df2d29dc4244e45, 0x2b020e7493d8de0a, 0x6cc8067e820c214d, 0x413779166feab90a },
{ 0x644d58a649fe1e44, 0x21fcaea231ad777e, 0x02441c5a887fd0d2, 0x4901aa7183c511f3 },
{ 0x08b1b7548c1af8f0, -0x31f08583db9d664c, -0x089f4f06e1f926c7, 0x41bb887b726d1213 }
},
},
{
{
{ -0x68267f1f55c6082e, 0x35d0384252c6b51c, 0x7d43f49307cd55aa, 0x56bd36cfb78ac362 },
{ -0x6d987f93a983b628, 0x066d04ccca791e6a, -0x5960a9ba1c33c6b5, 0x5c95b686a0788cd2 },
{ 0x2ac519c10d14a954, -0x150b8b4b6b4a0570, -0x19507c7d560785a6, 0x0dea6db1879be094 }
},
{
{ 0x15baeb74d6a8797a, 0x7ef55cf1fac41732, 0x29001f5a3c8b05c5, 0x0ad7cc8752eaccfb },
{ -0x559940ab8cbb1a55, -0x25eda77770e4bcf7, 0x5e87d2b3fd564b2f, 0x5b2c78885483b1dd },
{ 0x52151362793408cf, -0x14f0e8fce669c26c, -0x57cc4d0577c26b9a, 0x093a7fa775003c78 }
},
{
{ -0x47169fbb9f56ed7a, 0x7f3fd8047778d3de, 0x67d01e31bf8a5e2d, 0x7b038a06c27b653e },
{ -0x1aef8219c5e92842, -0x5c880023650ccd31, 0x70d5bf18440b677f, 0x6a252b19a4a31403 },
{ -0x6126e62a2c966f0d, 0x5213aebbdb4eb9f2, -0x38f715fab3466ecb, 0x58ded57f72260e56 }
},
{
{ -0x2592acd9a4f02b75, -0x769f7dce6c405678, -0x287536cd9e2a81d8, 0x79f2942d3a5c8143 },
{ 0x78e79dade9413d77, -0x0da8062a68d61983, 0x59db910ee37aa7e6, 0x6aa11b5bbb9e039c },
{ -0x6825d0da49377217, 0x251ba7eaacf20169, 0x09b44f87ef4eb4e4, 0x7d90ab1bbc6a7da5 }
},
{
{ 0x1a07a3f496b3c397, 0x11ceaa188f4e2532, 0x7d9498d5a7751bf0, 0x19ed161f508dd8a0 },
{ -0x6533597c58fe9402, -0x6fafa0b20d3af493, 0x6b610d5fcce435aa, 0x19a10d446198ff96 },
{ 0x560a2cd687dce6ca, 0x7f3568c48664cf4d, -0x78be16addd7fc5c8, 0x483bdab1595653fc }
},
{
{ -0x2930b2f54b257f0a, -0x7db7c1ba07cf8020, 0x05005269ae6f9da4, 0x1c7052909cf7877a },
{ -0x0587f0eb78cb05b7, 0x106f0b70360534e0, 0x2210776fe3e307bd, 0x3286c109dde6a0fe },
{ 0x32ee7de2874e98d4, 0x14c362e9b97e0c60, 0x5781dcde6a60a38a, 0x217dd5eaaa7aa840 }
},
{
{ -0x7420e0464173f138, 0x00bae7f8e30a0282, 0x4963991dad6c4f6c, 0x07058a6e5df6f60a },
{ -0x62483b2fdb71e150, -0x1f89681eb28b40ae, 0x1e6a9b173c562354, 0x7fa7c21f795a4965 },
{ -0x1614fd3b24ce0981, -0x12da0276ef4304d5, 0x46c8131f5c5cddb4, 0x33b21c13a0cb9bce }
},
{
{ -0x6550464fa11c73a5, -0x4062d2b1f8e5ec39, -0x7111919216ccd6f6, 0x1c3bab17ae109717 },
{ 0x360692f8087d8e31, -0x0b2339c82d8e9c09, 0x25a4e62065ea5963, 0x659bf72e5ac160d9 },
{ 0x1c9ab216c7cab7b0, 0x7d65d37407bbc3cc, 0x52744750504a58d5, 0x09f2606b131a2990 }
},
},
{
{
{ 0x7e234c597c6691ae, 0x64889d3d0a85b4c8, -0x251d36f3cab50519, 0x0a871e070c6a9e1d },
{ 0x40e87d44744346be, 0x1d48dad415b52b25, 0x7c3a8a18a13b603e, 0x4eb728c12fcdbdf7 },
{ 0x3301b5994bbc8989, 0x736bae3a5bdd4260, 0x0d61ade219d59e3c, 0x3ee7300f2685d464 }
},
{
{ 0x43fa7947841e7518, -0x1a3905a69c63b929, -0x5ef9a1e21cfad48c, 0x7d47c6a2cfb89030 },
{ -0x0a2daa1b61822949, -0x7fe9eea39ef4e154, 0x3c99975d92e187ca, 0x13815762979125c2 },
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{
{ -0x40844475bd568a04, -0x73a3c68869525ca8, -0x1d803890321255b8, 0x19735fd7f6bc20a6 },
{ 0x1abc92af49c5342e, -0x001127ee4d190530, -0x105d73720337b1d7, 0x11b5df18a44cc543 },
{ -0x1c546f2fbd37bd9a, -0x147b71f080e6ab82, 0x2503a1d065a497b9, 0x0fef911191df895f }
},
},
{
{
{ 0x6ab5dcb85b1c16b7, -0x6b3f0317c384d85b, -0x5b4ee3e58caae842, 0x499238d0ba0eafaa },
{ -0x4eaf835e54e39147, -0x42bb70c1e949784d, 0x3455fb7f2c7a91ab, 0x7579229e2f2adec1 },
{ -0x130b91ad854574a9, 0x15a08c478bd1647b, 0x7af1c6a65f706fef, 0x6345fa78f03a30d5 }
},
{
{ -0x6c2c341642270f5c, -0x24ead3e402e88cfe, 0x7dbddc6d7f17a875, 0x3e1a71cc8f426efe },
{ -0x20fd06a0efea185f, 0x790ec41da9b40263, 0x4d3a0ea133ea1107, 0x54f70be7e33af8c9 },
{ -0x37c35c1c6f45429e, -0x7f121c98fd6e37cd, -0x377fc7332c86ff3c, 0x2c5fc0231ec31fa1 }
},
{
{ -0x3bdd1b2efdba919b, -0x78beb53e352b846f, 0x1592e2bba2b6ffdd, 0x75d9d2bff5c2100f },
{ -0x01456ee8e8fc74b1, -0x1aedc8de3621107f, 0x1c97e4e75d0d8834, 0x68afae7a23dc3bc6 },
{ 0x5bd9b4763626e81c, -0x766996c9435fd123, 0x0a41193d61f077b3, 0x3097a24200ce5471 }
},
{
{ -0x5e9d18db996a3b7a, 0x131d633435a89607, 0x30521561a0d12a37, 0x56704bada6afb363 },
{ 0x57427734c7f8b84c, -0x0ebe5ec1fe4d8f17, 0x02d1adfeb4e564a6, 0x4bb23d92ce83bd48 },
{ -0x5093b558ad06ed47, 0x5e665f6cd86770c8, 0x4c35ac83a3c8cd58, 0x2b7a29c010a58a7e }
},
{
{ 0x33810a23bf00086e, -0x50316da118c90084, 0x3d60e670e24922d4, 0x11ce9e714f96061b },
{ -0x3bff80882f3e313d, -0x72efdf49453b6d08, 0x32ec29d57e69daaf, 0x599408759d95fce0 },
{ 0x219ef713d815bac1, -0x0ebeb9a2b7a41da4, 0x6d5447cc4e513c51, 0x174926be5ef44393 }
},
{
{ 0x3ef5d41593ea022e, 0x5cbcc1a20ed0eed6, -0x702db130f8c7d374, 0x6fa42ead06d8e1ad },
{ -0x4a214d0603a42a45, -0x6d2558d51e27ef1f, -0x503b302348d5e3a7, 0x497d78813fc22a24 },
{ -0x1d897db5e08cc8e1, 0x7f7cf01c4f5b6736, 0x7e201fe304fa46e7, 0x785a36a357808c96 }
},
{
{ 0x070442985d517bc3, 0x6acd56c7ae653678, 0x00a27983985a7763, 0x5167effae512662b },
{ -0x7da042029cfeb2d5, -0x37adc9639358a875, 0x5b2fcd285c0b5df0, 0x12ab214c58048c8f },
{ -0x42b1561ef0ac3b4a, 0x1673dc5f8ac91a14, -0x5707e5b1d533e546, 0x33a92a7924332a25 }
},
{
{ 0x7ba95ba0218f2ada, -0x300bdd78ccf04636, -0x2525b692a93926f9, 0x5380c296f4beee54 },
{ -0x622e0b66d86693fe, 0x0cb3b058e04d1752, 0x1f7e88967fd02c3e, 0x2f964268cb8b3eb1 },
{ -0x62b0d8fb997672f6, 0x3d0987990aff3f7a, -0x2f610c9d982545bb, 0x7761455e7b1c669c }
},
},
};
#elif defined(CURVED25519_ASM_32BIT)
static const ge_precomp base[64][8] = {
{
{
{ -0x0a73c47b, 0x2fbc93c6, -0x0473f1e7, -0x306cd23a, 0x643d42c2, 0x270b4898, 0x33d4ba65, 0x07cf9d3a },
{ -0x28bf6ec2, -0x62efc6fb, -0x2ebf414d, -0x02c660fb, 0x688f8a09, -0x5a3e7bcc, -0x6707ed99, 0x44fd2f92 },
{ 0x4b6fbb59, -0x2442ea99, -0x115d5a16, 0x41e13f00, -0x36a83906, -0x322b62e4, -0x50e91336, 0x4f0ebe1f }
},
{
{ -0x6cc38e29, -0x6ddb1804, 0x7a0ff5b5, -0x60b9626a, -0x1e29f8fe, 0x5aa69a65, -0x5782d1d2, 0x590c063f },
{ 0x42b4d5a8, -0x75665aa0, 0x4e60acf6, -0x70d47ef4, -0x4e91c856, -0x1f61dc95, 0x69c92555, 0x6bb595a6 },
{ -0x252c97fe, 0x6e347eaa, -0x7c11b7fb, -0x450ca66d, -0x19f897da, 0x3bcabe10, 0x165ed1b8, 0x49314f0a }
},
{
{ 0x4cee9730, -0x50da4f58, -0x1779b476, 0x025a8430, -0x60fe98ce, -0x3ee4affe, -0x657f070c, 0x7a164e1b },
{ -0x5b032d9b, 0x56611fe8, -0x1a3e4583, 0x3bd353fd, 0x214bd6bd, -0x7ece0ce6, 0x555bda62, 0x2ab91587 },
{ -0x0e98b7cc, -0x640dee0c, -0x09d2076b, -0x47b194e9, 0x5b722a4e, -0x282190f9, 0x63bb2a21, 0x549a04b9 }
},
{
{ -0x7103f661, 0x287351b9, 0x7dfd2538, 0x6765c6f4, -0x04f56d9b, -0x35cb72c3, 0x21e58727, 0x680e9103 },
{ 0x056818bf, -0x6a01faf6, 0x5660faa9, 0x327e8971, 0x06a05073, -0x3c171c33, 0x7445a49a, 0x27933f4c },
{ -0x1aebd950, -0x40e1ba14, 0x6dba0f94, -0x1cd439c3, -0x7307ad40, -0x1bd68b2b, -0x4f19b3e8, 0x44f079b1 }
},
{
{ 0x08a5bb33, -0x5ded43bc, -0x38a112fe, -0x72afb73d, 0x5abfec44, -0x22e414f4, 0x46e206eb, 0x2945ccf1 },
{ -0x5bb82946, 0x7f9182c3, 0x4b2729b7, -0x2affeb2f, -0x479b5f79, -0x1cc30ee4, -0x14e4aa0d, 0x154a7e73 },
{ -0x182ffc4d, -0x37cd5e87, 0x00124d7e, 0x5f729d0a, 0x0e6d8ff3, 0x62c1d4a1, 0x38b27a98, 0x68b8ac59 }
},
{
{ 0x77157131, 0x3a0ceeeb, 0x00c8af88, -0x64d8ea77, -0x25a658ca, -0x7f9a4998, -0x5d33c743, 0x51e57bb6 },
{ 0x7b7d8ca4, 0x499806b6, 0x27d22739, 0x575be284, 0x204553b9, -0x44f7a319, -0x51be877c, 0x38b64c41 },
{ 0x689de3a4, -0x7062526f, -0x07046ec9, 0x175f2428, -0x60304678, 0x050ab532, 0x1354c09f, 0x7865dfa2 }
},
{
{ -0x6bb15c41, 0x6b1a5cd0, -0x4c623f2e, 0x7470353a, 0x28542e49, 0x71b25282, 0x283c927e, 0x461bea69 },
{ -0x55cdde4f, -0x4590d366, 0x3bba23a7, 0x6ca02153, -0x6de6d3c6, -0x621589b1, 0x2e5317e0, 0x1d6edd5d },
{ -0x54f025ca, 0x217a8aac, 0x3d3549c8, -0x5ad739ac, 0x13ab7568, 0x37d05b8b, 0x3a2cbc37, 0x233cef62 }
},
{
{ 0x04dd3e8f, 0x59b75966, -0x1d778fd4, 0x6cb30377, 0x5ed9c323, -0x4ecc639a, 0x61bce52f, 0x0915e760 },
{ -0x0c6dcb27, -0x1d58a213, -0x1e4aa707, -0x69c28980, 0x6e3c23fb, 0x2c2741ac, 0x320e01c3, 0x3a9024a1 },
{ -0x57cb5c82, -0x208217cb, 0x689857ea, -0x741e6326, 0x7167b326, 0x2c118536, -0x24102a3e, 0x589eb3d9 }
},
},
{
{
{ 0x2d9021f6, 0x322d04a5, 0x75c6bf9c, -0x463e60cd, 0x42d20b09, 0x587a3a43, -0x559b019f, 0x143b1cf8 },
{ 0x553e2df3, 0x7ec851ca, -0x59b7874d, -0x58ed7b35, 0x3288d1e7, -0x194a1be7, 0x5a9a8883, 0x4cf210ec },
{ -0x69753555, -0x60798383, 0x27092729, 0x5f54258e, -0x15e7f68b, -0x2f582cb5, 0x374126e1, 0x21b546a3 }
},
{
{ -0x2e7ade71, 0x490a7a45, 0x46049335, -0x65eac888, -0x33ce1e0a, 0x0060ea09, -0x0791169b, 0x7e041577 },
{ -0x5d777cbd, -0x56b007a8, 0x5313ed3c, -0x31f12baa, -0x4a40cb06, -0x0aa3c231, -0x36154c8f, 0x0a653ca5 },
{ -0x31a4980d, 0x66b2a496, -0x42a9686a, -0x00ab6d28, 0x4a592cd0, 0x503cec29, 0x0813acb2, 0x56694365 }
},
{
{ 0x1dabb69d, 0x5672f9eb, -0x5017ac04, -0x458f4acb, 0x2796d66d, 0x47ac0f75, -0x6bee8d8b, 0x32a53517 },
{ 0x26620798, -0x47e724f4, 0x606e354a, 0x5d5c31d9, 0x00a8cdc7, 0x0982fa4f, 0x4653e2d4, 0x17e12bcd },
{ -0x209b7bc9, -0x2c59bb5a, -0x77f04023, 0x703b6559, -0x52c5e55b, -0x347adac0, -0x71b39b98, 0x0900b3f7 }
},
{
{ -0x37e952cf, -0x12d7f042, -0x2719101d, 0x52d9595b, -0x0939dc0b, 0x0fe71772, 0x051e293c, 0x4314030b },
{ 0x679d651b, 0x0a851b9f, 0x033342f2, -0x1ef7349f, -0x1774cf5d, -0x29fe0a81, -0x12d228ec, 0x371f3aca },
{ -0x040f4353, -0x2a9fffa2, -0x2e78f3a2, -0x7148f0d2, -0x2f7b1960, 0x201f9033, -0x31849990, 0x4c3a5ae1 }
},
{
{ -0x36c25f23, -0x45078a1c, 0x71b9294d, -0x46cd7d59, -0x0b393ba0, -0x7f29c049, -0x15993e7f, 0x6de9c73d },
{ -0x2347056b, 0x4138a434, 0x6c96840b, -0x78f30983, 0x297be82c, -0x21c77a8c, 0x7262a55a, 0x7c814db2 },
{ -0x5fb2070e, 0x478904d5, -0x4efebd2d, -0x050451b6, 0x555d0998, -0x0937539d, 0x2f90b104, 0x5aac4a41 }
},
{
{ -0x4280aecc, 0x603a0d0a, -0x1e2c51ba, -0x7f7636ce, -0x7867429d, -0x20da6ec7, 0x74ba0235, 0x1c145cd2 },
{ 0x3ac92908, -0x39b0cd95, -0x199c1e20, 0x5551b282, 0x4a1a4b83, 0x476b35f5, 0x189f68c2, 0x1b9da3fe },
{ 0x75f3d743, 0x32e83864, 0x6ae5d9ef, 0x365b8baf, 0x385b681e, -0x7dadc74a, 0x167d65e1, 0x234929c1 }
},
{
{ 0x1d099fcf, 0x48145cc2, -0x33d7281b, 0x4535c192, 0x48247e01, -0x7f183e1b, 0x3b2973ee, 0x4a5f2874 },
{ -0x5f885218, -0x67b21355, 0x19eb389d, 0x383f77ad, 0x2954d794, -0x38139482, -0x1483c586, 0x59c77b3a },
{ 0x225ccf62, -0x2c5228db, -0x4dead3a3, -0x6ee5cc7f, 0x5b08f87d, -0x274c6053, 0x4799fe3b, 0x6f05606b }
},
{
{ -0x06e49b7d, 0x5b433149, 0x5a2cbf62, -0x524a239b, 0x632827b3, -0x78057bee, -0x54b60728, 0x60895e91 },
{ 0x177ba962, -0x6001616e, 0x0de5cae1, -0x675118e3, 0x2d831044, 0x3ff4ae94, 0x58533ac8, 0x714de12e },
{ 0x0cf86c18, -0x16130d13, 0x0735dfd4, -0x4b92f9ee, 0x04b96be7, -0x43625f68, -0x26923d95, 0x73e2e62f }
},
},
{
{
{ 0x632f9c1d, 0x2eccdd0e, 0x76893115, 0x51d0b696, -0x579c85a8, 0x52dfb76b, -0x5ff110c7, 0x6dd37d49 },
{ 0x49aa515e, -0x12a49cac, 0x0bc6823a, -0x579a3b61, 0x5b42d1c4, -0x7af3e017, 0x03d315b9, 0x30d76d6f },
{ 0x2106e4c7, 0x6c444417, -0x6d728097, -0x04ac2980, 0x694d3f26, -0x4b8c615c, 0x2e864bb0, 0x10c69711 }
},
{
{ -0x7ca737fb, 0x0ca62aa0, 0x7a204247, 0x6a3d4ae3, 0x3b11eddc, 0x7464d3a6, 0x550806ef, 0x03bf9baf },
{ 0x7dbe5fde, 0x6493c427, 0x19ad7ea2, 0x265d4fad, 0x46304590, 0x0e00dfc8, -0x129901f7, 0x25e61cab },
{ -0x33a799fc, 0x3f13e128, -0x4ba68b82, 0x6f5873ec, -0x33ed970b, -0x5f49c213, 0x4586e22c, 0x566d7863 }
},
{
{ -0x39a5d030, -0x5efabd7b, -0x0ce9983d, 0x6c64112a, 0x731aee58, 0x680ae240, 0x4793b22a, 0x14fba5f3 },
{ -0x633ef7cc, 0x1637a49f, -0x57643baf, -0x4371a92b, 0x7f7fd2db, 0x1cb5ec0f, 0x5ecc35d9, 0x33975bca },
{ 0x6985f7d4, 0x3cd74616, -0x3637ffa9, 0x593e5e84, 0x7b61131e, 0x2fc3f2b6, -0x7c03ad94, 0x14829cea }
},
{
{ 0x4e71ecb8, 0x21e70b2f, 0x40a477e3, -0x19a92247, -0x31e2b080, -0x409aa932, 0x535d7b7e, 0x05fc3bc4 },
{ -0x68226a3e, -0x00bc847c, -0x55b14a59, 0x6c744e30, 0x3c85e88b, -0x61f3a29f, 0x5f758173, 0x2fd9c71e },
{ 0x52afdedd, 0x24b8b3ae, -0x12c4cf31, 0x3495638c, -0x56417e6b, 0x33a4bc83, 0x5c651f04, 0x37376747 }
},
{
{ 0x14246590, 0x634095cb, 0x16c15535, -0x10edebc0, -0x76ef43a0, -0x61c7ebf4, 0x30907c8c, 0x6bf59057 },
{ 0x40d1add9, 0x2fba99fd, -0x690b2fd9, -0x4cf8e991, 0x15f03bae, 0x4363f052, 0x3b18f999, 0x1fbea56c },
{ -0x1ebea476, 0x0fa778f1, -0x453c5882, 0x06409ff7, -0x655d65b0, 0x6f52d7b8, 0x7a635a56, 0x02521cf6 }
},
{
{ 0x772f5ee4, -0x4eeb98e0, -0x69f86532, -0x17076b4f, 0x00ac824a, 0x4af8224d, -0x0832933c, 0x001753d9 },
{ 0x0a9d5294, 0x513fee0b, 0x0fdf5a66, -0x706718a4, -0x401ef832, -0x2b9e7978, 0x71382ced, 0x3fa00a7e },
{ -0x69c224cc, 0x3c69232d, -0x4b68c7a8, 0x1dde87da, -0x5f6e0d7b, -0x55282e07, -0x5fb7124a, 0x12b5fe2f }
},
{
{ -0x5290e16e, -0x20d483da, 0x504b8913, 0x4b66d323, 0x751c8bc3, -0x73bf6240, 0x0796c7b8, 0x6f7e93c2 },
{ -0x69031cb3, 0x71f0fbc4, -0x520ca413, 0x73b9826b, -0x00d73a9f, -0x2dfb8d9f, 0x6fb1206f, 0x749b76f9 },
{ -0x515951fb, 0x1f5af604, -0x411b6367, -0x3edcae0f, -0x1100949a, 0x61a808b5, 0x01e02151, 0x0fcec10f }
},
{
{ -0x3bdbb1bb, 0x3df2d29d, -0x6c2721f6, 0x2b020e74, -0x7df3deb3, 0x6cc8067e, 0x6feab90a, 0x41377916 },
{ 0x49fe1e44, 0x644d58a6, 0x31ad777e, 0x21fcaea2, -0x77802f2e, 0x02441c5a, -0x7c3aee0d, 0x4901aa71 },
{ -0x73e50710, 0x08b1b754, 0x246299b4, -0x31f08584, 0x1e06d939, -0x089f4f07, 0x726d1213, 0x41bb887b }
},
},
{
{
{ -0x55c6082e, -0x68267f20, 0x52c6b51c, 0x35d03842, 0x07cd55aa, 0x7d43f493, -0x48753c9e, 0x56bd36cf },
{ 0x567c49d8, -0x6d987f94, -0x3586e196, 0x066d04cc, -0x1c33c6b5, -0x5960a9bb, -0x5f87732e, 0x5c95b686 },
{ 0x0d14a954, 0x2ac519c1, -0x6b4a0570, -0x150b8b4c, -0x560785a6, -0x19507c7e, -0x78641f6c, 0x0dea6db1 }
},
{
{ -0x29578686, 0x15baeb74, -0x053be8ce, 0x7ef55cf1, 0x3c8b05c5, 0x29001f5a, 0x52eaccfb, 0x0ad7cc87 },
{ 0x7344e5ab, -0x559940ac, -0x70e4bcf7, -0x25eda778, -0x02a9b4d1, 0x5e87d2b3, 0x5483b1dd, 0x5b2c7888 },
{ 0x793408cf, 0x52151362, 0x19963d94, -0x14f0e8fd, -0x77c26b9a, -0x57cc4d06, 0x75003c78, 0x093a7fa7 }
},
{
{ 0x60a91286, -0x47169fbc, 0x7778d3de, 0x7f3fd804, -0x4075a1d3, 0x67d01e31, -0x3d849ac2, 0x7b038a06 },
{ 0x3a16d7be, -0x1aef821a, -0x650ccd31, -0x5c880024, 0x440b677f, 0x70d5bf18, -0x5b5cebfd, 0x6a252b19 },
{ -0x2c966f0d, -0x6126e62b, -0x24b1460e, 0x5213aebb, 0x4cb99135, -0x38f715fb, 0x72260e56, 0x58ded57f }
},
{
{ 0x5b0fd48b, -0x2592acda, -0x6c405678, -0x769f7dcf, 0x61d57e28, -0x287536ce, 0x3a5c8143, 0x79f2942d },
{ -0x16bec289, 0x78e79dad, -0x68d61983, -0x0da8062b, -0x1c85581a, 0x59db910e, -0x4461fc64, 0x6aa11b5b },
{ -0x49377217, -0x6825d0db, -0x530dfe97, 0x251ba7ea, -0x10b14b1c, 0x09b44f87, -0x4395825b, 0x7d90ab1b }
},
{
{ -0x694c3c69, 0x1a07a3f4, -0x70b1dace, 0x11ceaa18, -0x588ae410, 0x7d9498d5, 0x508dd8a0, 0x19ed161f },
{ -0x58fe9402, -0x6533597d, -0x0d3af493, -0x6fafa0b3, -0x331bca56, 0x6b610d5f, 0x6198ff96, 0x19a10d44 },
{ -0x78231936, 0x560a2cd6, -0x799b30b3, 0x7f3568c4, 0x22803a38, -0x78be16ae, 0x595653fc, 0x483bdab1 }
},
{
{ -0x4b257f0a, -0x2930b2f6, -0x07cf8020, -0x7db7c1bb, -0x5190625c, 0x05005269, -0x63087886, 0x1c705290 },
{ -0x78cb05b7, -0x0587f0ec, 0x360534e0, 0x106f0b70, -0x1c1cf843, 0x2210776f, -0x22195f02, 0x3286c109 },
{ -0x78b1672c, 0x32ee7de2, -0x4681f3a0, 0x14c362e9, 0x6a60a38a, 0x5781dcde, -0x558557c0, 0x217dd5ea }
},
{
{ -0x4173f138, -0x7420e047, -0x1cf5fd7e, 0x00bae7f8, -0x5293b094, 0x4963991d, 0x5df6f60a, 0x07058a6e },
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{ -0x647d6154, -0x43e72353, -0x4a0a8630, 0x23ae7d28, 0x69384233, -0x3cb9edd6, -0x182b5377, 0x1a6110b2 },
{ -0x1babb850, -0x02f2a242, 0x092005ee, 0x6cec351a, 0x567579cb, -0x665b87bc, 0x16e7fa45, 0x59d242a2 },
{ -0x19966854, 0x4f833f6a, 0x361839a4, 0x6849762a, -0x68f54adb, 0x6985dec1, -0x234e0aba, 0x53045e89 }
},
{
{ -0x72ba01ee, -0x7b25c322, -0x1bbb1d2e, -0x42bd3de8, 0x1f7e3598, -0x57ae6988, 0x5616e2b2, 0x7642c93f },
{ -0x28acac25, -0x34744cba, -0x51aee1de, -0x03034db5, -0x2af51911, -0x345b72c0, -0x0b0834a3, 0x26e3bae5 },
{ 0x4595f8e4, 0x2323daa7, -0x7a85414c, -0x21977375, 0x1c59326e, 0x3fc48e96, 0x15c9b8ba, 0x0b2e73ca }
},
{
{ 0x79c03a55, 0x0e3fbfaf, 0x4cbb5acf, 0x3077af05, -0x24c21c61, -0x2a3aadbb, 0x476a4af7, 0x015e68c1 },
{ -0x3e80afda, -0x2944bbd8, -0x04a56359, -0x614d8ddd, 0x1919c644, -0x1c845afd, -0x4a6599fe, 0x21ce380d },
{ 0x20066a38, -0x3e2ad7ae, 0x3570aef3, -0x6a9fc1ae, 0x226b8a4d, -0x7cd9a659, 0x1f8eedc9, 0x5dd68909 }
},
{
{ -0x5acecf7c, 0x1d022591, -0x29d8f78e, -0x35d2b552, 0x2f0bfd20, -0x795ed47b, -0x528258b8, 0x56e6c439 },
{ -0x402c37aa, -0x34537b22, -0x4ca00dbc, 0x1624c348, 0x5d9cad07, -0x48077236, -0x5d3d1418, 0x3b0e574d },
{ 0x42bdbae6, -0x38fb00b7, -0x4d21e087, 0x5e21ade2, 0x5652fad8, -0x16a24c0d, -0x70f7143f, 0x0822b537 }
},
},
{
{
{ 0x62730383, -0x1e480d6d, -0x143575d4, 0x4b5279ff, -0x402becec, -0x25038876, -0x638d9ef1, 0x7deb1014 },
{ -0x70c78b8b, 0x51f04847, -0x634134c4, -0x4da2430c, -0x2660dfab, -0x6554edbc, 0x1c10a5d6, 0x2c709e6c },
{ -0x78991186, -0x349d5096, 0x5553cd0e, 0x66cbec04, 0x0f0be4b5, 0x58800138, -0x09d31d16, 0x08e68e9f }
},
{
{ 0x0ab8f2f9, 0x2f2d09d5, -0x3aa6dc21, -0x5346de73, 0x73766cb9, 0x4a8f3426, 0x38f719f5, 0x4cb13bd7 },
{ 0x4bc130ad, 0x34ad500a, 0x3d0bd49c, -0x72c724b7, 0x500a89be, -0x5da3c268, -0x1145c4f7, 0x2f1f3f87 },
{ -0x1aea49b6, -0x087b738b, -0x24b56fc8, -0x5a6afe46, 0x3f751b50, -0x3df2cec1, -0x3f51d118, 0x19a1e353 }
},
{
{ -0x2a694243, -0x4bde8d33, -0x671103c0, -0x6c1fbabd, -0x4bbef64b, -0x604eacb9, 0x0266ae34, 0x736bd399 },
{ -0x4505fa3d, 0x7d1c7560, -0x391aa19f, -0x4c1e5f60, -0x3f299b8d, -0x1cad68e8, -0x3df3cb7a, 0x41546b11 },
{ -0x6ccb4c4c, -0x7aacd2b0, 0x60816573, 0x46fd114b, 0x425c8375, -0x33a0a0d0, -0x478054a4, 0x412295a2 }
},
{
{ -0x1d6c153a, 0x2e655261, 0x2133acdb, -0x7ba56dfd, 0x7900996b, 0x460975cb, 0x195add80, 0x0760bb8d },
{ -0x0a812917, 0x19c99b88, 0x6df8c825, 0x5393cb26, -0x4cf52d8d, 0x5cee3213, -0x4ad2d1cc, 0x14e153eb },
{ -0x32197e76, 0x413e1a17, -0x12965f7c, 0x57156da9, 0x46caccb1, 0x2cbf268f, -0x3cc53a0e, 0x6b34be9b }
},
{
{ 0x6571f2d3, 0x11fc6965, 0x530e737a, -0x393617bb, -0x2b01afcb, -0x1cc5185e, 0x2e6dd30b, 0x01b9c7b6 },
{ 0x3a78c0b2, -0x0c20d09c, -0x0dd1fd84, 0x4c3e971e, 0x49c1b5a3, -0x1382e3a2, 0x0922dd2d, 0x2012c18f },
{ 0x5ac89d29, -0x77f4aa1b, 0x45a0a763, 0x1483241f, -0x3d1893e1, 0x3d36efdf, 0x4e4bade8, 0x08af5b78 }
},
{
{ -0x7633d3b5, -0x1d8ceb2e, -0x5d78e873, 0x4be4bd11, -0x05cc9b32, 0x18d528d6, -0x50267d92, 0x6423c1d5 },
{ -0x77e0dacd, 0x283499dc, 0x779323b6, -0x62fada26, 0x673441f4, -0x76852205, 0x163a168d, 0x32b79d71 },
{ -0x12034c96, -0x337a0727, 0x3746e5f9, 0x22bcc28f, -0x061a2c33, -0x1b621cc8, -0x3ec1d234, 0x480a5efb }
},
{
{ 0x42ce221f, -0x499eb31c, 0x4c053928, 0x6e199dcc, -0x23e341fd, 0x663fb4a4, 0x691c8e06, 0x24b31d47 },
{ 0x01622071, 0x0b51e70b, -0x74e2503b, 0x06b505cf, -0x10a55433, 0x2c6bb061, 0x0cb7bf31, 0x47aa2760 },
{ -0x3fea073d, 0x2a541eed, 0x7c693f7c, 0x11a4fe7e, 0x4ea278d6, -0x0f5099ed, 0x14dda094, 0x545b585d }
},
{
{ -0x1c4cde1f, 0x6204e4d0, 0x28ff1e95, 0x3baa637a, 0x5b99bd9e, 0x0b0ccffd, 0x64c8d071, 0x4d22dc3e },
{ -0x5f2bc5f1, 0x67bf275e, 0x089beebe, -0x521971cc, -0x2b8618d2, 0x4289134c, 0x32ba5454, 0x0f62f9c3 },
{ -0x29c4a0c7, -0x034b9a77, 0x57cbcf61, 0x5cae6a3f, -0x6ac505fb, -0x01453d2e, 0x36371436, 0x1c0fa01a }
},
},
{
{
{ 0x54c53fae, -0x3ee11a18, 0x2b4f3ff4, 0x6a0b06c1, -0x1f49858e, 0x33540f80, -0x32f81c11, 0x15f18fc3 },
{ -0x4383296e, -0x18ab8bb7, -0x1908c221, 0x0f9abeaa, 0x00837e29, 0x4af01ca7, 0x3f1bc183, 0x63ab1b5d },
{ -0x4fd70b74, 0x32750763, 0x556a065f, 0x06020740, -0x3cb6a4a8, -0x2ac427ee, -0x79a0af73, 0x08706c9b }
},
{
{ 0x38b41246, -0x3366e4bf, 0x6f9ac26b, 0x243b9c52, -0x48345443, -0x4610b6b3, -0x2f7d1300, 0x5fba433d },
{ 0x3d343dff, -0x0c835d55, -0x7f5439e9, 0x1a8c6a2d, -0x2b330036, -0x71b61fcb, -0x455e2e47, 0x48b46bee },
{ -0x366be530, -0x63b61cab, 0x74498f84, -0x468cb522, 0x66663e5c, 0x41c3fed0, -0x1718ef4d, 0x0ecfedf8 }
},
{
{ -0x16bfc89e, 0x744f7463, -0x72033637, -0x08657212, 0x55e4cde3, 0x163a6496, -0x4d7b0bcb, 0x3b61788d },
{ -0x632b8f27, 0x76430f9f, -0x5bd09ff8, -0x49d53365, 0x59adad5e, 0x1898297c, -0x4873af80, 0x7789dd2d },
{ 0x0d6ef6b2, -0x4dddd7e7, 0x46ce4bfa, -0x56b5994e, 0x4f0b6cc7, 0x46c1a77a, -0x148cc731, 0x4236ccff }
},
{
{ -0x2588820a, 0x3bd82dbf, 0x0b98369e, 0x71b177cc, -0x7af3c967, 0x1d0e8463, 0x48e2d1f1, 0x5a71945b },
{ 0x0d55e274, -0x7b68bfb3, -0x3b52d4ad, 0x6c6663d9, -0x5256a8cc, -0x13d04f27, -0x324708c4, 0x2617e120 },
{ 0x405b4b42, 0x6f203dd5, 0x10b24509, 0x327ec604, -0x53d577ba, -0x63cb8dd0, 0x11ffeb6a, 0x77de29fc }
},
{
{ -0x13312d36, -0x7ca1ec71, -0x1569c466, -0x736150ed, -0x4de9f15a, -0x36a04040, -0x5278876e, 0x575e66f3 },
{ -0x7c488758, -0x4f53a837, -0x28016ed4, 0x53cdcca9, -0x00e0a624, 0x61c2b854, -0x0f218254, 0x3a1a2cf0 },
{ -0x377034c6, -0x667fc5d9, 0x275ec0b0, 0x345a6789, -0x0093d41b, 0x459789d0, 0x1e70a8b2, 0x62f88265 }
},
{
{ 0x698a19e0, 0x6d822986, 0x74d78a71, -0x2367de1f, -0x0934e0b9, 0x41a85f31, -0x432563af, 0x352721c2 },
{ 0x59ff1be4, 0x085ae2c7, 0x3b0e40b7, 0x149145c9, 0x7ff27379, -0x3b981806, -0x2a38c56b, 0x4eeecf0a },
{ 0x213fc985, 0x48329952, 0x368a1746, 0x1087cf0d, 0x66c15aa5, -0x71ad9e4f, 0x2ed24c21, 0x2d5b2d84 }
},
{
{ 0x196ac533, 0x5eb7d13d, -0x247f41d5, 0x377234ec, 0x7cf5ae24, -0x1ebb3004, -0x3bbe5314, 0x5226bcf9 },
{ -0x142c212f, 0x02cfebd9, 0x39021974, -0x2ba4de89, -0x01cf5e49, 0x7576f813, -0x5cb1093e, 0x5691b6f9 },
{ 0x23e5b547, 0x79ee6c72, -0x7ccf2987, 0x6f5f5076, 0x6d8adce9, -0x128c1e17, 0x1d8ccc03, 0x27c3da1e }
},
{
{ 0x630ef9f6, 0x28302e71, 0x2b64cee0, -0x3d2b5dfd, 0x4b6292be, 0x09082030, -0x57d520e8, 0x5fca747a },
{ 0x3fe24c74, 0x7eb9efb2, 0x1651be01, 0x3e50f49f, 0x21858dea, 0x3ea732dc, 0x5bb810f9, 0x17377bd7 },
{ 0x5c258ea5, 0x232a03c3, 0x6bcb0cf1, -0x790dc5d4, 0x2e442166, 0x3dad8d0d, -0x548979d5, 0x04a8933c }
},
},
{
{
{ -0x736c95b0, 0x69082b0e, -0x3e253a4a, -0x06365fcb, -0x3b2049cc, 0x6fb73e54, 0x1d2bc140, 0x4005419b },
{ 0x22943dff, -0x2d39fb4a, 0x44cfb3a0, -0x43734132, -0x687f7988, 0x5d254ff3, 0x3b1ca6bf, 0x0fa3614f },
{ -0x46417d10, -0x5ffc0143, 0x3a44ac90, 0x2089c1af, 0x1954fa8e, -0x07b6606f, -0x10bf54be, 0x1fba218a }
},
{
{ 0x3e7b0194, 0x4f3e5704, 0x08daaf7f, -0x57e2c112, -0x6623210f, -0x37c63955, -0x00889e2b, 0x6c535d13 },
{ -0x05370ac2, -0x54ab6bb8, 0x7ba63741, -0x7e091766, 0x6c2b5e01, 0x74fd6c7d, -0x573791be, 0x392e3aca },
{ 0x3e8a35af, 0x4cbd34e9, 0x5887e816, 0x2e078144, -0x0d654f55, 0x19319c76, -0x2af53ec5, 0x25e17fe4 }
},
{
{ 0x76f121a7, -0x6ea0800b, 0x2fcd87e3, -0x3cb5cdd9, 0x4d1be526, -0x3345d022, -0x76967665, 0x6bba828f },
{ 0x1e04f676, 0x0a289bd7, -0x29bdf06b, 0x208e1c52, 0x34691fab, 0x5186d8b0, 0x2a9fb351, 0x25575144 },
{ -0x6f01c6ff, -0x1d2e439a, -0x5f66852b, 0x4cb54a18, -0x507b9f2c, -0x68e296ec, 0x7f6b7be4, 0x559d504f }
},
{
{ -0x092d9903, -0x63b76e19, 0x0307781b, 0x0744a19b, 0x6061e23b, -0x77c770e3, 0x354bd50e, 0x123ea6a3 },
{ -0x4c14ab2b, -0x588c7c88, -0x5aaac384, 0x1d69d366, -0x06d7ff46, 0x0a26cf62, -0x7f81cde9, 0x01ab12d5 },
{ 0x41e32d96, 0x118d1890, -0x27cea7b8, -0x46121c3e, -0x27cdba27, 0x1eab4271, -0x36e75eac, 0x4a3961e2 }
},
{
{ -0x0cdcc0e2, 0x0327d644, 0x34fcf016, 0x499a260e, -0x0d254687, -0x7c4a58ea, -0x642beee1, 0x68aceead },
{ -0x07194460, 0x71dc3be0, 0x7effe30a, -0x293107cc, -0x1ec5b896, -0x566dbda1, -0x04e2489d, 0x2cd6bce3 },
{ -0x0c283df0, 0x38b4c90e, -0x4852fbf4, 0x308e6e24, -0x4818c1dd, 0x3860d9f1, -0x4af70a69, 0x595760d5 }
},
{
{ -0x02fdd870, -0x77d53415, -0x3beea8a0, -0x7650ccfb, 0x7d3473f4, 0x65f492e3, 0x54515a2b, 0x2cb2c5df },
{ 0x04aa6397, 0x6129bfe1, -0x5b580335, -0x7069fff8, 0x7d909458, 0x3f8bc089, -0x234d6e57, 0x709fa43e },
{ 0x63fd2aca, -0x14f5a274, 0x2e694eff, -0x2dd43e9a, -0x07344fc6, 0x2723f36e, -0x0f37ece1, 0x70f029ec }
},
{
{ 0x5e10b0b9, 0x2a6aafaa, -0x10fbe557, 0x78f0a370, -0x55c529e1, 0x773efb77, -0x58b4261f, 0x44eca5a2 },
{ 0x2eed3e33, 0x461307b3, -0x5baa7e19, -0x51fbd0cd, 0x195f0366, -0x36bbb62d, 0x6c314858, 0x0b7d5d8a },
{ 0x7b95d543, 0x25d44832, -0x5ccbf0e3, 0x70d38300, 0x60e1c52b, -0x21e3ace4, 0x2c7de9e4, 0x27222451 }
},
{
{ 0x42a975fc, -0x40844476, -0x69525ca8, -0x73a3c689, -0x321255b8, -0x1d803891, -0x0943df5a, 0x19735fd7 },
{ 0x49c5342e, 0x1abc92af, -0x4d190530, -0x001127ef, -0x0337b1d7, -0x105d7373, -0x5bb33abd, 0x11b5df18 },
{ 0x42c84266, -0x1c546f30, 0x7f19547e, -0x147b71f1, 0x65a497b9, 0x2503a1d0, -0x6e2076a1, 0x0fef9111 }
},
},
{
{
{ 0x5b1c16b7, 0x6ab5dcb8, 0x3c7b27a5, -0x6b3f0318, 0x735517be, -0x5b4ee3e6, -0x45f15056, 0x499238d0 },
{ -0x54e39147, -0x4eaf835f, 0x16b687b3, -0x42bb70c2, 0x2c7a91ab, 0x3455fb7f, 0x2f2adec1, 0x7579229e },
{ 0x7aba8b57, -0x130b91ae, -0x742e9b85, 0x15a08c47, 0x5f706fef, 0x7af1c6a6, -0x0fc5cf2b, 0x6345fa78 }
},
{
{ -0x42270f5c, -0x6c2c3417, -0x02e88cfe, -0x24ead3e5, 0x7f17a875, 0x7dbddc6d, -0x70bd9102, 0x3e1a71cc },
{ 0x1015e7a1, -0x20fd06a1, -0x564bfd9d, 0x790ec41d, 0x33ea1107, 0x4d3a0ea1, -0x1cc50737, 0x54f70be7 },
{ -0x6f45429e, -0x37c35c1d, 0x0291c833, -0x7f121c99, -0x2c86ff3c, -0x377fc734, 0x1ec31fa1, 0x2c5fc023 }
},
{
{ 0x02456e65, -0x3bdd1b2f, -0x352b846f, -0x78beb53f, -0x5d490023, 0x1592e2bb, -0x0a3deff1, 0x75d9d2bf },
{ 0x17038b4f, -0x01456ee9, -0x3621107f, -0x1aedc8df, 0x5d0d8834, 0x1c97e4e7, 0x23dc3bc6, 0x68afae7a },
{ 0x3626e81c, 0x5bd9b476, -0x435fd123, -0x766996ca, 0x61f077b3, 0x0a41193d, 0x00ce5471, 0x3097a242 }
},
{
{ 0x6695c486, -0x5e9d18dc, 0x35a89607, 0x131d6334, -0x5f2ed5c9, 0x30521561, -0x59504c9d, 0x56704bad },
{ -0x380747b4, 0x57427734, 0x01b270e9, -0x0ebe5ec2, -0x4b1a9b5a, 0x02d1adfe, -0x317c42b8, 0x4bb23d92 },
{ 0x52f912b9, -0x5093b559, -0x27988f38, 0x5e665f6c, -0x5c3732a8, 0x4c35ac83, 0x10a58a7e, 0x2b7a29c0 }
},
{
{ -0x40fff792, 0x33810a23, -0x18c90084, -0x50316da2, -0x1db6dd2c, 0x3d60e670, 0x4f96061b, 0x11ce9e71 },
{ -0x2f3e313d, -0x3bff8089, -0x453b6d08, -0x72efdf4a, 0x7e69daaf, 0x32ec29d5, -0x626a0320, 0x59940875 },
{ -0x27ea453f, 0x219ef713, 0x485be25c, -0x0ebeb9a3, 0x4e513c51, 0x6d5447cc, 0x5ef44393, 0x174926be }
},
{
{ -0x6c15fdd2, 0x3ef5d415, 0x0ed0eed6, 0x5cbcc1a2, 0x07382c8c, -0x702db131, 0x06d8e1ad, 0x6fa42ead },
{ -0x03a42a45, -0x4a214d07, -0x1e27ef1f, -0x6d2558d6, -0x48d5e3a7, -0x503b3024, 0x3fc22a24, 0x497d7881 },
{ 0x1f73371f, -0x1d897db6, 0x4f5b6736, 0x7f7cf01c, 0x04fa46e7, 0x7e201fe3, 0x57808c96, 0x785a36a3 }
},
{
{ 0x5d517bc3, 0x07044298, -0x519ac988, 0x6acd56c7, -0x67a5889d, 0x00a27983, -0x1aed99d5, 0x5167effa },
{ 0x63014d2b, -0x7da04203, 0x6ca7578b, -0x37adc964, 0x5c0b5df0, 0x5b2fcd28, 0x58048c8f, 0x12ab214c },
{ 0x0f53c4b6, -0x42b1561f, -0x7536e5ec, 0x1673dc5f, 0x2acc1aba, -0x5707e5b2, 0x24332a25, 0x33a92a79 }
},
{
{ 0x218f2ada, 0x7ba95ba0, 0x330fb9ca, -0x300bdd79, 0x56c6d907, -0x2525b693, -0x0b4111ac, 0x5380c296 },
{ 0x27996c02, -0x622e0b67, -0x1fb2e8ae, 0x0cb3b058, 0x7fd02c3e, 0x1f7e8896, -0x3474c14f, 0x2f964268 },
{ 0x66898d0a, -0x62b0d8fc, 0x0aff3f7a, 0x3d098799, 0x67daba45, -0x2f610c9e, 0x7b1c669c, 0x7761455e }
},
},
};
#elif defined(CURVED25519_128BIT)
static const ge_precomp base[32][8] = {
{
{
{ 0x493c6f58c3b85, 0x0df7181c325f7, 0x0f50b0b3e4cb7, 0x5329385a44c32, 0x07cf9d3a33d4b },
{ 0x03905d740913e, 0x0ba2817d673a2, 0x23e2827f4e67c, 0x133d2e0c21a34, 0x44fd2f9298f81 },
{ 0x11205877aaa68, 0x479955893d579, 0x50d66309b67a0, 0x2d42d0dbee5ee, 0x6f117b689f0c6 },
},
{
{ 0x4e7fc933c71d7, 0x2cf41feb6b244, 0x7581c0a7d1a76, 0x7172d534d32f0, 0x590c063fa87d2 },
{ 0x1a56042b4d5a8, 0x189cc159ed153, 0x5b8deaa3cae04, 0x2aaf04f11b5d8, 0x6bb595a669c92 },
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{
{ 0x731167e5124ca, 0x17b38e8bbe13f, 0x3d55b942f9056, 0x09c1495be913f, 0x3aa4e241afb6d },
{ 0x739d23f9179a2, 0x632fadbb9e8c4, 0x7c8522bfe0c48, 0x6ed0983ef5aa9, 0x0d2237687b5f4 },
{ 0x138bf2a3305f5, 0x1f45d24d86598, 0x5274bad2160fe, 0x1b6041d58d12a, 0x32fcaa6e4687a },
},
{
{ 0x7a4732787ccdf, 0x11e427c7f0640, 0x03659385f8c64, 0x5f4ead9766bfb, 0x746f6336c2600 },
{ 0x56e8dc57d9af5, 0x5b3be17be4f78, 0x3bf928cf82f4b, 0x52e55600a6f11, 0x4627e9cefebd6 },
{ 0x2f345ab6c971c, 0x653286e63e7e9, 0x51061b78a23ad, 0x14999acb54501, 0x7b4917007ed66 },
},
{
{ 0x41b28dd53a2dd, 0x37be85f87ea86, 0x74be3d2a85e41, 0x1be87fac96ca6, 0x1d03620fe08cd },
{ 0x5fb5cab84b064, 0x2513e778285b0, 0x457383125e043, 0x6bda3b56e223d, 0x122ba376f844f },
{ 0x232cda2b4e554, 0x0422ba30ff840, 0x751e7667b43f5, 0x6261755da5f3e, 0x02c70bf52b68e },
},
{
{ 0x532bf458d72e1, 0x40f96e796b59c, 0x22ef79d6f9da3, 0x501ab67beca77, 0x6b0697e3feb43 },
{ 0x7ec4b5d0b2fbb, 0x200e910595450, 0x742057105715e, 0x2f07022530f60, 0x26334f0a409ef },
{ 0x0f04adf62a3c0, 0x5e0edb48bb6d9, 0x7c34aa4fbc003, 0x7d74e4e5cac24, 0x1cc37f43441b2 },
},
{
{ 0x656f1c9ceaeb9, 0x7031cacad5aec, 0x1308cd0716c57, 0x41c1373941942, 0x3a346f772f196 },
{ 0x7565a5cc7324f, 0x01ca0d5244a11, 0x116b067418713, 0x0a57d8c55edae, 0x6c6809c103803 },
{ 0x55112e2da6ac8, 0x6363d0a3dba5a, 0x319c98ba6f40c, 0x2e84b03a36ec7, 0x05911b9f6ef7c },
},
},
{
{
{ 0x1acf3512eeaef, 0x2639839692a69, 0x669a234830507, 0x68b920c0603d4, 0x555ef9d1c64b2 },
{ 0x39983f5df0ebb, 0x1ea2589959826, 0x6ce638703cdd6, 0x6311678898505, 0x6b3cecf9aa270 },
{ 0x770ba3b73bd08, 0x11475f7e186d4, 0x0251bc9892bbc, 0x24eab9bffcc5a, 0x675f4de133817 },
},
{
{ 0x7f6d93bdab31d, 0x1f3aca5bfd425, 0x2fa521c1c9760, 0x62180ce27f9cd, 0x60f450b882cd3 },
{ 0x452036b1782fc, 0x02d95b07681c5, 0x5901cf99205b2, 0x290686e5eecb4, 0x13d99df70164c },
{ 0x35ec321e5c0ca, 0x13ae337f44029, 0x4008e813f2da7, 0x640272f8e0c3a, 0x1c06de9e55eda },
},
{
{ 0x52b40ff6d69aa, 0x31b8809377ffa, 0x536625cd14c2c, 0x516af252e17d1, 0x78096f8e7d32b },
{ 0x77ad6a33ec4e2, 0x717c5dc11d321, 0x4a114559823e4, 0x306ce50a1e2b1, 0x4cf38a1fec2db },
{ 0x2aa650dfa5ce7, 0x54916a8f19415, 0x00dc96fe71278, 0x55f2784e63eb8, 0x373cad3a26091 },
},
{
{ 0x6a8fb89ddbbad, 0x78c35d5d97e37, 0x66e3674ef2cb2, 0x34347ac53dd8f, 0x21547eda5112a },
{ 0x4634d82c9f57c, 0x4249268a6d652, 0x6336d687f2ff7, 0x4fe4f4e26d9a0, 0x0040f3d945441 },
{ 0x5e939fd5986d3, 0x12a2147019bdf, 0x4c466e7d09cb2, 0x6fa5b95d203dd, 0x63550a334a254 },
},
{
{ 0x2584572547b49, 0x75c58811c1377, 0x4d3c637cc171b, 0x33d30747d34e3, 0x39a92bafaa7d7 },
{ 0x7d6edb569cf37, 0x60194a5dc2ca0, 0x5af59745e10a6, 0x7a8f53e004875, 0x3eea62c7daf78 },
{ 0x4c713e693274e, 0x6ed1b7a6eb3a4, 0x62ace697d8e15, 0x266b8292ab075, 0x68436a0665c9c },
},
{
{ 0x6d317e820107c, 0x090815d2ca3ca, 0x03ff1eb1499a1, 0x23960f050e319, 0x5373669c91611 },
{ 0x235e8202f3f27, 0x44c9f2eb61780, 0x630905b1d7003, 0x4fcc8d274ead1, 0x17b6e7f68ab78 },
{ 0x014ab9a0e5257, 0x09939567f8ba5, 0x4b47b2a423c82, 0x688d7e57ac42d, 0x1cb4b5a678f87 },
},
{
{ 0x4aa62a2a007e7, 0x61e0e38f62d6e, 0x02f888fcc4782, 0x7562b83f21c00, 0x2dc0fd2d82ef6 },
{ 0x4c06b394afc6c, 0x4931b4bf636cc, 0x72b60d0322378, 0x25127c6818b25, 0x330bca78de743 },
{ 0x6ff841119744e, 0x2c560e8e49305, 0x7254fefe5a57a, 0x67ae2c560a7df, 0x3c31be1b369f1 },
},
{
{ 0x0bc93f9cb4272, 0x3f8f9db73182d, 0x2b235eabae1c4, 0x2ddbf8729551a, 0x41cec1097e7d5 },
{ 0x4864d08948aee, 0x5d237438df61e, 0x2b285601f7067, 0x25dbcbae6d753, 0x330b61134262d },
{ 0x619d7a26d808a, 0x3c3b3c2adbef2, 0x6877c9eec7f52, 0x3beb9ebe1b66d, 0x26b44cd91f287 },
},
},
{
{
{ 0x7f29362730383, 0x7fd7951459c36, 0x7504c512d49e7, 0x087ed7e3bc55f, 0x7deb10149c726 },
{ 0x048478f387475, 0x69397d9678a3e, 0x67c8156c976f3, 0x2eb4d5589226c, 0x2c709e6c1c10a },
{ 0x2af6a8766ee7a, 0x08aaa79a1d96c, 0x42f92d59b2fb0, 0x1752c40009c07, 0x08e68e9ff62ce },
},
{
{ 0x509d50ab8f2f9, 0x1b8ab247be5e5, 0x5d9b2e6b2e486, 0x4faa5479a1339, 0x4cb13bd738f71 },
{ 0x5500a4bc130ad, 0x127a17a938695, 0x02a26fa34e36d, 0x584d12e1ecc28, 0x2f1f3f87eeba3 },
{ 0x48c75e515b64a, 0x75b6952071ef0, 0x5d46d42965406, 0x7746106989f9f, 0x19a1e353c0ae2 },
},
{
{ 0x172cdd596bdbd, 0x0731ddf881684, 0x10426d64f8115, 0x71a4fd8a9a3da, 0x736bd3990266a },
{ 0x47560bafa05c3, 0x418dcabcc2fa3, 0x35991cecf8682, 0x24371a94b8c60, 0x41546b11c20c3 },
{ 0x32d509334b3b4, 0x16c102cae70aa, 0x1720dd51bf445, 0x5ae662faf9821, 0x412295a2b87fa },
},
{
{ 0x55261e293eac6, 0x06426759b65cc, 0x40265ae116a48, 0x6c02304bae5bc, 0x0760bb8d195ad },
{ 0x19b88f57ed6e9, 0x4cdbf1904a339, 0x42b49cd4e4f2c, 0x71a2e771909d9, 0x14e153ebb52d2 },
{ 0x61a17cde6818a, 0x53dad34108827, 0x32b32c55c55b6, 0x2f9165f9347a3, 0x6b34be9bc33ac },
},
{
{ 0x469656571f2d3, 0x0aa61ce6f423f, 0x3f940d71b27a1, 0x185f19d73d16a, 0x01b9c7b62e6dd },
{ 0x72f643a78c0b2, 0x3de45c04f9e7b, 0x706d68d30fa5c, 0x696f63e8e2f24, 0x2012c18f0922d },
{ 0x355e55ac89d29, 0x3e8b414ec7101, 0x39db07c520c90, 0x6f41e9b77efe1, 0x08af5b784e4ba },
},
{
{ 0x314d289cc2c4b, 0x23450e2f1bc4e, 0x0cd93392f92f4, 0x1370c6a946b7d, 0x6423c1d5afd98 },
{ 0x499dc881f2533, 0x34ef26476c506, 0x4d107d2741497, 0x346c4bd6efdb3, 0x32b79d71163a1 },
{ 0x5f8d9edfcb36a, 0x1e6e8dcbf3990, 0x7974f348af30a, 0x6e6724ef19c7c, 0x480a5efbc13e2 },
},
{
{ 0x14ce442ce221f, 0x18980a72516cc, 0x072f80db86677, 0x703331fda526e, 0x24b31d47691c8 },
{ 0x1e70b01622071, 0x1f163b5f8a16a, 0x56aaf341ad417, 0x7989635d830f7, 0x47aa27600cb7b },
{ 0x41eedc015f8c3, 0x7cf8d27ef854a, 0x289e3584693f9, 0x04a7857b309a7, 0x545b585d14dda },
},
{
{ 0x4e4d0e3b321e1, 0x7451fe3d2ac40, 0x666f678eea98d, 0x038858667fead, 0x4d22dc3e64c8d },
{ 0x7275ea0d43a0f, 0x681137dd7ccf7, 0x1e79cbab79a38, 0x22a214489a66a, 0x0f62f9c332ba5 },
{ 0x46589d63b5f39, 0x7eaf979ec3f96, 0x4ebe81572b9a8, 0x21b7f5d61694a, 0x1c0fa01a36371 },
},
},
{
{
{ 0x02b0e8c936a50, 0x6b83b58b6cd21, 0x37ed8d3e72680, 0x0a037db9f2a62, 0x4005419b1d2bc },
{ 0x604b622943dff, 0x1c899f6741a58, 0x60219e2f232fb, 0x35fae92a7f9cb, 0x0fa3614f3b1ca },
{ 0x3febdb9be82f0, 0x5e74895921400, 0x553ea38822706, 0x5a17c24cfc88c, 0x1fba218aef40a },
},
{
{ 0x657043e7b0194, 0x5c11b55efe9e7, 0x7737bc6a074fb, 0x0eae41ce355cc, 0x6c535d13ff776 },
{ 0x49448fac8f53e, 0x34f74c6e8356a, 0x0ad780607dba2, 0x7213a7eb63eb6, 0x392e3acaa8c86 },
{ 0x534e93e8a35af, 0x08b10fd02c997, 0x26ac2acb81e05, 0x09d8c98ce3b79, 0x25e17fe4d50ac },
},
{
{ 0x77ff576f121a7, 0x4e5f9b0fc722b, 0x46f949b0d28c8, 0x4cde65d17ef26, 0x6bba828f89698 },
{ 0x09bd71e04f676, 0x25ac841f2a145, 0x1a47eac823871, 0x1a8a8c36c581a, 0x255751442a9fb },
{ 0x1bc6690fe3901, 0x314132f5abc5a, 0x611835132d528, 0x5f24b8eb48a57, 0x559d504f7f6b7 },
},
{
{ 0x091e7f6d266fd, 0x36060ef037389, 0x18788ec1d1286, 0x287441c478eb0, 0x123ea6a3354bd },
{ 0x38378b3eb54d5, 0x4d4aaa78f94ee, 0x4a002e875a74d, 0x10b851367b17c, 0x01ab12d5807e3 },
{ 0x5189041e32d96, 0x05b062b090231, 0x0c91766e7b78f, 0x0aa0f55a138ec, 0x4a3961e2c918a },
},
{
{ 0x7d644f3233f1e, 0x1c69f9e02c064, 0x36ae5e5266898, 0x08fc1dad38b79, 0x68aceead9bd41 },
{ 0x43be0f8e6bba0, 0x68fdffc614e3b, 0x4e91dab5b3be0, 0x3b1d4c9212ff0, 0x2cd6bce3fb1db },
{ 0x4c90ef3d7c210, 0x496f5a0818716, 0x79cf88cc239b8, 0x2cb9c306cf8db, 0x595760d5b508f },
},
{
{ 0x2cbebfd022790, 0x0b8822aec1105, 0x4d1cfd226bccc, 0x515b2fa4971be, 0x2cb2c5df54515 },
{ 0x1bfe104aa6397, 0x11494ff996c25, 0x64251623e5800, 0x0d49fc5e044be, 0x709fa43edcb29 },
{ 0x25d8c63fd2aca, 0x4c5cd29dffd61, 0x32ec0eb48af05, 0x18f9391f9b77c, 0x70f029ecf0c81 },
},
{
{ 0x2afaa5e10b0b9, 0x61de08355254d, 0x0eb587de3c28d, 0x4f0bb9f7dbbd5, 0x44eca5a2a74bd },
{ 0x307b32eed3e33, 0x6748ab03ce8c2, 0x57c0d9ab810bc, 0x42c64a224e98c, 0x0b7d5d8a6c314 },
{ 0x448327b95d543, 0x0146681e3a4ba, 0x38714adc34e0c, 0x4f26f0e298e30, 0x272224512c7de },
},
{
{ 0x3bb8a42a975fc, 0x6f2d5b46b17ef, 0x7b6a9223170e5, 0x053713fe3b7e6, 0x19735fd7f6bc2 },
{ 0x492af49c5342e, 0x2365cdf5a0357, 0x32138a7ffbb60, 0x2a1f7d14646fe, 0x11b5df18a44cc },
{ 0x390d042c84266, 0x1efe32a8fdc75, 0x6925ee7ae1238, 0x4af9281d0e832, 0x0fef911191df8 },
},
},
};
#else
/* base[i][j] = (j+1)*256^i*B */
static const ge_precomp base[32][8] = {
{
{
{ 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
{ -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
{ -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
},
{
{ -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 },
{ -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 },
{ 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 },
},
{
{ 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
{ 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
{ 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
},
{
{ -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 },
{ 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 },
{ 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 },
},
{
{ 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
{ 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
{ 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
},
{
{ -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 },
{ -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 },
{ -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 },
},
{
{ 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
{ -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
{ 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
},
{
{ 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 },
{ -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 },
{ 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 },
},
},
{
{
{ -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 },
{ 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 },
{ 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 },
},
{
{ -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 },
{ 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 },
{ 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 },
},
{
{ -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 },
{ 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 },
{ 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 },
},
{
{ -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 },
{ -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 },
{ -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 },
},
{
{ 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 },
{ 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 },
{ 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 },
},
{
{ -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 },
{ -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 },
{ -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 },
},
{
{ 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 },
{ -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 },
{ -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 },
},
{
{ 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 },
{ 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 },
{ 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 },
},
},
{
{
{ 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 },
{ 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 },
{ -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 },
},
{
{ 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 },
{ -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 },
{ -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 },
},
{
{ -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 },
{ 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 },
{ 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 },
},
{
{ -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 },
{ 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 },
{ 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 },
},
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},
{
{ -5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647 },
{ 13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511 },
{ -29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032 },
},
},
{
{
{ 9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834 },
{ -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 },
{ 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 },
},
{
{ -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 },
{ -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 },
{ -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 },
},
{
{ -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 },
{ -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 },
{ 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 },
},
{
{ -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 },
{ -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 },
{ 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 },
},
{
{ -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 },
{ 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 },
{ -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 },
},
{
{ 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 },
{ 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 },
{ -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 },
},
{
{ -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 },
{ -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 },
{ -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 },
},
{
{ -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 },
{ 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 },
{ -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 },
},
},
} ;
#endif
static void ge_select(ge_precomp *t,int pos,signed char b)
{
#ifndef CURVED25519_ASM
ge_precomp minust;
unsigned char bnegative = negative(b);
unsigned char babs = b - (((-bnegative) & b) << 1);
ge_precomp_0(t);
cmov(t,&base[pos][0],babs,1);
cmov(t,&base[pos][1],babs,2);
cmov(t,&base[pos][2],babs,3);
cmov(t,&base[pos][3],babs,4);
cmov(t,&base[pos][4],babs,5);
cmov(t,&base[pos][5],babs,6);
cmov(t,&base[pos][6],babs,7);
cmov(t,&base[pos][7],babs,8);
fe_cswap(t->yminusx, t->yplusx, bnegative);
fe_neg(minust.xy2d,t->xy2d);
fe_cmov(t->xy2d,minust.xy2d,bnegative);
#else
fe_cmov_table((fe*)t, (fe*)base[pos], b);
#endif
}
/*
h = a * B
where a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.
Preconditions:
a[31] <= 127
*/
void ge_scalarmult_base(ge_p3 *h,const unsigned char *a)
{
signed char e[64];
signed char carry;
ge_p1p1 r;
#ifndef CURVED25519_ASM
ge_p2 s;
#endif
ge_precomp t;
int i;
for (i = 0;i < 32;++i) {
e[2 * i + 0] = (a[i] >> 0) & 15;
e[2 * i + 1] = (a[i] >> 4) & 15;
}
/* each e[i] is between 0 and 15 */
/* e[63] is between 0 and 7 */
carry = 0;
for (i = 0;i < 63;++i) {
e[i] += carry;
carry = e[i] + 8;
carry >>= 4;
e[i] -= carry << 4;
}
e[63] += carry;
/* each e[i] is between -8 and 8 */
#ifndef CURVED25519_ASM
ge_select(&t,0,e[1]);
fe_sub(h->X, t.yplusx, t.yminusx);
fe_add(h->Y, t.yplusx, t.yminusx);
fe_0(h->Z);
h->Z[0] = 4;
fe_mul(h->T,h->X,h->Y);
fe_add(h->X, h->X, h->X);
fe_add(h->Y, h->Y, h->Y);
for (i = 3;i < 64;i += 2) {
ge_select(&t,i / 2,e[i]);
ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
}
ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r);
ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r);
for (i = 0;i < 64;i += 2) {
ge_select(&t,i / 2,e[i]);
ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
}
#else
ge_select(&t, 0, e[0]);
fe_sub(h->X, t.yplusx, t.yminusx);
fe_add(h->Y, t.yplusx, t.yminusx);
fe_0(h->Z);
h->Z[0] = 2;
fe_copy(h->T, t.xy2d);
for (i = 1; i < 64; i++) {
ge_select(&t, i, e[i]);
ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
}
#endif
}
/* ge double scalar mult */
static void slide(signed char *r,const unsigned char *a)
{
int i;
int b;
int k;
for (i = 0;i < 256;++i)
r[i] = 1 & (a[i >> 3] >> (i & 7));
for (i = 0;i < 256;++i)
if (r[i]) {
for (b = 1;b <= 6 && i + b < 256;++b) {
if (r[i + b]) {
if (r[i] + (r[i + b] << b) <= 15) {
r[i] += r[i + b] << b; r[i + b] = 0;
} else if (r[i] - (r[i + b] << b) >= -15) {
r[i] -= r[i + b] << b;
for (k = i + b;k < 256;++k) {
if (!r[k]) {
r[k] = 1;
break;
}
r[k] = 0;
}
} else
break;
}
}
}
}
#ifdef CURVED25519_ASM_64BIT
static const ge_precomp Bi[8] = {
{
{ 0x2fbc93c6f58c3b85, -0x306cd2390473f1e7, 0x270b4898643d42c2, 0x07cf9d3a33d4ba65, },
{ -0x62efc6fa28bf6ec2, -0x02c660fa2ebf414d, -0x5a3e7bcb977075f7, 0x44fd2f9298f81267, },
{ -0x5436edfa78855598, 0x26d9e823ccaac49e, 0x5a1b7dcbdd43598c, 0x6f117b689f0c65a8, },
},
{
{ -0x50da4f57b31168d0, 0x025a8430e8864b8a, -0x3ee4affd60fe98ce, 0x7a164e1b9a80f8f4, },
{ 0x56611fe8a4fcd265, 0x3bd353fde5c1ba7d, -0x7ece0ce5deb42943, 0x2ab91587555bda62, },
{ 0x14ae933f0dd0d889, 0x589423221c35da62, -0x2e8f1aba730d24b4, 0x5a2826af12b9b4c6, },
},
{
{ -0x5ded43bbf75a44cd, -0x72afb73c38a112fe, -0x22e414f3a54013bc, 0x2945ccf146e206eb, },
{ 0x7f9182c3a447d6ba, -0x2affeb2eb4d8d649, -0x1cc30ee3479b5f79, 0x154a7e73eb1b55f3, },
{ -0x4344240e7ed57d7b, 0x270e0807d0bdd1fc, -0x4be498f4e44258d3, 0x43aabe696b3bb69a, },
},
{
{ 0x6b1a5cd0944ea3bf, 0x7470353ab39dc0d2, 0x71b2528228542e49, 0x461bea69283c927e, },
{ -0x4590d36555cdde4f, 0x6ca021533bba23a7, -0x621589b06de6d3c6, 0x1d6edd5d2e5317e0, },
{ -0x0e7c9237fe474c5e, -0x4cfca0b8fac15b66, 0x529c41ba5877adf3, 0x7a9fbb1c6a0f90a7, },
},
{
{ -0x64d1987559579cd1, -0x59af6190ae43b93b, -0x314dcc3639790a4b, 0x34b9ed338add7f59, },
{ -0x0c91de81fc627f9c, -0x675f7e490adfbe65, -0x693439f718a14fbc, 0x49c05a51fadc9c8f, },
{ 0x06b4e8bf9045af1b, -0x1d007c1758e62dd1, -0x550903d66c2b30ea, 0x73c172021b008b06, },
},
{
{ 0x2fbf00848a802ade, -0x1a260130fdcfd1d9, 0x113e847117703406, 0x4275aae2546d8faf, },
{ 0x315f5b0249864348, 0x3ed6b36977088381, -0x5c5f8aaa9572146b, 0x18ab598029d5c77f, },
{ -0x27d4d33a029f7617, 0x031eb4a13282e4a4, 0x44311199b51a8622, 0x3dc65522b53df948, },
},
{
{ -0x408f3ddd5dff8093, -0x407b4c654a432125, 0x537a0e12fb07ba07, 0x234fd7eec346f241, },
{ 0x506f013b327fbf93, -0x5103143664889095, -0x62ed4dcd5552a698, 0x0267882d176024a7, },
{ 0x5360a119732ea378, 0x2437e6b1df8dd471, -0x5d10c8076e581acd, 0x497ba6fdaa097863, },
},
{
{ 0x24cecc0313cfeaa0, -0x79b73d72e763db93, 0x2dbdbdfac1f2d4d0, 0x61e22917f12de72b, },
{ 0x040bcd86468ccf0b, -0x2c7d645bd566ef2a, 0x7508300807b25192, 0x43b5cd4218d05ebf, },
{ 0x5d9a762f9bd0b516, -0x14c750b1c8c02112, 0x032e5a7d93d64270, 0x511d61210ae4d842, },
},
};
#elif defined(CURVED25519_ASM_32BIT)
static const ge_precomp Bi[8] = {
{
{ -0x0a73c47b, 0x2fbc93c6, -0x0473f1e7, -0x306cd23a, 0x643d42c2, 0x270b4898, 0x33d4ba65, 0x07cf9d3a, },
{ -0x28bf6ec2, -0x62efc6fb, -0x2ebf414d, -0x02c660fb, 0x688f8a09, -0x5a3e7bcc, -0x6707ed99, 0x44fd2f92, },
{ -0x78855598, -0x5436edfb, -0x33553b62, 0x26d9e823, -0x22bca674, 0x5a1b7dcb, -0x60f39a58, 0x6f117b68, },
},
{
{ 0x4cee9730, -0x50da4f58, -0x1779b476, 0x025a8430, -0x60fe98ce, -0x3ee4affe, -0x657f070c, 0x7a164e1b, },
{ -0x5b032d9b, 0x56611fe8, -0x1a3e4583, 0x3bd353fd, 0x214bd6bd, -0x7ece0ce6, 0x555bda62, 0x2ab91587, },
{ 0x0dd0d889, 0x14ae933f, 0x1c35da62, 0x58942322, -0x730d24b4, -0x2e8f1abb, 0x12b9b4c6, 0x5a2826af, },
},
{
{ 0x08a5bb33, -0x5ded43bc, -0x38a112fe, -0x72afb73d, 0x5abfec44, -0x22e414f4, 0x46e206eb, 0x2945ccf1, },
{ -0x5bb82946, 0x7f9182c3, 0x4b2729b7, -0x2affeb2f, -0x479b5f79, -0x1cc30ee4, -0x14e4aa0d, 0x154a7e73, },
{ -0x7ed57d7b, -0x4344240f, -0x2f422e04, 0x270e0807, 0x1bbda72d, -0x4be498f5, 0x6b3bb69a, 0x43aabe69, },
},
{
{ -0x6bb15c41, 0x6b1a5cd0, -0x4c623f2e, 0x7470353a, 0x28542e49, 0x71b25282, 0x283c927e, 0x461bea69, },
{ -0x55cdde4f, -0x4590d366, 0x3bba23a7, 0x6ca02153, -0x6de6d3c6, -0x621589b1, 0x2e5317e0, 0x1d6edd5d, },
{ 0x01b8b3a2, -0x0e7c9238, 0x053ea49a, -0x4cfca0b9, 0x5877adf3, 0x529c41ba, 0x6a0f90a7, 0x7a9fbb1c, },
},
{
{ -0x59579cd1, -0x64d19876, 0x51bc46c5, -0x59af6191, -0x39790a4b, -0x314dcc37, -0x752280a7, 0x34b9ed33, },
{ 0x039d8064, -0x0c91de82, -0x0adfbe65, -0x675f7e4a, -0x18a14fbc, -0x693439f8, -0x05236371, 0x49c05a51, },
{ -0x6fba50e5, 0x06b4e8bf, -0x58e62dd1, -0x1d007c18, -0x6c2b30ea, -0x550903d7, 0x1b008b06, 0x73c17202, },
},
{
{ -0x757fd522, 0x2fbf0084, 0x02302e27, -0x1a260131, 0x17703406, 0x113e8471, 0x546d8faf, 0x4275aae2, },
{ 0x49864348, 0x315f5b02, 0x77088381, 0x3ed6b369, 0x6a8deb95, -0x5c5f8aab, 0x29d5c77f, 0x18ab5980, },
{ -0x029f7617, -0x27d4d33b, 0x3282e4a4, 0x031eb4a1, -0x4ae579de, 0x44311199, -0x4ac206b8, 0x3dc65522, },
},
{
{ -0x5dff8093, -0x408f3dde, -0x4a432125, -0x407b4c66, -0x04f845f9, 0x537a0e12, -0x3cb90dbf, 0x234fd7ee, },
{ 0x327fbf93, 0x506f013b, -0x64889095, -0x51031437, -0x5552a698, -0x62ed4dce, 0x176024a7, 0x0267882d, },
{ 0x732ea378, 0x5360a119, -0x20722b8f, 0x2437e6b1, -0x6e581acd, -0x5d10c808, -0x55f6879d, 0x497ba6fd, },
},
{
{ 0x13cfeaa0, 0x24cecc03, 0x189c246d, -0x79b73d73, -0x3e0d2b30, 0x2dbdbdfa, -0x0ed218d5, 0x61e22917, },
{ 0x468ccf0b, 0x040bcd86, 0x2a9910d6, -0x2c7d645c, 0x07b25192, 0x75083008, 0x18d05ebf, 0x43b5cd42, },
{ -0x642f4aea, 0x5d9a762f, 0x373fdeee, -0x14c750b2, -0x6c29bd90, 0x032e5a7d, 0x0ae4d842, 0x511d6121, },
},
};
#elif defined(CURVED25519_128BIT)
static const ge_precomp Bi[8] = {
{
{ 0x493c6f58c3b85, 0x0df7181c325f7, 0x0f50b0b3e4cb7, 0x5329385a44c32, 0x07cf9d3a33d4b },
{ 0x03905d740913e, 0x0ba2817d673a2, 0x23e2827f4e67c, 0x133d2e0c21a34, 0x44fd2f9298f81 },
{ 0x11205877aaa68, 0x479955893d579, 0x50d66309b67a0, 0x2d42d0dbee5ee, 0x6f117b689f0c6 },
},
{
{ 0x5b0a84cee9730, 0x61d10c97155e4, 0x4059cc8096a10, 0x47a608da8014f, 0x7a164e1b9a80f },
{ 0x11fe8a4fcd265, 0x7bcb8374faacc, 0x52f5af4ef4d4f, 0x5314098f98d10, 0x2ab91587555bd },
{ 0x6933f0dd0d889, 0x44386bb4c4295, 0x3cb6d3162508c, 0x26368b872a2c6, 0x5a2826af12b9b },
},
{
{ 0x2bc4408a5bb33, 0x078ebdda05442, 0x2ffb112354123, 0x375ee8df5862d, 0x2945ccf146e20 },
{ 0x182c3a447d6ba, 0x22964e536eff2, 0x192821f540053, 0x2f9f19e788e5c, 0x154a7e73eb1b5 },
{ 0x3dbf1812a8285, 0x0fa17ba3f9797, 0x6f69cb49c3820, 0x34d5a0db3858d, 0x43aabe696b3bb },
},
{
{ 0x25cd0944ea3bf, 0x75673b81a4d63, 0x150b925d1c0d4, 0x13f38d9294114, 0x461bea69283c9 },
{ 0x72c9aaa3221b1, 0x267774474f74d, 0x064b0e9b28085, 0x3f04ef53b27c9, 0x1d6edd5d2e531 },
{ 0x36dc801b8b3a2, 0x0e0a7d4935e30, 0x1deb7cecc0d7d, 0x053a94e20dd2c, 0x7a9fbb1c6a0f9 },
},
{
{ 0x6678aa6a8632f, 0x5ea3788d8b365, 0x21bd6d6994279, 0x7ace75919e4e3, 0x34b9ed338add7 },
{ 0x6217e039d8064, 0x6dea408337e6d, 0x57ac112628206, 0x647cb65e30473, 0x49c05a51fadc9 },
{ 0x4e8bf9045af1b, 0x514e33a45e0d6, 0x7533c5b8bfe0f, 0x583557b7e14c9, 0x73c172021b008 },
},
{
{ 0x700848a802ade, 0x1e04605c4e5f7, 0x5c0d01b9767fb, 0x7d7889f42388b, 0x4275aae2546d8 },
{ 0x75b0249864348, 0x52ee11070262b, 0x237ae54fb5acd, 0x3bfd1d03aaab5, 0x18ab598029d5c },
{ 0x32cc5fd6089e9, 0x426505c949b05, 0x46a18880c7ad2, 0x4a4221888ccda, 0x3dc65522b53df },
},
{
{ 0x0c222a2007f6d, 0x356b79bdb77ee, 0x41ee81efe12ce, 0x120a9bd07097d, 0x234fd7eec346f },
{ 0x7013b327fbf93, 0x1336eeded6a0d, 0x2b565a2bbf3af, 0x253ce89591955, 0x0267882d17602 },
{ 0x0a119732ea378, 0x63bf1ba8e2a6c, 0x69f94cc90df9a, 0x431d1779bfc48, 0x497ba6fdaa097 },
},
{
{ 0x6cc0313cfeaa0, 0x1a313848da499, 0x7cb534219230a, 0x39596dedefd60, 0x61e22917f12de },
{ 0x3cd86468ccf0b, 0x48553221ac081, 0x6c9464b4e0a6e, 0x75fba84180403, 0x43b5cd4218d05 },
{ 0x2762f9bd0b516, 0x1c6e7fbddcbb3, 0x75909c3ace2bd, 0x42101972d3ec9, 0x511d61210ae4d },
},
};
#else
static const ge_precomp Bi[8] = {
{
{ 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
{ -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
{ -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
},
{
{ 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
{ 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
{ 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
},
{
{ 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
{ 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
{ 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
},
{
{ 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
{ -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
{ 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
},
{
{ -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 },
{ -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 },
{ 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 },
},
{
{ -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 },
{ 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 },
{ 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 },
},
{
{ -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 },
{ -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 },
{ -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 },
},
{
{ -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 },
{ -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 },
{ -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 },
},
} ;
#endif
/*
r = a * A + b * B
where a = a[0]+256*a[1]+...+256^31 a[31].
and b = b[0]+256*b[1]+...+256^31 b[31].
B is the Ed25519 base point (x,4/5) with x positive.
*/
int ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a,
const ge_p3 *A, const unsigned char *b)
{
signed char aslide[256];
signed char bslide[256];
ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
ge_p1p1 t;
ge_p3 u;
ge_p3 A2;
int i;
slide(aslide,a);
slide(bslide,b);
ge_p3_to_cached(&Ai[0],A);
ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);
ge_p2_0(r);
for (i = 255;i >= 0;--i) {
if (aslide[i] || bslide[i]) break;
}
for (;i >= 0;--i) {
ge_p2_dbl(&t,r);
if (aslide[i] > 0) {
ge_p1p1_to_p3(&u,&t);
ge_add(&t,&u,&Ai[aslide[i]/2]);
} else if (aslide[i] < 0) {
ge_p1p1_to_p3(&u,&t);
ge_sub(&t,&u,&Ai[(-aslide[i])/2]);
}
if (bslide[i] > 0) {
ge_p1p1_to_p3(&u,&t);
ge_madd(&t,&u,&Bi[bslide[i]/2]);
} else if (bslide[i] < 0) {
ge_p1p1_to_p3(&u,&t);
ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
}
ge_p1p1_to_p2(r,&t);
}
return 0;
}
#ifdef CURVED25519_ASM_64BIT
static const ge d = {
0x75eb4dca135978a3, 0x00700a4d4141d8ab, -0x7338bf8688861768, 0x52036cee2b6ffe73,
};
#elif defined(CURVED25519_ASM_32BIT)
static const ge d = {
0x135978a3, 0x75eb4dca, 0x4141d8ab, 0x00700a4d, 0x7779e898, -0x7338bf87, 0x2b6ffe73, 0x52036cee,
};
#elif defined(CURVED25519_128BIT)
static const ge d = {
0x34dca135978a3, 0x1a8283b156ebd, 0x5e7a26001c029, 0x739c663a03cbb,
0x52036cee2b6ff
};
#else
static const ge d = {
-10913610,13857413,-15372611,6949391,114729,
-8787816,-6275908,-3247719,-18696448,-12055116
};
#endif
#ifdef CURVED25519_ASM_64BIT
static const ge sqrtm1 = {
-0x3b11e4d8b5f15f50, 0x2f431806ad2fe478, 0x2b4d00993dfbd7a7, 0x2b8324804fc1df0b,
};
#elif defined(CURVED25519_ASM_32BIT)
static const ge sqrtm1 = {
0x4a0ea0b0, -0x3b11e4d9, -0x52d01b88, 0x2f431806, 0x3dfbd7a7, 0x2b4d0099, 0x4fc1df0b, 0x2b832480,
};
#elif defined(CURVED25519_128BIT)
static const ge sqrtm1 = {
0x61b274a0ea0b0, 0x0d5a5fc8f189d, 0x7ef5e9cbd0c60, 0x78595a6804c9e,
0x2b8324804fc1d
};
#else
static const ge sqrtm1 = {
-32595792,-7943725,9377950,3500415,12389472,
-272473,-25146209,-2005654,326686,11406482
};
#endif
int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
{
ge u;
ge v;
ge v3;
ge vxx;
ge check;
fe_frombytes(h->Y,s);
fe_1(h->Z);
fe_sq(u,h->Y);
fe_mul(v,u,d);
fe_sub(u,u,h->Z); /* u = y^2-1 */
fe_add(v,v,h->Z); /* v = dy^2+1 */
fe_sq(v3,v);
fe_mul(v3,v3,v); /* v3 = v^3 */
fe_sq(h->X,v3);
fe_mul(h->X,h->X,v);
fe_mul(h->X,h->X,u); /* x = uv^7 */
fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
fe_mul(h->X,h->X,v3);
fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */
fe_sq(vxx,h->X);
fe_mul(vxx,vxx,v);
fe_sub(check,vxx,u); /* vx^2-u */
if (fe_isnonzero(check)) {
fe_add(check,vxx,u); /* vx^2+u */
if (fe_isnonzero(check)) return -1;
fe_mul(h->X,h->X,sqrtm1);
}
if (fe_isnegative(h->X) == (s[31] >> 7))
fe_neg(h->X,h->X);
fe_mul(h->T,h->X,h->Y);
return 0;
}
/* ge madd */
/*
r = p + q
*/
static WC_INLINE void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
#ifndef CURVED25519_ASM
ge t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->yplusx);
fe_mul(r->Y,r->Y,q->yminusx);
fe_mul(r->T,q->xy2d,p->T);
fe_add(t0,p->Z,p->Z);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_add(r->Z,t0,r->T);
fe_sub(r->T,t0,r->T);
#else
fe_ge_madd(r->X, r->Y, r->Z, r->T, p->X, p->Y, p->Z, p->T, q->xy2d,
q->yplusx, q->yminusx);
#endif
}
/* ge msub */
/*
r = p - q
*/
static WC_INLINE void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
#ifndef CURVED25519_ASM
ge t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->yminusx);
fe_mul(r->Y,r->Y,q->yplusx);
fe_mul(r->T,q->xy2d,p->T);
fe_add(t0,p->Z,p->Z);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_sub(r->Z,t0,r->T);
fe_add(r->T,t0,r->T);
#else
fe_ge_msub(r->X, r->Y, r->Z, r->T, p->X, p->Y, p->Z, p->T, q->xy2d,
q->yplusx, q->yminusx);
#endif
}
/* ge p1p1 to p2 */
/*
r = p
*/
static void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p)
{
#ifndef CURVED25519_ASM
fe_mul(r->X,p->X,p->T);
fe_mul(r->Y,p->Y,p->Z);
fe_mul(r->Z,p->Z,p->T);
#else
fe_ge_to_p2(r->X, r->Y, r->Z, p->X, p->Y, p->Z, p->T);
#endif
}
/* ge p1p1 to p3 */
/*
r = p
*/
static WC_INLINE void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p)
{
#ifndef CURVED25519_ASM
fe_mul(r->X,p->X,p->T);
fe_mul(r->Y,p->Y,p->Z);
fe_mul(r->Z,p->Z,p->T);
fe_mul(r->T,p->X,p->Y);
#else
fe_ge_to_p3(r->X, r->Y, r->Z, r->T, p->X, p->Y, p->Z, p->T);
#endif
}
/* ge p2 0 */
static void ge_p2_0(ge_p2 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
}
/* ge p2 dbl */
/*
r = 2 * p
*/
static WC_INLINE void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
{
#ifndef CURVED25519_ASM
ge t0;
fe_sq(r->X,p->X);
fe_sq(r->Z,p->Y);
fe_sq2(r->T,p->Z);
fe_add(r->Y,p->X,p->Y);
fe_sq(t0,r->Y);
fe_add(r->Y,r->Z,r->X);
fe_sub(r->Z,r->Z,r->X);
fe_sub(r->X,t0,r->Y);
fe_sub(r->T,r->T,r->Z);
#else
fe_ge_dbl(r->X, r->Y, r->Z, r->T, p->X, p->Y, p->Z);
#endif
}
/* ge p3 dble */
/*
r = 2 * p
*/
static void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p)
{
ge_p2 q;
ge_p3_to_p2(&q,p);
ge_p2_dbl(r,&q);
}
/* ge p3 to cached */
/*
r = p
*/
#ifdef CURVED25519_ASM_64BIT
static const ge d2 = {
-0x1429646bd94d0ea7, 0x00e0149a8283b156, 0x198e80f2eef3d130, 0x2406d9dc56dffce7,
};
#elif defined(CURVED25519_ASM_32BIT)
static const ge d2 = {
0x26b2f159, -0x1429646c, -0x7d7c4eaa, 0x00e0149a, -0x110c2ed0, 0x198e80f2, 0x56dffce7, 0x2406d9dc,
};
#elif defined(CURVED25519_128BIT)
static const ge d2 = {
0x69b9426b2f159, 0x35050762add7a, 0x3cf44c0038052, 0x6738cc7407977,
0x2406d9dc56dff
};
#else
static const ge d2 = {
-21827239,-5839606,-30745221,13898782,229458,
15978800,-12551817,-6495438,29715968,9444199
} ;
#endif
static WC_INLINE void ge_p3_to_cached(ge_cached *r,const ge_p3 *p)
{
fe_add(r->YplusX,p->Y,p->X);
fe_sub(r->YminusX,p->Y,p->X);
fe_copy(r->Z,p->Z);
fe_mul(r->T2d,p->T,d2);
}
/* ge p3 to p2 */
/*
r = p
*/
static void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p)
{
fe_copy(r->X,p->X);
fe_copy(r->Y,p->Y);
fe_copy(r->Z,p->Z);
}
/* ge p3 tobytes */
void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
{
ge recip;
ge x;
ge y;
fe_invert(recip,h->Z);
fe_mul(x,h->X,recip);
fe_mul(y,h->Y,recip);
fe_tobytes(s,y);
s[31] ^= fe_isnegative(x) << 7;
}
#ifndef CURVED25519_ASM
/* ge_precomp_0 */
static void ge_precomp_0(ge_precomp *h)
{
fe_1(h->yplusx);
fe_1(h->yminusx);
fe_0(h->xy2d);
}
#endif
/* ge_sub */
/*
r = p - q
*/
static WC_INLINE void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
#ifndef CURVED25519_ASM
ge t0;
fe_add(r->X,p->Y,p->X);
fe_sub(r->Y,p->Y,p->X);
fe_mul(r->Z,r->X,q->YminusX);
fe_mul(r->Y,r->Y,q->YplusX);
fe_mul(r->T,q->T2d,p->T);
fe_mul(r->X,p->Z,q->Z);
fe_add(t0,r->X,r->X);
fe_sub(r->X,r->Z,r->Y);
fe_add(r->Y,r->Z,r->Y);
fe_sub(r->Z,t0,r->T);
fe_add(r->T,t0,r->T);
#else
fe_ge_sub(r->X, r->Y, r->Z, r->T, p->X, p->Y, p->Z, p->T, q->Z, q->T2d,
q->YplusX, q->YminusX);
#endif
}
/* ge tobytes */
void ge_tobytes(unsigned char *s,const ge_p2 *h)
{
ge recip;
ge x;
ge y;
fe_invert(recip,h->Z);
fe_mul(x,h->X,recip);
fe_mul(y,h->Y,recip);
fe_tobytes(s,y);
s[31] ^= fe_isnegative(x) << 7;
}
#endif /* !ED25519_SMALL */
#endif /* HAVE_ED25519 */