wolf SSL
wolfSSL SSL/TLS library, support up to TLS1.3
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wolfcrypt/src/ge_operations.c
- Committer:
- wolfSSL
- Date:
- 2017-08-22
- Revision:
- 13:f67a6c6013ca
File content as of revision 13:f67a6c6013ca:
/* ge_operations.c
*
* Copyright (C) 2006-2016 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
/*
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)
*/
/*
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 s0 = 2097151 & load_3(s);
int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
int64_t s8 = 2097151 & load_3(s + 21);
int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
int64_t s16 = 2097151 & load_3(s + 42);
int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
int64_t s23 = (load_4(s + 60) >> 3);
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s23 = 0;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s22 = 0;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s21 = 0;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s20 = 0;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s19 = 0;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
s18 = 0;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s17 = 0;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s16 = 0;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s15 = 0;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s14 = 0;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s13 = 0;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
s[0] = (byte)(s0 >> 0);
s[1] = (byte)(s0 >> 8);
s[2] = (byte)((s0 >> 16) | (s1 << 5));
s[3] = (byte)(s1 >> 3);
s[4] = (byte)(s1 >> 11);
s[5] = (byte)((s1 >> 19) | (s2 << 2));
s[6] = (byte)(s2 >> 6);
s[7] = (byte)((s2 >> 14) | (s3 << 7));
s[8] = (byte)(s3 >> 1);
s[9] = (byte)(s3 >> 9);
s[10] = (byte)((s3 >> 17) | (s4 << 4));
s[11] = (byte)(s4 >> 4);
s[12] = (byte)(s4 >> 12);
s[13] = (byte)((s4 >> 20) | (s5 << 1));
s[14] = (byte)(s5 >> 7);
s[15] = (byte)((s5 >> 15) | (s6 << 6));
s[16] = (byte)(s6 >> 2);
s[17] = (byte)(s6 >> 10);
s[18] = (byte)((s6 >> 18) | (s7 << 3));
s[19] = (byte)(s7 >> 5);
s[20] = (byte)(s7 >> 13);
s[21] = (byte)(s8 >> 0);
s[22] = (byte)(s8 >> 8);
s[23] = (byte)((s8 >> 16) | (s9 << 5));
s[24] = (byte)(s9 >> 3);
s[25] = (byte)(s9 >> 11);
s[26] = (byte)((s9 >> 19) | (s10 << 2));
s[27] = (byte)(s10 >> 6);
s[28] = (byte)((s10 >> 14) | (s11 << 7));
s[29] = (byte)(s11 >> 1);
s[30] = (byte)(s11 >> 9);
s[31] = (byte)(s11 >> 17);
/* hush warnings after setting values to 0 */
(void)s12;
(void)s13;
(void)s14;
(void)s15;
(void)s16;
(void)s17;
(void)s18;
(void)s19;
(void)s20;
(void)s21;
(void)s22;
(void)s23;
}
/*
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)
{
int64_t a0 = 2097151 & load_3(a);
int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
int64_t a8 = 2097151 & load_3(a + 21);
int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
int64_t a11 = (load_4(a + 28) >> 7);
int64_t b0 = 2097151 & load_3(b);
int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
int64_t b8 = 2097151 & load_3(b + 21);
int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
int64_t b11 = (load_4(b + 28) >> 7);
int64_t c0 = 2097151 & load_3(c);
int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
int64_t c8 = 2097151 & load_3(c + 21);
int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
int64_t c11 = (load_4(c + 28) >> 7);
int64_t s0;
int64_t s1;
int64_t s2;
int64_t s3;
int64_t s4;
int64_t s5;
int64_t s6;
int64_t s7;
int64_t s8;
int64_t s9;
int64_t s10;
int64_t s11;
int64_t s12;
int64_t s13;
int64_t s14;
int64_t s15;
int64_t s16;
int64_t s17;
int64_t s18;
int64_t s19;
int64_t s20;
int64_t s21;
int64_t s22;
int64_t s23;
int64_t carry0;
int64_t carry1;
int64_t carry2;
int64_t carry3;
int64_t carry4;
int64_t carry5;
int64_t carry6;
int64_t carry7;
int64_t carry8;
int64_t carry9;
int64_t carry10;
int64_t carry11;
int64_t carry12;
int64_t carry13;
int64_t carry14;
int64_t carry15;
int64_t carry16;
int64_t carry17;
int64_t carry18;
int64_t carry19;
int64_t carry20;
int64_t carry21;
int64_t carry22;
s0 = c0 + a0*b0;
s1 = c1 + a0*b1 + a1*b0;
s2 = c2 + a0*b2 + a1*b1 + a2*b0;
s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1
+ a8*b0;
s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2
+ a8*b1 + a9*b0;
s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3
+ a8*b2 + a9*b1 + a10*b0;
s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4
+ a8*b3 + a9*b2 + a10*b1 + a11*b0;
s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3
+ a10*b2 + a11*b1;
s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3
+ a11*b2;
s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4
+ a11*b3;
s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
s20 = a9*b11 + a10*b10 + a11*b9;
s21 = a10*b11 + a11*b10;
s22 = a11*b11;
s23 = 0;
carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s23 = 0;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s22 = 0;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s21 = 0;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s20 = 0;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s19 = 0;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
s18 = 0;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s17 = 0;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s16 = 0;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s15 = 0;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s14 = 0;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s13 = 0;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
s[0] = (byte)(s0 >> 0);
s[1] = (byte)(s0 >> 8);
s[2] = (byte)((s0 >> 16) | (s1 << 5));
s[3] = (byte)(s1 >> 3);
s[4] = (byte)(s1 >> 11);
s[5] = (byte)((s1 >> 19) | (s2 << 2));
s[6] = (byte)(s2 >> 6);
s[7] = (byte)((s2 >> 14) | (s3 << 7));
s[8] = (byte)(s3 >> 1);
s[9] = (byte)(s3 >> 9);
s[10] = (byte)((s3 >> 17) | (s4 << 4));
s[11] = (byte)(s4 >> 4);
s[12] = (byte)(s4 >> 12);
s[13] = (byte)((s4 >> 20) | (s5 << 1));
s[14] = (byte)(s5 >> 7);
s[15] = (byte)((s5 >> 15) | (s6 << 6));
s[16] = (byte)(s6 >> 2);
s[17] = (byte)(s6 >> 10);
s[18] = (byte)((s6 >> 18) | (s7 << 3));
s[19] = (byte)(s7 >> 5);
s[20] = (byte)(s7 >> 13);
s[21] = (byte)(s8 >> 0);
s[22] = (byte)(s8 >> 8);
s[23] = (byte)((s8 >> 16) | (s9 << 5));
s[24] = (byte)(s9 >> 3);
s[25] = (byte)(s9 >> 11);
s[26] = (byte)((s9 >> 19) | (s10 << 2));
s[27] = (byte)(s10 >> 6);
s[28] = (byte)((s10 >> 14) | (s11 << 7));
s[29] = (byte)(s11 >> 1);
s[30] = (byte)(s11 >> 9);
s[31] = (byte)(s11 >> 17);
/* hush warnings after setting values to 0 */
(void)s12;
(void)s13;
(void)s14;
(void)s15;
(void)s16;
(void)s17;
(void)s18;
(void)s19;
(void)s20;
(void)s21;
(void)s22;
(void)s23;
}
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
*/
void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
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);
}
/* 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 y;
}
static unsigned char negative(signed char b)
{
unsigned long long x = b; /* 18446744073709551361..18446744073709551615:
yes; 0..255: no */
x >>= 63; /* 1: yes; 0: no */
return (unsigned char)x;
}
static void cmov(ge_precomp *t,const ge_precomp *u,unsigned char b)
{
fe_cmov(t->yplusx,u->yplusx,b);
fe_cmov(t->yminusx,u->yminusx,b);
fe_cmov(t->xy2d,u->xy2d,b);
}
#ifdef 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 },
{ 0x2a8b3a59b7a5f, 0x3abb359ef087f, 0x4f5a8c4db05af, 0x5b9a807d04205, 0x701af5b13ea50 },
},
{
{ 0x5b0a84cee9730, 0x61d10c97155e4, 0x4059cc8096a10, 0x47a608da8014f, 0x7a164e1b9a80f },
{ 0x11fe8a4fcd265, 0x7bcb8374faacc, 0x52f5af4ef4d4f, 0x5314098f98d10, 0x2ab91587555bd },
{ 0x6933f0dd0d889, 0x44386bb4c4295, 0x3cb6d3162508c, 0x26368b872a2c6, 0x5a2826af12b9b },
},
{
{ 0x351b98efc099f, 0x68fbfa4a7050e, 0x42a49959d971b, 0x393e51a469efd, 0x680e910321e58 },
{ 0x6050a056818bf, 0x62acc1f5532bf, 0x28141ccc9fa25, 0x24d61f471e683, 0x27933f4c7445a },
{ 0x3fbe9c476ff09, 0x0af6b982e4b42, 0x0ad1251ba78e5, 0x715aeedee7c88, 0x7f9d0cbf63553 },
},
{
{ 0x2bc4408a5bb33, 0x078ebdda05442, 0x2ffb112354123, 0x375ee8df5862d, 0x2945ccf146e20 },
{ 0x182c3a447d6ba, 0x22964e536eff2, 0x192821f540053, 0x2f9f19e788e5c, 0x154a7e73eb1b5 },
{ 0x3dbf1812a8285, 0x0fa17ba3f9797, 0x6f69cb49c3820, 0x34d5a0db3858d, 0x43aabe696b3bb },
},
{
{ 0x4eeeb77157131, 0x1201915f10741, 0x1669cda6c9c56, 0x45ec032db346d, 0x51e57bb6a2cc3 },
{ 0x006b67b7d8ca4, 0x084fa44e72933, 0x1154ee55d6f8a, 0x4425d842e7390, 0x38b64c41ae417 },
{ 0x4326702ea4b71, 0x06834376030b5, 0x0ef0512f9c380, 0x0f1a9f2512584, 0x10b8e91a9f0d6 },
},
{
{ 0x25cd0944ea3bf, 0x75673b81a4d63, 0x150b925d1c0d4, 0x13f38d9294114, 0x461bea69283c9 },
{ 0x72c9aaa3221b1, 0x267774474f74d, 0x064b0e9b28085, 0x3f04ef53b27c9, 0x1d6edd5d2e531 },
{ 0x36dc801b8b3a2, 0x0e0a7d4935e30, 0x1deb7cecc0d7d, 0x053a94e20dd2c, 0x7a9fbb1c6a0f9 },
},
{
{ 0x7596604dd3e8f, 0x6fc510e058b36, 0x3670c8db2cc0d, 0x297d899ce332f, 0x0915e76061bce },
{ 0x75dedf39234d9, 0x01c36ab1f3c54, 0x0f08fee58f5da, 0x0e19613a0d637, 0x3a9024a1320e0 },
{ 0x1f5d9c9a2911a, 0x7117994fafcf8, 0x2d8a8cae28dc5, 0x74ab1b2090c87, 0x26907c5c2ecc4 },
},
},
{
{
{ 0x4dd0e632f9c1d, 0x2ced12622a5d9, 0x18de9614742da, 0x79ca96fdbb5d4, 0x6dd37d49a00ee },
{ 0x3635449aa515e, 0x3e178d0475dab, 0x50b4712a19712, 0x2dcc2860ff4ad, 0x30d76d6f03d31 },
{ 0x444172106e4c7, 0x01251afed2d88, 0x534fc9bed4f5a, 0x5d85a39cf5234, 0x10c697112e864 },
},
{
{ 0x62aa08358c805, 0x46f440848e194, 0x447b771a8f52b, 0x377ba3269d31d, 0x03bf9baf55080 },
{ 0x3c4277dbe5fde, 0x5a335afd44c92, 0x0c1164099753e, 0x70487006fe423, 0x25e61cabed66f },
{ 0x3e128cc586604, 0x5968b2e8fc7e2, 0x049a3d5bd61cf, 0x116505b1ef6e6, 0x566d78634586e },
},
{
{ 0x54285c65a2fd0, 0x55e62ccf87420, 0x46bb961b19044, 0x1153405712039, 0x14fba5f34793b },
{ 0x7a49f9cc10834, 0x2b513788a22c6, 0x5ff4b6ef2395b, 0x2ec8e5af607bf, 0x33975bca5ecc3 },
{ 0x746166985f7d4, 0x09939000ae79a, 0x5844c7964f97a, 0x13617e1f95b3d, 0x14829cea83fc5 },
},
{
{ 0x70b2f4e71ecb8, 0x728148efc643c, 0x0753e03995b76, 0x5bf5fb2ab6767, 0x05fc3bc4535d7 },
{ 0x37b8497dd95c2, 0x61549d6b4ffe8, 0x217a22db1d138, 0x0b9cf062eb09e, 0x2fd9c71e5f758 },
{ 0x0b3ae52afdedd, 0x19da76619e497, 0x6fa0654d2558e, 0x78219d25e41d4, 0x373767475c651 },
},
{
{ 0x095cb14246590, 0x002d82aa6ac68, 0x442f183bc4851, 0x6464f1c0a0644, 0x6bf5905730907 },
{ 0x299fd40d1add9, 0x5f2de9a04e5f7, 0x7c0eebacc1c59, 0x4cca1b1f8290a, 0x1fbea56c3b18f },
{ 0x778f1e1415b8a, 0x6f75874efc1f4, 0x28a694019027f, 0x52b37a96bdc4d, 0x02521cf67a635 },
},
{
{ 0x46720772f5ee4, 0x632c0f359d622, 0x2b2092ba3e252, 0x662257c112680, 0x001753d9f7cd6 },
{ 0x7ee0b0a9d5294, 0x381fbeb4cca27, 0x7841f3a3e639d, 0x676ea30c3445f, 0x3fa00a7e71382 },
{ 0x1232d963ddb34, 0x35692e70b078d, 0x247ca14777a1f, 0x6db556be8fcd0, 0x12b5fe2fa048e },
},
{
{ 0x37c26ad6f1e92, 0x46a0971227be5, 0x4722f0d2d9b4c, 0x3dc46204ee03a, 0x6f7e93c20796c },
{ 0x0fbc496fce34d, 0x575be6b7dae3e, 0x4a31585cee609, 0x037e9023930ff, 0x749b76f96fb12 },
{ 0x2f604aea6ae05, 0x637dc939323eb, 0x3fdad9b048d47, 0x0a8b0d4045af7, 0x0fcec10f01e02 },
},
{
{ 0x2d29dc4244e45, 0x6927b1bc147be, 0x0308534ac0839, 0x4853664033f41, 0x413779166feab },
{ 0x558a649fe1e44, 0x44635aeefcc89, 0x1ff434887f2ba, 0x0f981220e2d44, 0x4901aa7183c51 },
{ 0x1b7548c1af8f0, 0x7848c53368116, 0x01b64e7383de9, 0x109fbb0587c8f, 0x41bb887b726d1 },
},
},
{
{
{ 0x34c597c6691ae, 0x7a150b6990fc4, 0x52beb9d922274, 0x70eed7164861a, 0x0a871e070c6a9 },
{ 0x07d44744346be, 0x282b6a564a81d, 0x4ed80f875236b, 0x6fbbe1d450c50, 0x4eb728c12fcdb },
{ 0x1b5994bbc8989, 0x74b7ba84c0660, 0x75678f1cdaeb8, 0x23206b0d6f10c, 0x3ee7300f2685d },
},
{
{ 0x27947841e7518, 0x32c7388dae87f, 0x414add3971be9, 0x01850832f0ef1, 0x7d47c6a2cfb89 },
{ 0x255e49e7dd6b7, 0x38c2163d59eba, 0x3861f2a005845, 0x2e11e4ccbaec9, 0x1381576297912 },
{ 0x2d0148ef0d6e0, 0x3522a8de787fb, 0x2ee055e74f9d2, 0x64038f6310813, 0x148cf58d34c9e },
},
{
{ 0x72f7d9ae4756d, 0x7711e690ffc4a, 0x582a2355b0d16, 0x0dccfe885b6b4, 0x278febad4eaea },
{ 0x492f67934f027, 0x7ded0815528d4, 0x58461511a6612, 0x5ea2e50de1544, 0x3ff2fa1ebd5db },
{ 0x2681f8c933966, 0x3840521931635, 0x674f14a308652, 0x3bd9c88a94890, 0x4104dd02fe9c6 },
},
{
{ 0x14e06db096ab8, 0x1219c89e6b024, 0x278abd486a2db, 0x240b292609520, 0x0165b5a48efca },
{ 0x2bf5e1124422a, 0x673146756ae56, 0x14ad99a87e830, 0x1eaca65b080fd, 0x2c863b00afaf5 },
{ 0x0a474a0846a76, 0x099a5ef981e32, 0x2a8ae3c4bbfe6, 0x45c34af14832c, 0x591b67d9bffec },
},
{
{ 0x1b3719f18b55d, 0x754318c83d337, 0x27c17b7919797, 0x145b084089b61, 0x489b4f8670301 },
{ 0x70d1c80b49bfa, 0x3d57e7d914625, 0x3c0722165e545, 0x5e5b93819e04f, 0x3de02ec7ca8f7 },
{ 0x2102d3aeb92ef, 0x68c22d50c3a46, 0x42ea89385894e, 0x75f9ebf55f38c, 0x49f5fbba496cb },
},
{
{ 0x5628c1e9c572e, 0x598b108e822ab, 0x55d8fae29361a, 0x0adc8d1a97b28, 0x06a1a6c288675 },
{ 0x49a108a5bcfd4, 0x6178c8e7d6612, 0x1f03473710375, 0x73a49614a6098, 0x5604a86dcbfa6 },
{ 0x0d1d47c1764b6, 0x01c08316a2e51, 0x2b3db45c95045, 0x1634f818d300c, 0x20989e89fe274 },
},
{
{ 0x4278b85eaec2e, 0x0ef59657be2ce, 0x72fd169588770, 0x2e9b205260b30, 0x730b9950f7059 },
{ 0x777fd3a2dcc7f, 0x594a9fb124932, 0x01f8e80ca15f0, 0x714d13cec3269, 0x0403ed1d0ca67 },
{ 0x32d35874ec552, 0x1f3048df1b929, 0x300d73b179b23, 0x6e67be5a37d0b, 0x5bd7454308303 },
},
{
{ 0x4932115e7792a, 0x457b9bbb930b8, 0x68f5d8b193226, 0x4164e8f1ed456, 0x5bb7db123067f },
{ 0x2d19528b24cc2, 0x4ac66b8302ff3, 0x701c8d9fdad51, 0x6c1b35c5b3727, 0x133a78007380a },
{ 0x1f467c6ca62be, 0x2c4232a5dc12c, 0x7551dc013b087, 0x0690c11b03bcd, 0x740dca6d58f0e },
},
},
{
{
{ 0x28c570478433c, 0x1d8502873a463, 0x7641e7eded49c, 0x1ecedd54cf571, 0x2c03f5256c2b0 },
{ 0x0ee0752cfce4e, 0x660dd8116fbe9, 0x55167130fffeb, 0x1c682b885955c, 0x161d25fa963ea },
{ 0x718757b53a47d, 0x619e18b0f2f21, 0x5fbdfe4c1ec04, 0x5d798c81ebb92, 0x699468bdbd96b },
},
{
{ 0x53de66aa91948, 0x045f81a599b1b, 0x3f7a8bd214193, 0x71d4da412331a, 0x293e1c4e6c4a2 },
{ 0x72f46f4dafecf, 0x2948ffadef7a3, 0x11ecdfdf3bc04, 0x3c2e98ffeed25, 0x525219a473905 },
{ 0x6134b925112e1, 0x6bb942bb406ed, 0x070c445c0dde2, 0x411d822c4d7a3, 0x5b605c447f032 },
},
{
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{
{ 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 },
},
{
{ -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 },
{ 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 },
{ -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 },
},
{
{ -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 },
{ -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 },
{ 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 },
},
{
{ 32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995 },
{ -30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596 },
{ -11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891 },
},
{
{ 31947069,-14366651,-4640583,-15339921,-15125977,-6039709,-14756777,-16411740,19072640,-9511060 },
{ 11685058,11822410,3158003,-13952594,33402194,-4165066,5977896,-5215017,473099,5040608 },
{ -20290863,8198642,-27410132,11602123,1290375,-2799760,28326862,1721092,-19558642,-3131606 },
},
},
{
{
{ 7881532,10687937,7578723,7738378,-18951012,-2553952,21820786,8076149,-27868496,11538389 },
{ -19935666,3899861,18283497,-6801568,-15728660,-11249211,8754525,7446702,-5676054,5797016 },
{ -11295600,-3793569,-15782110,-7964573,12708869,-8456199,2014099,-9050574,-2369172,-5877341 },
},
{
{ -22472376,-11568741,-27682020,1146375,18956691,16640559,1192730,-3714199,15123619,10811505 },
{ 14352098,-3419715,-18942044,10822655,32750596,4699007,-70363,15776356,-28886779,-11974553 },
{ -28241164,-8072475,-4978962,-5315317,29416931,1847569,-20654173,-16484855,4714547,-9600655 },
},
{
{ 15200332,8368572,19679101,15970074,-31872674,1959451,24611599,-4543832,-11745876,12340220 },
{ 12876937,-10480056,33134381,6590940,-6307776,14872440,9613953,8241152,15370987,9608631 },
{ -4143277,-12014408,8446281,-391603,4407738,13629032,-7724868,15866074,-28210621,-8814099 },
},
{
{ 26660628,-15677655,8393734,358047,-7401291,992988,-23904233,858697,20571223,8420556 },
{ 14620715,13067227,-15447274,8264467,14106269,15080814,33531827,12516406,-21574435,-12476749 },
{ 236881,10476226,57258,-14677024,6472998,2466984,17258519,7256740,8791136,15069930 },
},
{
{ 1276410,-9371918,22949635,-16322807,-23493039,-5702186,14711875,4874229,-30663140,-2331391 },
{ 5855666,4990204,-13711848,7294284,-7804282,1924647,-1423175,-7912378,-33069337,9234253 },
{ 20590503,-9018988,31529744,-7352666,-2706834,10650548,31559055,-11609587,18979186,13396066 },
},
{
{ 24474287,4968103,22267082,4407354,24063882,-8325180,-18816887,13594782,33514650,7021958 },
{ -11566906,-6565505,-21365085,15928892,-26158305,4315421,-25948728,-3916677,-21480480,12868082 },
{ -28635013,13504661,19988037,-2132761,21078225,6443208,-21446107,2244500,-12455797,-8089383 },
},
{
{ -30595528,13793479,-5852820,319136,-25723172,-6263899,33086546,8957937,-15233648,5540521 },
{ -11630176,-11503902,-8119500,-7643073,2620056,1022908,-23710744,-1568984,-16128528,-14962807 },
{ 23152971,775386,27395463,14006635,-9701118,4649512,1689819,892185,-11513277,-15205948 },
},
{
{ 9770129,9586738,26496094,4324120,1556511,-3550024,27453819,4763127,-19179614,5867134 },
{ -32765025,1927590,31726409,-4753295,23962434,-16019500,27846559,5931263,-29749703,-16108455 },
{ 27461885,-2977536,22380810,1815854,-23033753,-3031938,7283490,-15148073,-19526700,7734629 },
},
},
{
{
{ -8010264,-9590817,-11120403,6196038,29344158,-13430885,7585295,-3176626,18549497,15302069 },
{ -32658337,-6171222,-7672793,-11051681,6258878,13504381,10458790,-6418461,-8872242,8424746 },
{ 24687205,8613276,-30667046,-3233545,1863892,-1830544,19206234,7134917,-11284482,-828919 },
},
{
{ 11334899,-9218022,8025293,12707519,17523892,-10476071,10243738,-14685461,-5066034,16498837 },
{ 8911542,6887158,-9584260,-6958590,11145641,-9543680,17303925,-14124238,6536641,10543906 },
{ -28946384,15479763,-17466835,568876,-1497683,11223454,-2669190,-16625574,-27235709,8876771 },
},
{
{ -25742899,-12566864,-15649966,-846607,-33026686,-796288,-33481822,15824474,-604426,-9039817 },
{ 10330056,70051,7957388,-9002667,9764902,15609756,27698697,-4890037,1657394,3084098 },
{ 10477963,-7470260,12119566,-13250805,29016247,-5365589,31280319,14396151,-30233575,15272409 },
},
{
{ -12288309,3169463,28813183,16658753,25116432,-5630466,-25173957,-12636138,-25014757,1950504 },
{ -26180358,9489187,11053416,-14746161,-31053720,5825630,-8384306,-8767532,15341279,8373727 },
{ 28685821,7759505,-14378516,-12002860,-31971820,4079242,298136,-10232602,-2878207,15190420 },
},
{
{ -32932876,13806336,-14337485,-15794431,-24004620,10940928,8669718,2742393,-26033313,-6875003 },
{ -1580388,-11729417,-25979658,-11445023,-17411874,-10912854,9291594,-16247779,-12154742,6048605 },
{ -30305315,14843444,1539301,11864366,20201677,1900163,13934231,5128323,11213262,9168384 },
},
{
{ -26280513,11007847,19408960,-940758,-18592965,-4328580,-5088060,-11105150,20470157,-16398701 },
{ -23136053,9282192,14855179,-15390078,-7362815,-14408560,-22783952,14461608,14042978,5230683 },
{ 29969567,-2741594,-16711867,-8552442,9175486,-2468974,21556951,3506042,-5933891,-12449708 },
},
{
{ -3144746,8744661,19704003,4581278,-20430686,6830683,-21284170,8971513,-28539189,15326563 },
{ -19464629,10110288,-17262528,-3503892,-23500387,1355669,-15523050,15300988,-20514118,9168260 },
{ -5353335,4488613,-23803248,16314347,7780487,-15638939,-28948358,9601605,33087103,-9011387 },
},
{
{ -19443170,-15512900,-20797467,-12445323,-29824447,10229461,-27444329,-15000531,-5996870,15664672 },
{ 23294591,-16632613,-22650781,-8470978,27844204,11461195,13099750,-2460356,18151676,13417686 },
{ -24722913,-4176517,-31150679,5988919,-26858785,6685065,1661597,-12551441,15271676,-15452665 },
},
},
{
{
{ 11433042,-13228665,8239631,-5279517,-1985436,-725718,-18698764,2167544,-6921301,-13440182 },
{ -31436171,15575146,30436815,12192228,-22463353,9395379,-9917708,-8638997,12215110,12028277 },
{ 14098400,6555944,23007258,5757252,-15427832,-12950502,30123440,4617780,-16900089,-655628 },
},
{
{ -4026201,-15240835,11893168,13718664,-14809462,1847385,-15819999,10154009,23973261,-12684474 },
{ -26531820,-3695990,-1908898,2534301,-31870557,-16550355,18341390,-11419951,32013174,-10103539 },
{ -25479301,10876443,-11771086,-14625140,-12369567,1838104,21911214,6354752,4425632,-837822 },
},
{
{ -10433389,-14612966,22229858,-3091047,-13191166,776729,-17415375,-12020462,4725005,14044970 },
{ 19268650,-7304421,1555349,8692754,-21474059,-9910664,6347390,-1411784,-19522291,-16109756 },
{ -24864089,12986008,-10898878,-5558584,-11312371,-148526,19541418,8180106,9282262,10282508 },
},
{
{ -26205082,4428547,-8661196,-13194263,4098402,-14165257,15522535,8372215,5542595,-10702683 },
{ -10562541,14895633,26814552,-16673850,-17480754,-2489360,-2781891,6993761,-18093885,10114655 },
{ -20107055,-929418,31422704,10427861,-7110749,6150669,-29091755,-11529146,25953725,-106158 },
},
{
{ -4234397,-8039292,-9119125,3046000,2101609,-12607294,19390020,6094296,-3315279,12831125 },
{ -15998678,7578152,5310217,14408357,-33548620,-224739,31575954,6326196,7381791,-2421839 },
{ -20902779,3296811,24736065,-16328389,18374254,7318640,6295303,8082724,-15362489,12339664 },
},
{
{ 27724736,2291157,6088201,-14184798,1792727,5857634,13848414,15768922,25091167,14856294 },
{ -18866652,8331043,24373479,8541013,-701998,-9269457,12927300,-12695493,-22182473,-9012899 },
{ -11423429,-5421590,11632845,3405020,30536730,-11674039,-27260765,13866390,30146206,9142070 },
},
{
{ 3924129,-15307516,-13817122,-10054960,12291820,-668366,-27702774,9326384,-8237858,4171294 },
{ -15921940,16037937,6713787,16606682,-21612135,2790944,26396185,3731949,345228,-5462949 },
{ -21327538,13448259,25284571,1143661,20614966,-8849387,2031539,-12391231,-16253183,-13582083 },
},
{
{ 31016211,-16722429,26371392,-14451233,-5027349,14854137,17477601,3842657,28012650,-16405420 },
{ -5075835,9368966,-8562079,-4600902,-15249953,6970560,-9189873,16292057,-8867157,3507940 },
{ 29439664,3537914,23333589,6997794,-17555561,-11018068,-15209202,-15051267,-9164929,6580396 },
},
},
{
{
{ -12185861,-7679788,16438269,10826160,-8696817,-6235611,17860444,-9273846,-2095802,9304567 },
{ 20714564,-4336911,29088195,7406487,11426967,-5095705,14792667,-14608617,5289421,-477127 },
{ -16665533,-10650790,-6160345,-13305760,9192020,-1802462,17271490,12349094,26939669,-3752294 },
},
{
{ -12889898,9373458,31595848,16374215,21471720,13221525,-27283495,-12348559,-3698806,117887 },
{ 22263325,-6560050,3984570,-11174646,-15114008,-566785,28311253,5358056,-23319780,541964 },
{ 16259219,3261970,2309254,-15534474,-16885711,-4581916,24134070,-16705829,-13337066,-13552195 },
},
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{ 21426655,-5650218,-13648287,-5347537,-28812189,-4920970,-18275391,-14621414,13040862,-12112948 },
},
{
{ 11293895,12478086,-27136401,15083750,-29307421,14748872,14555558,-13417103,1613711,4896935 },
{ -25894883,15323294,-8489791,-8057900,25967126,-13425460,2825960,-4897045,-23971776,-11267415 },
{ -15924766,-5229880,-17443532,6410664,3622847,10243618,20615400,12405433,-23753030,-8436416 },
},
{
{ -7091295,12556208,-20191352,9025187,-17072479,4333801,4378436,2432030,23097949,-566018 },
{ 4565804,-16025654,20084412,-7842817,1724999,189254,24767264,10103221,-18512313,2424778 },
{ 366633,-11976806,8173090,-6890119,30788634,5745705,-7168678,1344109,-3642553,12412659 },
},
{
{ -24001791,7690286,14929416,-168257,-32210835,-13412986,24162697,-15326504,-3141501,11179385 },
{ 18289522,-14724954,8056945,16430056,-21729724,7842514,-6001441,-1486897,-18684645,-11443503 },
{ 476239,6601091,-6152790,-9723375,17503545,-4863900,27672959,13403813,11052904,5219329 },
},
},
{
{
{ 20678546,-8375738,-32671898,8849123,-5009758,14574752,31186971,-3973730,9014762,-8579056 },
{ -13644050,-10350239,-15962508,5075808,-1514661,-11534600,-33102500,9160280,8473550,-3256838 },
{ 24900749,14435722,17209120,-15292541,-22592275,9878983,-7689309,-16335821,-24568481,11788948 },
},
{
{ -3118155,-11395194,-13802089,14797441,9652448,-6845904,-20037437,10410733,-24568470,-1458691 },
{ -15659161,16736706,-22467150,10215878,-9097177,7563911,11871841,-12505194,-18513325,8464118 },
{ -23400612,8348507,-14585951,-861714,-3950205,-6373419,14325289,8628612,33313881,-8370517 },
},
{
{ -20186973,-4967935,22367356,5271547,-1097117,-4788838,-24805667,-10236854,-8940735,-5818269 },
{ -6948785,-1795212,-32625683,-16021179,32635414,-7374245,15989197,-12838188,28358192,-4253904 },
{ -23561781,-2799059,-32351682,-1661963,-9147719,10429267,-16637684,4072016,-5351664,5596589 },
},
{
{ -28236598,-3390048,12312896,6213178,3117142,16078565,29266239,2557221,1768301,15373193 },
{ -7243358,-3246960,-4593467,-7553353,-127927,-912245,-1090902,-4504991,-24660491,3442910 },
{ -30210571,5124043,14181784,8197961,18964734,-11939093,22597931,7176455,-18585478,13365930 },
},
{
{ -7877390,-1499958,8324673,4690079,6261860,890446,24538107,-8570186,-9689599,-3031667 },
{ 25008904,-10771599,-4305031,-9638010,16265036,15721635,683793,-11823784,15723479,-15163481 },
{ -9660625,12374379,-27006999,-7026148,-7724114,-12314514,11879682,5400171,519526,-1235876 },
},
{
{ 22258397,-16332233,-7869817,14613016,-22520255,-2950923,-20353881,7315967,16648397,7605640 },
{ -8081308,-8464597,-8223311,9719710,19259459,-15348212,23994942,-5281555,-9468848,4763278 },
{ -21699244,9220969,-15730624,1084137,-25476107,-2852390,31088447,-7764523,-11356529,728112 },
},
{
{ 26047220,-11751471,-6900323,-16521798,24092068,9158119,-4273545,-12555558,-29365436,-5498272 },
{ 17510331,-322857,5854289,8403524,17133918,-3112612,-28111007,12327945,10750447,10014012 },
{ -10312768,3936952,9156313,-8897683,16498692,-994647,-27481051,-666732,3424691,7540221 },
},
{
{ 30322361,-6964110,11361005,-4143317,7433304,4989748,-7071422,-16317219,-9244265,15258046 },
{ 13054562,-2779497,19155474,469045,-12482797,4566042,5631406,2711395,1062915,-5136345 },
{ -19240248,-11254599,-29509029,-7499965,-5835763,13005411,-6066489,12194497,32960380,1459310 },
},
},
{
{
{ 19852034,7027924,23669353,10020366,8586503,-6657907,394197,-6101885,18638003,-11174937 },
{ 31395534,15098109,26581030,8030562,-16527914,-5007134,9012486,-7584354,-6643087,-5442636 },
{ -9192165,-2347377,-1997099,4529534,25766844,607986,-13222,9677543,-32294889,-6456008 },
},
{
{ -2444496,-149937,29348902,8186665,1873760,12489863,-30934579,-7839692,-7852844,-8138429 },
{ -15236356,-15433509,7766470,746860,26346930,-10221762,-27333451,10754588,-9431476,5203576 },
{ 31834314,14135496,-770007,5159118,20917671,-16768096,-7467973,-7337524,31809243,7347066 },
},
{
{ -9606723,-11874240,20414459,13033986,13716524,-11691881,19797970,-12211255,15192876,-2087490 },
{ -12663563,-2181719,1168162,-3804809,26747877,-14138091,10609330,12694420,33473243,-13382104 },
{ 33184999,11180355,15832085,-11385430,-1633671,225884,15089336,-11023903,-6135662,14480053 },
},
{
{ 31308717,-5619998,31030840,-1897099,15674547,-6582883,5496208,13685227,27595050,8737275 },
{ -20318852,-15150239,10933843,-16178022,8335352,-7546022,-31008351,-12610604,26498114,66511 },
{ 22644454,-8761729,-16671776,4884562,-3105614,-13559366,30540766,-4286747,-13327787,-7515095 },
},
{
{ -28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439 },
{ 23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939 },
{ -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 },
},
{
{ 2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310 },
{ 3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608 },
{ -32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079 },
},
{
{ -23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101 },
{ 21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418 },
{ 18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576 },
},
{
{ 30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356 },
{ 9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996 },
{ -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 },
},
},
{
{
{ -26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728 },
{ -13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658 },
{ -10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242 },
},
{
{ -21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001 },
{ -4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766 },
{ 18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373 },
},
{
{ 26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458 },
{ -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 },
{ -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 },
},
{
{ -23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062 },
{ 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 },
{ 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 },
},
{
{ 24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383 },
{ -25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814 },
{ -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 },
},
{
{ 30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417 },
{ 2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222 },
{ 33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444 },
},
{
{ -20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597 },
{ 23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970 },
{ 1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799 },
},
{
{ -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)
{
ge_precomp minust;
unsigned char bnegative = negative(b);
unsigned char babs = b - (((-bnegative) & b) << 1);
ge_precomp_0(t);
cmov(t,&base[pos][0],equal(babs,1));
cmov(t,&base[pos][1],equal(babs,2));
cmov(t,&base[pos][2],equal(babs,3));
cmov(t,&base[pos][3],equal(babs,4));
cmov(t,&base[pos][4],equal(babs,5));
cmov(t,&base[pos][5],equal(babs,6));
cmov(t,&base[pos][6],equal(babs,7));
cmov(t,&base[pos][7],equal(babs,8));
fe_copy(minust.yplusx,t->yminusx);
fe_copy(minust.yminusx,t->yplusx);
fe_neg(minust.xy2d,t->xy2d);
cmov(t,&minust,bnegative);
}
/*
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;
ge_p2 s;
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 */
ge_p3_0(h);
for (i = 1;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);
}
}
/* 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_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_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_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
*/
void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
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);
}
/* ge msub */
/*
r = p - q
*/
void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
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);
}
/* ge p1p1 to p2 */
/*
r = p
*/
extern void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p)
{
fe_mul(r->X,p->X,p->T);
fe_mul(r->Y,p->Y,p->Z);
fe_mul(r->Z,p->Z,p->T);
}
/* ge p1p1 to p3 */
/*
r = p
*/
extern void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p)
{
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);
}
/* ge p2 0 */
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
*/
void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
{
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);
}
/* ge p3 0 */
void ge_p3_0(ge_p3 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
fe_0(h->T);
}
/* ge p3 dble */
/*
r = 2 * p
*/
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_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
extern 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
*/
extern 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;
}
/* ge_precomp_0 */
void ge_precomp_0(ge_precomp *h)
{
fe_1(h->yplusx);
fe_1(h->yminusx);
fe_0(h->xy2d);
}
/* ge_sub */
/*
r = p - q
*/
void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
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);
}
/* 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 */