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heimdal/lib/hcrypto/x25519/ed25519_ref10.c
Luke Howard beda11a079 hcrypto: Add X25519 
The X25519 implementation comes from libsodium. Explicit copyright
notices have been added to each file as well as some portability changes
(e.g. align.h).
2020-04-25 23:19:30 -05:00

2887 lines
78 KiB
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/*
* ISC License
*
* Copyright (c) 2013-2019
* Frank Denis <j at pureftpd dot org>
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#include <roken.h>
#include <stddef.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include "ed25519_ref10.h"
#include "align.h"
static inline 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;
}
static inline 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;
}
/*
* Field arithmetic:
* Use 5*51 bit limbs on 64-bit systems with support for 128 bit arithmetic,
* and 10*25.5 bit limbs elsewhere.
*
* Functions used elsewhere that are candidates for inlining are defined
* via "private/curve25519_ref10.h".
*/
#ifdef HAVE_TI_MODE
# include "fe_51/constants.h"
# include "fe_51/fe.h"
#else
# include "fe_25_5/constants.h"
# include "fe_25_5/fe.h"
#endif
void
fe25519_invert(fe25519 out, const fe25519 z)
{
fe25519 t0;
fe25519 t1;
fe25519 t2;
fe25519 t3;
int i;
fe25519_sq(t0, z);
fe25519_sq(t1, t0);
fe25519_sq(t1, t1);
fe25519_mul(t1, z, t1);
fe25519_mul(t0, t0, t1);
fe25519_sq(t2, t0);
fe25519_mul(t1, t1, t2);
fe25519_sq(t2, t1);
for (i = 1; i < 5; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t2, t1);
for (i = 1; i < 10; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t2, t2, t1);
fe25519_sq(t3, t2);
for (i = 1; i < 20; ++i) {
fe25519_sq(t3, t3);
}
fe25519_mul(t2, t3, t2);
fe25519_sq(t2, t2);
for (i = 1; i < 10; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t2, t1);
for (i = 1; i < 50; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t2, t2, t1);
fe25519_sq(t3, t2);
for (i = 1; i < 100; ++i) {
fe25519_sq(t3, t3);
}
fe25519_mul(t2, t3, t2);
fe25519_sq(t2, t2);
for (i = 1; i < 50; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t1, t1);
for (i = 1; i < 5; ++i) {
fe25519_sq(t1, t1);
}
fe25519_mul(out, t1, t0);
}
static void
fe25519_pow22523(fe25519 out, const fe25519 z)
{
fe25519 t0;
fe25519 t1;
fe25519 t2;
int i;
fe25519_sq(t0, z);
fe25519_sq(t1, t0);
fe25519_sq(t1, t1);
fe25519_mul(t1, z, t1);
fe25519_mul(t0, t0, t1);
fe25519_sq(t0, t0);
fe25519_mul(t0, t1, t0);
fe25519_sq(t1, t0);
for (i = 1; i < 5; ++i) {
fe25519_sq(t1, t1);
}
fe25519_mul(t0, t1, t0);
fe25519_sq(t1, t0);
for (i = 1; i < 10; ++i) {
fe25519_sq(t1, t1);
}
fe25519_mul(t1, t1, t0);
fe25519_sq(t2, t1);
for (i = 1; i < 20; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t1, t1);
for (i = 1; i < 10; ++i) {
fe25519_sq(t1, t1);
}
fe25519_mul(t0, t1, t0);
fe25519_sq(t1, t0);
for (i = 1; i < 50; ++i) {
fe25519_sq(t1, t1);
}
fe25519_mul(t1, t1, t0);
fe25519_sq(t2, t1);
for (i = 1; i < 100; ++i) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t1, t1);
for (i = 1; i < 50; ++i) {
fe25519_sq(t1, t1);
}
fe25519_mul(t0, t1, t0);
fe25519_sq(t0, t0);
fe25519_sq(t0, t0);
fe25519_mul(out, t0, z);
}
static inline void
fe25519_cneg(fe25519 h, const fe25519 f, unsigned int b)
{
fe25519 negf;
fe25519_neg(negf, f);
fe25519_copy(h, f);
fe25519_cmov(h, negf, b);
}
static inline void
fe25519_abs(fe25519 h, const fe25519 f)
{
fe25519_cneg(h, f, fe25519_isnegative(f));
}
/*
r = p + q
*/
void
ge25519_add(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q)
{
fe25519 t0;
fe25519_add(r->X, p->Y, p->X);
fe25519_sub(r->Y, p->Y, p->X);
fe25519_mul(r->Z, r->X, q->YplusX);
fe25519_mul(r->Y, r->Y, q->YminusX);
fe25519_mul(r->T, q->T2d, p->T);
fe25519_mul(r->X, p->Z, q->Z);
fe25519_add(t0, r->X, r->X);
fe25519_sub(r->X, r->Z, r->Y);
fe25519_add(r->Y, r->Z, r->Y);
fe25519_add(r->Z, t0, r->T);
fe25519_sub(r->T, t0, r->T);
}
static void
slide_vartime(signed char *r, const unsigned char *a)
{
int i;
int b;
int k;
int ribs;
int cmp;
for (i = 0; i < 256; ++i) {
r[i] = 1 & (a[i >> 3] >> (i & 7));
}
for (i = 0; i < 256; ++i) {
if (! r[i]) {
continue;
}
for (b = 1; b <= 6 && i + b < 256; ++b) {
if (! r[i + b]) {
continue;
}
ribs = r[i + b] << b;
cmp = r[i] + ribs;
if (cmp <= 15) {
r[i] = cmp;
r[i + b] = 0;
} else {
cmp = r[i] - ribs;
if (cmp < -15) {
break;
}
r[i] = cmp;
for (k = i + b; k < 256; ++k) {
if (! r[k]) {
r[k] = 1;
break;
}
r[k] = 0;
}
}
}
}
}
int
ge25519_frombytes(ge25519_p3 *h, const unsigned char *s)
{
fe25519 u;
fe25519 v;
fe25519 v3;
fe25519 vxx;
fe25519 m_root_check, p_root_check;
fe25519 negx;
fe25519 x_sqrtm1;
int has_m_root, has_p_root;
fe25519_frombytes(h->Y, s);
fe25519_1(h->Z);
fe25519_sq(u, h->Y);
fe25519_mul(v, u, d);
fe25519_sub(u, u, h->Z); /* u = y^2-1 */
fe25519_add(v, v, h->Z); /* v = dy^2+1 */
fe25519_sq(v3, v);
fe25519_mul(v3, v3, v); /* v3 = v^3 */
fe25519_sq(h->X, v3);
fe25519_mul(h->X, h->X, v);
fe25519_mul(h->X, h->X, u); /* x = uv^7 */
fe25519_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
fe25519_mul(h->X, h->X, v3);
fe25519_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
fe25519_sq(vxx, h->X);
fe25519_mul(vxx, vxx, v);
fe25519_sub(m_root_check, vxx, u); /* vx^2-u */
fe25519_add(p_root_check, vxx, u); /* vx^2+u */
has_m_root = fe25519_iszero(m_root_check);
has_p_root = fe25519_iszero(p_root_check);
fe25519_mul(x_sqrtm1, h->X, sqrtm1); /* x*sqrt(-1) */
fe25519_cmov(h->X, x_sqrtm1, 1 - has_m_root);
fe25519_neg(negx, h->X);
fe25519_cmov(h->X, negx, fe25519_isnegative(h->X) ^ (s[31] >> 7));
fe25519_mul(h->T, h->X, h->Y);
return (has_m_root | has_p_root) - 1;
}
int
ge25519_frombytes_negate_vartime(ge25519_p3 *h, const unsigned char *s)
{
fe25519 u;
fe25519 v;
fe25519 v3;
fe25519 vxx;
fe25519 m_root_check, p_root_check;
fe25519_frombytes(h->Y, s);
fe25519_1(h->Z);
fe25519_sq(u, h->Y);
fe25519_mul(v, u, d);
fe25519_sub(u, u, h->Z); /* u = y^2-1 */
fe25519_add(v, v, h->Z); /* v = dy^2+1 */
fe25519_sq(v3, v);
fe25519_mul(v3, v3, v); /* v3 = v^3 */
fe25519_sq(h->X, v3);
fe25519_mul(h->X, h->X, v);
fe25519_mul(h->X, h->X, u); /* x = uv^7 */
fe25519_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
fe25519_mul(h->X, h->X, v3);
fe25519_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
fe25519_sq(vxx, h->X);
fe25519_mul(vxx, vxx, v);
fe25519_sub(m_root_check, vxx, u); /* vx^2-u */
if (fe25519_iszero(m_root_check) == 0) {
fe25519_add(p_root_check, vxx, u); /* vx^2+u */
if (fe25519_iszero(p_root_check) == 0) {
return -1;
}
fe25519_mul(h->X, h->X, sqrtm1);
}
if (fe25519_isnegative(h->X) == (s[31] >> 7)) {
fe25519_neg(h->X, h->X);
}
fe25519_mul(h->T, h->X, h->Y);
return 0;
}
/*
r = p + q
*/
static void
ge25519_madd(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q)
{
fe25519 t0;
fe25519_add(r->X, p->Y, p->X);
fe25519_sub(r->Y, p->Y, p->X);
fe25519_mul(r->Z, r->X, q->yplusx);
fe25519_mul(r->Y, r->Y, q->yminusx);
fe25519_mul(r->T, q->xy2d, p->T);
fe25519_add(t0, p->Z, p->Z);
fe25519_sub(r->X, r->Z, r->Y);
fe25519_add(r->Y, r->Z, r->Y);
fe25519_add(r->Z, t0, r->T);
fe25519_sub(r->T, t0, r->T);
}
/*
r = p - q
*/
static void
ge25519_msub(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_precomp *q)
{
fe25519 t0;
fe25519_add(r->X, p->Y, p->X);
fe25519_sub(r->Y, p->Y, p->X);
fe25519_mul(r->Z, r->X, q->yminusx);
fe25519_mul(r->Y, r->Y, q->yplusx);
fe25519_mul(r->T, q->xy2d, p->T);
fe25519_add(t0, p->Z, p->Z);
fe25519_sub(r->X, r->Z, r->Y);
fe25519_add(r->Y, r->Z, r->Y);
fe25519_sub(r->Z, t0, r->T);
fe25519_add(r->T, t0, r->T);
}
/*
r = p
*/
void
ge25519_p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
{
fe25519_mul(r->X, p->X, p->T);
fe25519_mul(r->Y, p->Y, p->Z);
fe25519_mul(r->Z, p->Z, p->T);
}
/*
r = p
*/
void
ge25519_p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
{
fe25519_mul(r->X, p->X, p->T);
fe25519_mul(r->Y, p->Y, p->Z);
fe25519_mul(r->Z, p->Z, p->T);
fe25519_mul(r->T, p->X, p->Y);
}
static void
ge25519_p2_0(ge25519_p2 *h)
{
fe25519_0(h->X);
fe25519_1(h->Y);
fe25519_1(h->Z);
}
/*
r = 2 * p
*/
static void
ge25519_p2_dbl(ge25519_p1p1 *r, const ge25519_p2 *p)
{
fe25519 t0;
fe25519_sq(r->X, p->X);
fe25519_sq(r->Z, p->Y);
fe25519_sq2(r->T, p->Z);
fe25519_add(r->Y, p->X, p->Y);
fe25519_sq(t0, r->Y);
fe25519_add(r->Y, r->Z, r->X);
fe25519_sub(r->Z, r->Z, r->X);
fe25519_sub(r->X, t0, r->Y);
fe25519_sub(r->T, r->T, r->Z);
}
static void
ge25519_p3_0(ge25519_p3 *h)
{
fe25519_0(h->X);
fe25519_1(h->Y);
fe25519_1(h->Z);
fe25519_0(h->T);
}
static void
ge25519_cached_0(ge25519_cached *h)
{
fe25519_1(h->YplusX);
fe25519_1(h->YminusX);
fe25519_1(h->Z);
fe25519_0(h->T2d);
}
/*
r = p
*/
void
ge25519_p3_to_cached(ge25519_cached *r, const ge25519_p3 *p)
{
fe25519_add(r->YplusX, p->Y, p->X);
fe25519_sub(r->YminusX, p->Y, p->X);
fe25519_copy(r->Z, p->Z);
fe25519_mul(r->T2d, p->T, d2);
}
static void
ge25519_p3_to_precomp(ge25519_precomp *pi, const ge25519_p3 *p)
{
fe25519 recip;
fe25519 x;
fe25519 y;
fe25519 xy;
fe25519_invert(recip, p->Z);
fe25519_mul(x, p->X, recip);
fe25519_mul(y, p->Y, recip);
fe25519_add(pi->yplusx, y, x);
fe25519_sub(pi->yminusx, y, x);
fe25519_mul(xy, x, y);
fe25519_mul(pi->xy2d, xy, d2);
}
/*
r = p
*/
static void
ge25519_p3_to_p2(ge25519_p2 *r, const ge25519_p3 *p)
{
fe25519_copy(r->X, p->X);
fe25519_copy(r->Y, p->Y);
fe25519_copy(r->Z, p->Z);
}
void
ge25519_p3_tobytes(unsigned char *s, const ge25519_p3 *h)
{
fe25519 recip;
fe25519 x;
fe25519 y;
fe25519_invert(recip, h->Z);
fe25519_mul(x, h->X, recip);
fe25519_mul(y, h->Y, recip);
fe25519_tobytes(s, y);
s[31] ^= fe25519_isnegative(x) << 7;
}
/*
r = 2 * p
*/
static void
ge25519_p3_dbl(ge25519_p1p1 *r, const ge25519_p3 *p)
{
ge25519_p2 q;
ge25519_p3_to_p2(&q, p);
ge25519_p2_dbl(r, &q);
}
static void
ge25519_precomp_0(ge25519_precomp *h)
{
fe25519_1(h->yplusx);
fe25519_1(h->yminusx);
fe25519_0(h->xy2d);
}
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 = (uint32_t) 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)
{
/* 18446744073709551361..18446744073709551615: yes; 0..255: no */
uint64_t x = b;
x >>= 63; /* 1: yes; 0: no */
return x;
}
static void
ge25519_cmov(ge25519_precomp *t, const ge25519_precomp *u, unsigned char b)
{
fe25519_cmov(t->yplusx, u->yplusx, b);
fe25519_cmov(t->yminusx, u->yminusx, b);
fe25519_cmov(t->xy2d, u->xy2d, b);
}
static void
ge25519_cmov_cached(ge25519_cached *t, const ge25519_cached *u, unsigned char b)
{
fe25519_cmov(t->YplusX, u->YplusX, b);
fe25519_cmov(t->YminusX, u->YminusX, b);
fe25519_cmov(t->Z, u->Z, b);
fe25519_cmov(t->T2d, u->T2d, b);
}
static void
ge25519_cmov8(ge25519_precomp *t, const ge25519_precomp precomp[8], const signed char b)
{
ge25519_precomp minust;
const unsigned char bnegative = negative(b);
const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1));
ge25519_precomp_0(t);
ge25519_cmov(t, &precomp[0], equal(babs, 1));
ge25519_cmov(t, &precomp[1], equal(babs, 2));
ge25519_cmov(t, &precomp[2], equal(babs, 3));
ge25519_cmov(t, &precomp[3], equal(babs, 4));
ge25519_cmov(t, &precomp[4], equal(babs, 5));
ge25519_cmov(t, &precomp[5], equal(babs, 6));
ge25519_cmov(t, &precomp[6], equal(babs, 7));
ge25519_cmov(t, &precomp[7], equal(babs, 8));
fe25519_copy(minust.yplusx, t->yminusx);
fe25519_copy(minust.yminusx, t->yplusx);
fe25519_neg(minust.xy2d, t->xy2d);
ge25519_cmov(t, &minust, bnegative);
}
static void
ge25519_cmov8_base(ge25519_precomp *t, const int pos, const signed char b)
{
static const ge25519_precomp base[32][8] = { /* base[i][j] = (j+1)*256^i*B */
#ifdef HAVE_TI_MODE
# include "fe_51/base.h"
#else
# include "fe_25_5/base.h"
#endif
};
ge25519_cmov8(t, base[pos], b);
}
static void
ge25519_cmov8_cached(ge25519_cached *t, const ge25519_cached cached[8], const signed char b)
{
ge25519_cached minust;
const unsigned char bnegative = negative(b);
const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1));
ge25519_cached_0(t);
ge25519_cmov_cached(t, &cached[0], equal(babs, 1));
ge25519_cmov_cached(t, &cached[1], equal(babs, 2));
ge25519_cmov_cached(t, &cached[2], equal(babs, 3));
ge25519_cmov_cached(t, &cached[3], equal(babs, 4));
ge25519_cmov_cached(t, &cached[4], equal(babs, 5));
ge25519_cmov_cached(t, &cached[5], equal(babs, 6));
ge25519_cmov_cached(t, &cached[6], equal(babs, 7));
ge25519_cmov_cached(t, &cached[7], equal(babs, 8));
fe25519_copy(minust.YplusX, t->YminusX);
fe25519_copy(minust.YminusX, t->YplusX);
fe25519_copy(minust.Z, t->Z);
fe25519_neg(minust.T2d, t->T2d);
ge25519_cmov_cached(t, &minust, bnegative);
}
/*
r = p - q
*/
void
ge25519_sub(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_cached *q)
{
fe25519 t0;
fe25519_add(r->X, p->Y, p->X);
fe25519_sub(r->Y, p->Y, p->X);
fe25519_mul(r->Z, r->X, q->YminusX);
fe25519_mul(r->Y, r->Y, q->YplusX);
fe25519_mul(r->T, q->T2d, p->T);
fe25519_mul(r->X, p->Z, q->Z);
fe25519_add(t0, r->X, r->X);
fe25519_sub(r->X, r->Z, r->Y);
fe25519_add(r->Y, r->Z, r->Y);
fe25519_sub(r->Z, t0, r->T);
fe25519_add(r->T, t0, r->T);
}
void
ge25519_tobytes(unsigned char *s, const ge25519_p2 *h)
{
fe25519 recip;
fe25519 x;
fe25519 y;
fe25519_invert(recip, h->Z);
fe25519_mul(x, h->X, recip);
fe25519_mul(y, h->Y, recip);
fe25519_tobytes(s, y);
s[31] ^= fe25519_isnegative(x) << 7;
}
/*
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.
Only used for signatures verification.
*/
void
ge25519_double_scalarmult_vartime(ge25519_p2 *r, const unsigned char *a,
const ge25519_p3 *A, const unsigned char *b)
{
static const ge25519_precomp Bi[8] = {
#ifdef HAVE_TI_MODE
# include "fe_51/base2.h"
#else
# include "fe_25_5/base2.h"
#endif
};
signed char aslide[256];
signed char bslide[256];
ge25519_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
ge25519_p1p1 t;
ge25519_p3 u;
ge25519_p3 A2;
int i;
slide_vartime(aslide, a);
slide_vartime(bslide, b);
ge25519_p3_to_cached(&Ai[0], A);
ge25519_p3_dbl(&t, A);
ge25519_p1p1_to_p3(&A2, &t);
ge25519_add(&t, &A2, &Ai[0]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[1], &u);
ge25519_add(&t, &A2, &Ai[1]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[2], &u);
ge25519_add(&t, &A2, &Ai[2]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[3], &u);
ge25519_add(&t, &A2, &Ai[3]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[4], &u);
ge25519_add(&t, &A2, &Ai[4]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[5], &u);
ge25519_add(&t, &A2, &Ai[5]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[6], &u);
ge25519_add(&t, &A2, &Ai[6]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[7], &u);
ge25519_p2_0(r);
for (i = 255; i >= 0; --i) {
if (aslide[i] || bslide[i]) {
break;
}
}
for (; i >= 0; --i) {
ge25519_p2_dbl(&t, r);
if (aslide[i] > 0) {
ge25519_p1p1_to_p3(&u, &t);
ge25519_add(&t, &u, &Ai[aslide[i] / 2]);
} else if (aslide[i] < 0) {
ge25519_p1p1_to_p3(&u, &t);
ge25519_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
}
if (bslide[i] > 0) {
ge25519_p1p1_to_p3(&u, &t);
ge25519_madd(&t, &u, &Bi[bslide[i] / 2]);
} else if (bslide[i] < 0) {
ge25519_p1p1_to_p3(&u, &t);
ge25519_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
}
ge25519_p1p1_to_p2(r, &t);
}
}
/*
h = a * p
where a = a[0]+256*a[1]+...+256^31 a[31]
Preconditions:
a[31] <= 127
p is public
*/
void
ge25519_scalarmult(ge25519_p3 *h, const unsigned char *a, const ge25519_p3 *p)
{
signed char e[64];
signed char carry;
ge25519_p1p1 r;
ge25519_p2 s;
ge25519_p1p1 t2, t3, t4, t5, t6, t7, t8;
ge25519_p3 p2, p3, p4, p5, p6, p7, p8;
ge25519_cached pi[8];
ge25519_cached t;
int i;
ge25519_p3_to_cached(&pi[1 - 1], p); /* p */
ge25519_p3_dbl(&t2, p);
ge25519_p1p1_to_p3(&p2, &t2);
ge25519_p3_to_cached(&pi[2 - 1], &p2); /* 2p = 2*p */
ge25519_add(&t3, p, &pi[2 - 1]);
ge25519_p1p1_to_p3(&p3, &t3);
ge25519_p3_to_cached(&pi[3 - 1], &p3); /* 3p = 2p+p */
ge25519_p3_dbl(&t4, &p2);
ge25519_p1p1_to_p3(&p4, &t4);
ge25519_p3_to_cached(&pi[4 - 1], &p4); /* 4p = 2*2p */
ge25519_add(&t5, p, &pi[4 - 1]);
ge25519_p1p1_to_p3(&p5, &t5);
ge25519_p3_to_cached(&pi[5 - 1], &p5); /* 5p = 4p+p */
ge25519_p3_dbl(&t6, &p3);
ge25519_p1p1_to_p3(&p6, &t6);
ge25519_p3_to_cached(&pi[6 - 1], &p6); /* 6p = 2*3p */
ge25519_add(&t7, p, &pi[6 - 1]);
ge25519_p1p1_to_p3(&p7, &t7);
ge25519_p3_to_cached(&pi[7 - 1], &p7); /* 7p = 6p+p */
ge25519_p3_dbl(&t8, &p4);
ge25519_p1p1_to_p3(&p8, &t8);
ge25519_p3_to_cached(&pi[8 - 1], &p8); /* 8p = 2*4p */
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 * ((signed char) 1 << 4);
}
e[63] += carry;
/* each e[i] is between -8 and 8 */
ge25519_p3_0(h);
for (i = 63; i != 0; i--) {
ge25519_cmov8_cached(&t, pi, e[i]);
ge25519_add(&r, h, &t);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p3(h, &r); /* *16 */
}
ge25519_cmov8_cached(&t, pi, e[i]);
ge25519_add(&r, h, &t);
ge25519_p1p1_to_p3(h, &r);
}
/*
h = a * B (with precomputation)
where a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive
(as bytes: 0x5866666666666666666666666666666666666666666666666666666666666666)
Preconditions:
a[31] <= 127
*/
void
ge25519_scalarmult_base(ge25519_p3 *h, const unsigned char *a)
{
signed char e[64];
signed char carry;
ge25519_p1p1 r;
ge25519_p2 s;
ge25519_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 * ((signed char) 1 << 4);
}
e[63] += carry;
/* each e[i] is between -8 and 8 */
ge25519_p3_0(h);
for (i = 1; i < 64; i += 2) {
ge25519_cmov8_base(&t, i / 2, e[i]);
ge25519_madd(&r, h, &t);
ge25519_p1p1_to_p3(h, &r);
}
ge25519_p3_dbl(&r, h);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p2(&s, &r);
ge25519_p2_dbl(&r, &s);
ge25519_p1p1_to_p3(h, &r);
for (i = 0; i < 64; i += 2) {
ge25519_cmov8_base(&t, i / 2, e[i]);
ge25519_madd(&r, h, &t);
ge25519_p1p1_to_p3(h, &r);
}
}
/* multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493 */
static void
ge25519_mul_l(ge25519_p3 *r, const ge25519_p3 *A)
{
static const signed char aslide[253] = {
13, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
};
ge25519_cached Ai[8];
ge25519_p1p1 t;
ge25519_p3 u;
ge25519_p3 A2;
int i;
ge25519_p3_to_cached(&Ai[0], A);
ge25519_p3_dbl(&t, A);
ge25519_p1p1_to_p3(&A2, &t);
ge25519_add(&t, &A2, &Ai[0]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[1], &u);
ge25519_add(&t, &A2, &Ai[1]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[2], &u);
ge25519_add(&t, &A2, &Ai[2]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[3], &u);
ge25519_add(&t, &A2, &Ai[3]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[4], &u);
ge25519_add(&t, &A2, &Ai[4]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[5], &u);
ge25519_add(&t, &A2, &Ai[5]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[6], &u);
ge25519_add(&t, &A2, &Ai[6]);
ge25519_p1p1_to_p3(&u, &t);
ge25519_p3_to_cached(&Ai[7], &u);
ge25519_p3_0(r);
for (i = 252; i >= 0; --i) {
ge25519_p3_dbl(&t, r);
if (aslide[i] > 0) {
ge25519_p1p1_to_p3(&u, &t);
ge25519_add(&t, &u, &Ai[aslide[i] / 2]);
} else if (aslide[i] < 0) {
ge25519_p1p1_to_p3(&u, &t);
ge25519_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
}
ge25519_p1p1_to_p3(r, &t);
}
}
int
ge25519_is_on_curve(const ge25519_p3 *p)
{
fe25519 x2;
fe25519 y2;
fe25519 z2;
fe25519 z4;
fe25519 t0;
fe25519 t1;
fe25519_sq(x2, p->X);
fe25519_sq(y2, p->Y);
fe25519_sq(z2, p->Z);
fe25519_sub(t0, y2, x2);
fe25519_mul(t0, t0, z2);
fe25519_mul(t1, x2, y2);
fe25519_mul(t1, t1, d);
fe25519_sq(z4, z2);
fe25519_add(t1, t1, z4);
fe25519_sub(t0, t0, t1);
return fe25519_iszero(t0);
}
int
ge25519_is_on_main_subgroup(const ge25519_p3 *p)
{
ge25519_p3 pl;
ge25519_mul_l(&pl, p);
return fe25519_iszero(pl.X);
}
int
ge25519_is_canonical(const unsigned char *s)
{
unsigned char c;
unsigned char d;
unsigned int i;
c = (s[31] & 0x7f) ^ 0x7f;
for (i = 30; i > 0; i--) {
c |= s[i] ^ 0xff;
}
c = (((unsigned int) c) - 1U) >> 8;
d = (0xed - 1U - (unsigned int) s[0]) >> 8;
return 1 - (c & d & 1);
}
int
ge25519_has_small_order(const unsigned char s[32])
{
CRYPTO_ALIGN(16)
static const unsigned char blacklist[][32] = {
/* 0 (order 4) */
{ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
/* 1 (order 1) */
{ 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
/* 2707385501144840649318225287225658788936804267575313519463743609750303402022
(order 8) */
{ 0x26, 0xe8, 0x95, 0x8f, 0xc2, 0xb2, 0x27, 0xb0, 0x45, 0xc3, 0xf4,
0x89, 0xf2, 0xef, 0x98, 0xf0, 0xd5, 0xdf, 0xac, 0x05, 0xd3, 0xc6,
0x33, 0x39, 0xb1, 0x38, 0x02, 0x88, 0x6d, 0x53, 0xfc, 0x05 },
/* 55188659117513257062467267217118295137698188065244968500265048394206261417927
(order 8) */
{ 0xc7, 0x17, 0x6a, 0x70, 0x3d, 0x4d, 0xd8, 0x4f, 0xba, 0x3c, 0x0b,
0x76, 0x0d, 0x10, 0x67, 0x0f, 0x2a, 0x20, 0x53, 0xfa, 0x2c, 0x39,
0xcc, 0xc6, 0x4e, 0xc7, 0xfd, 0x77, 0x92, 0xac, 0x03, 0x7a },
/* p-1 (order 2) */
{ 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f },
/* p (=0, order 4) */
{ 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f },
/* p+1 (=1, order 1) */
{ 0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f }
};
unsigned char c[7] = { 0 };
unsigned int k;
size_t i, j;
#define COMPILER_ASSERT(X) (void) sizeof(char[(X) ? 1 : -1])
COMPILER_ASSERT(7 == sizeof blacklist / sizeof blacklist[0]);
for (j = 0; j < 31; j++) {
for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) {
c[i] |= s[j] ^ blacklist[i][j];
}
}
for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) {
c[i] |= (s[j] & 0x7f) ^ blacklist[i][j];
}
k = 0;
for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) {
k |= (c[i] - 1);
}
return (int) ((k >> 8) & 1);
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
b[0]+256*b[1]+...+256^31*b[31] = b
*
Output:
s[0]+256*s[1]+...+256^31*s[31] = (ab) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
void
sc25519_mul(unsigned char s[32], const unsigned char a[32], const unsigned char b[32])
{
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 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 = a0 * b0;
s1 = a0 * b1 + a1 * b0;
s2 = a0 * b2 + a1 * b1 + a2 * b0;
s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
a6 * b1 + a7 * b0;
s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
a6 * b2 + a7 * b1 + a8 * b0;
s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
s11 = 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 + (int64_t) (1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry18 = (s18 + (int64_t) (1L << 20)) >> 21;
s19 += carry18;
s18 -= carry18 * ((uint64_t) 1L << 21);
carry20 = (s20 + (int64_t) (1L << 20)) >> 21;
s21 += carry20;
s20 -= carry20 * ((uint64_t) 1L << 21);
carry22 = (s22 + (int64_t) (1L << 20)) >> 21;
s23 += carry22;
s22 -= carry22 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
carry17 = (s17 + (int64_t) (1L << 20)) >> 21;
s18 += carry17;
s17 -= carry17 * ((uint64_t) 1L << 21);
carry19 = (s19 + (int64_t) (1L << 20)) >> 21;
s20 += carry19;
s19 -= carry19 * ((uint64_t) 1L << 21);
carry21 = (s21 + (int64_t) (1L << 20)) >> 21;
s22 += carry21;
s21 -= carry21 * ((uint64_t) 1L << 21);
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 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 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 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
sc25519_muladd(unsigned char s[32], const unsigned char a[32],
const unsigned char b[32], const unsigned char c[32])
{
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 + (int64_t) (1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry18 = (s18 + (int64_t) (1L << 20)) >> 21;
s19 += carry18;
s18 -= carry18 * ((uint64_t) 1L << 21);
carry20 = (s20 + (int64_t) (1L << 20)) >> 21;
s21 += carry20;
s20 -= carry20 * ((uint64_t) 1L << 21);
carry22 = (s22 + (int64_t) (1L << 20)) >> 21;
s23 += carry22;
s22 -= carry22 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
carry17 = (s17 + (int64_t) (1L << 20)) >> 21;
s18 += carry17;
s17 -= carry17 * ((uint64_t) 1L << 21);
carry19 = (s19 + (int64_t) (1L << 20)) >> 21;
s20 += carry19;
s19 -= carry19 * ((uint64_t) 1L << 21);
carry21 = (s21 + (int64_t) (1L << 20)) >> 21;
s22 += carry21;
s21 -= carry21 * ((uint64_t) 1L << 21);
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 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 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
/*
Input:
a[0]+256*a[1]+...+256^31*a[31] = a
*
Output:
s[0]+256*s[1]+...+256^31*s[31] = a^2 mod l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
static inline void
sc25519_sq(unsigned char *s, const unsigned char *a)
{
sc25519_mul(s, a, a);
}
/*
Input:
s[0]+256*a[1]+...+256^31*a[31] = a
n
*
Output:
s[0]+256*s[1]+...+256^31*s[31] = x * s^(s^n) mod l
where l = 2^252 + 27742317777372353535851937790883648493.
Overwrites s in place.
*/
static inline void
sc25519_sqmul(unsigned char s[32], const int n, const unsigned char a[32])
{
int i;
for (i = 0; i < n; i++) {
sc25519_sq(s, s);
}
sc25519_mul(s, s, a);
}
void
sc25519_invert(unsigned char recip[32], const unsigned char s[32])
{
unsigned char _10[32], _100[32], _11[32], _101[32], _111[32],
_1001[32], _1011[32], _1111[32];
sc25519_sq(_10, s);
sc25519_sq(_100, _10);
sc25519_mul(_11, _10, s);
sc25519_mul(_101, _10, _11);
sc25519_mul(_111, _10, _101);
sc25519_mul(_1001, _10, _111);
sc25519_mul(_1011, _10, _1001);
sc25519_mul(_1111, _100, _1011);
sc25519_mul(recip, _1111, s);
sc25519_sqmul(recip, 123 + 3, _101);
sc25519_sqmul(recip, 2 + 2, _11);
sc25519_sqmul(recip, 1 + 4, _1111);
sc25519_sqmul(recip, 1 + 4, _1111);
sc25519_sqmul(recip, 4, _1001);
sc25519_sqmul(recip, 2, _11);
sc25519_sqmul(recip, 1 + 4, _1111);
sc25519_sqmul(recip, 1 + 3, _101);
sc25519_sqmul(recip, 3 + 3, _101);
sc25519_sqmul(recip, 3, _111);
sc25519_sqmul(recip, 1 + 4, _1111);
sc25519_sqmul(recip, 2 + 3, _111);
sc25519_sqmul(recip, 2 + 2, _11);
sc25519_sqmul(recip, 1 + 4, _1011);
sc25519_sqmul(recip, 2 + 4, _1011);
sc25519_sqmul(recip, 6 + 4, _1001);
sc25519_sqmul(recip, 2 + 2, _11);
sc25519_sqmul(recip, 3 + 2, _11);
sc25519_sqmul(recip, 3 + 2, _11);
sc25519_sqmul(recip, 1 + 4, _1001);
sc25519_sqmul(recip, 1 + 3, _111);
sc25519_sqmul(recip, 2 + 4, _1111);
sc25519_sqmul(recip, 1 + 4, _1011);
sc25519_sqmul(recip, 3, _101);
sc25519_sqmul(recip, 2 + 4, _1111);
sc25519_sqmul(recip, 3, _101);
sc25519_sqmul(recip, 1 + 2, _11);
}
/*
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
sc25519_reduce(unsigned char s[64])
{
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;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
s13 += carry12;
s12 -= carry12 * ((uint64_t) 1L << 21);
carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
s15 += carry14;
s14 -= carry14 * ((uint64_t) 1L << 21);
carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
s17 += carry16;
s16 -= carry16 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
s14 += carry13;
s13 -= carry13 * ((uint64_t) 1L << 21);
carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
s16 += carry15;
s15 -= carry15 * ((uint64_t) 1L << 21);
s5 += s17 * 666643;
s6 += s17 * 470296;
s7 += s17 * 654183;
s8 -= s17 * 997805;
s9 += s17 * 136657;
s10 -= s17 * 683901;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
s12 = 0;
carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 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 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
carry11 = s11 >> 21;
s12 += carry11;
s11 -= carry11 * ((uint64_t) 1L << 21);
s0 += s12 * 666643;
s1 += s12 * 470296;
s2 += s12 * 654183;
s3 -= s12 * 997805;
s4 += s12 * 136657;
s5 -= s12 * 683901;
carry0 = s0 >> 21;
s1 += carry0;
s0 -= carry0 * ((uint64_t) 1L << 21);
carry1 = s1 >> 21;
s2 += carry1;
s1 -= carry1 * ((uint64_t) 1L << 21);
carry2 = s2 >> 21;
s3 += carry2;
s2 -= carry2 * ((uint64_t) 1L << 21);
carry3 = s3 >> 21;
s4 += carry3;
s3 -= carry3 * ((uint64_t) 1L << 21);
carry4 = s4 >> 21;
s5 += carry4;
s4 -= carry4 * ((uint64_t) 1L << 21);
carry5 = s5 >> 21;
s6 += carry5;
s5 -= carry5 * ((uint64_t) 1L << 21);
carry6 = s6 >> 21;
s7 += carry6;
s6 -= carry6 * ((uint64_t) 1L << 21);
carry7 = s7 >> 21;
s8 += carry7;
s7 -= carry7 * ((uint64_t) 1L << 21);
carry8 = s8 >> 21;
s9 += carry8;
s8 -= carry8 * ((uint64_t) 1L << 21);
carry9 = s9 >> 21;
s10 += carry9;
s9 -= carry9 * ((uint64_t) 1L << 21);
carry10 = s10 >> 21;
s11 += carry10;
s10 -= carry10 * ((uint64_t) 1L << 21);
s[0] = s0 >> 0;
s[1] = s0 >> 8;
s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
s[3] = s1 >> 3;
s[4] = s1 >> 11;
s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
s[6] = s2 >> 6;
s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
s[8] = s3 >> 1;
s[9] = s3 >> 9;
s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
s[11] = s4 >> 4;
s[12] = s4 >> 12;
s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
s[14] = s5 >> 7;
s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
s[16] = s6 >> 2;
s[17] = s6 >> 10;
s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
s[19] = s7 >> 5;
s[20] = s7 >> 13;
s[21] = s8 >> 0;
s[22] = s8 >> 8;
s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
s[24] = s9 >> 3;
s[25] = s9 >> 11;
s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
s[27] = s10 >> 6;
s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
s[29] = s11 >> 1;
s[30] = s11 >> 9;
s[31] = s11 >> 17;
}
int
sc25519_is_canonical(const unsigned char s[32])
{
/* 2^252+27742317777372353535851937790883648493 */
static const unsigned char L[32] = {
0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7,
0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
};
unsigned char c = 0;
unsigned char n = 1;
unsigned int i = 32;
do {
i--;
c |= ((s[i] - L[i]) >> 8) & n;
n &= ((s[i] ^ L[i]) - 1) >> 8;
} while (i != 0);
return (c != 0);
}
static void
chi25519(fe25519 out, const fe25519 z)
{
fe25519 t0, t1, t2, t3;
int i;
fe25519_sq(t0, z);
fe25519_mul(t1, t0, z);
fe25519_sq(t0, t1);
fe25519_sq(t2, t0);
fe25519_sq(t2, t2);
fe25519_mul(t2, t2, t0);
fe25519_mul(t1, t2, z);
fe25519_sq(t2, t1);
for (i = 1; i < 5; i++) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t2, t1);
for (i = 1; i < 10; i++) {
fe25519_sq(t2, t2);
}
fe25519_mul(t2, t2, t1);
fe25519_sq(t3, t2);
for (i = 1; i < 20; i++) {
fe25519_sq(t3, t3);
}
fe25519_mul(t2, t3, t2);
fe25519_sq(t2, t2);
for (i = 1; i < 10; i++) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t2, t1);
for (i = 1; i < 50; i++) {
fe25519_sq(t2, t2);
}
fe25519_mul(t2, t2, t1);
fe25519_sq(t3, t2);
for (i = 1; i < 100; i++) {
fe25519_sq(t3, t3);
}
fe25519_mul(t2, t3, t2);
fe25519_sq(t2, t2);
for (i = 1; i < 50; i++) {
fe25519_sq(t2, t2);
}
fe25519_mul(t1, t2, t1);
fe25519_sq(t1, t1);
for (i = 1; i < 4; i++) {
fe25519_sq(t1, t1);
}
fe25519_mul(out, t1, t0);
}
static void
ge25519_elligator2(unsigned char s[32], const fe25519 r, const unsigned char x_sign)
{
fe25519 e;
fe25519 negx;
fe25519 rr2;
fe25519 x, x2, x3;
ge25519_p3 p3;
ge25519_p1p1 p1;
ge25519_p2 p2;
unsigned int e_is_minus_1;
fe25519_sq2(rr2, r);
rr2[0]++;
fe25519_invert(rr2, rr2);
fe25519_mul(x, curve25519_A, rr2);
fe25519_neg(x, x);
fe25519_sq(x2, x);
fe25519_mul(x3, x, x2);
fe25519_add(e, x3, x);
fe25519_mul(x2, x2, curve25519_A);
fe25519_add(e, x2, e);
chi25519(e, e);
fe25519_tobytes(s, e);
e_is_minus_1 = s[1] & 1;
fe25519_neg(negx, x);
fe25519_cmov(x, negx, e_is_minus_1);
fe25519_0(x2);
fe25519_cmov(x2, curve25519_A, e_is_minus_1);
fe25519_sub(x, x, x2);
/* yed = (x-1)/(x+1) */
{
fe25519 one;
fe25519 x_plus_one;
fe25519 x_plus_one_inv;
fe25519 x_minus_one;
fe25519 yed;
fe25519_1(one);
fe25519_add(x_plus_one, x, one);
fe25519_sub(x_minus_one, x, one);
fe25519_invert(x_plus_one_inv, x_plus_one);
fe25519_mul(yed, x_minus_one, x_plus_one_inv);
fe25519_tobytes(s, yed);
}
/* recover x */
s[31] |= x_sign;
if (ge25519_frombytes(&p3, s) != 0) {
abort(); /* LCOV_EXCL_LINE */
}
/* multiply by the cofactor */
ge25519_p3_dbl(&p1, &p3);
ge25519_p1p1_to_p2(&p2, &p1);
ge25519_p2_dbl(&p1, &p2);
ge25519_p1p1_to_p2(&p2, &p1);
ge25519_p2_dbl(&p1, &p2);
ge25519_p1p1_to_p3(&p3, &p1);
ge25519_p3_tobytes(s, &p3);
}
void
ge25519_from_uniform(unsigned char s[32], const unsigned char r[32])
{
fe25519 r_fe;
unsigned char x_sign;
memcpy(s, r, 32);
x_sign = s[31] & 0x80;
s[31] &= 0x7f;
fe25519_frombytes(r_fe, s);
ge25519_elligator2(s, r_fe, x_sign);
}
void
ge25519_from_hash(unsigned char s[32], const unsigned char h[64])
{
unsigned char fl[32];
unsigned char gl[32];
fe25519 fe_f;
fe25519 fe_g;
size_t i;
unsigned char x_sign;
x_sign = h[0] & 0x80;
for (i = 0; i < 32; i++) {
fl[i] = h[63 - i];
gl[i] = h[31 - i];
}
fl[31] &= 0x7f;
gl[31] &= 0x7f;
fe25519_frombytes(fe_f, fl);
fe25519_frombytes(fe_g, gl);
fe_f[0] += (h[32] >> 7) * 19;
for (i = 0; i < sizeof (fe25519) / sizeof fe_f[0]; i++) {
fe_f[i] += 38 * fe_g[i];
}
fe25519_reduce(fe_f, fe_f);
ge25519_elligator2(s, fe_f, x_sign);
}
/* Ristretto group */
static int
ristretto255_sqrt_ratio_m1(fe25519 x, const fe25519 u, const fe25519 v)
{
fe25519 v3;
fe25519 vxx;
fe25519 m_root_check, p_root_check, f_root_check;
fe25519 x_sqrtm1;
int has_m_root, has_p_root, has_f_root;
fe25519_sq(v3, v);
fe25519_mul(v3, v3, v); /* v3 = v^3 */
fe25519_sq(x, v3);
fe25519_mul(x, x, v);
fe25519_mul(x, x, u); /* x = uv^7 */
fe25519_pow22523(x, x); /* x = (uv^7)^((q-5)/8) */
fe25519_mul(x, x, v3);
fe25519_mul(x, x, u); /* x = uv^3(uv^7)^((q-5)/8) */
fe25519_sq(vxx, x);
fe25519_mul(vxx, vxx, v); /* vx^2 */
fe25519_sub(m_root_check, vxx, u); /* vx^2-u */
fe25519_add(p_root_check, vxx, u); /* vx^2+u */
fe25519_mul(f_root_check, u, sqrtm1); /* u*sqrt(-1) */
fe25519_add(f_root_check, vxx, f_root_check); /* vx^2+u*sqrt(-1) */
has_m_root = fe25519_iszero(m_root_check);
has_p_root = fe25519_iszero(p_root_check);
has_f_root = fe25519_iszero(f_root_check);
fe25519_mul(x_sqrtm1, x, sqrtm1); /* x*sqrt(-1) */
fe25519_cmov(x, x_sqrtm1, has_p_root | has_f_root);
fe25519_abs(x, x);
return has_m_root | has_p_root;
}
static int
ristretto255_is_canonical(const unsigned char *s)
{
unsigned char c;
unsigned char d;
unsigned int i;
c = (s[31] & 0x7f) ^ 0x7f;
for (i = 30; i > 0; i--) {
c |= s[i] ^ 0xff;
}
c = (((unsigned int) c) - 1U) >> 8;
d = (0xed - 1U - (unsigned int) s[0]) >> 8;
return 1 - (((c & d) | s[0]) & 1);
}
int
ristretto255_frombytes(ge25519_p3 *h, const unsigned char *s)
{
fe25519 inv_sqrt;
fe25519 one;
fe25519 s_;
fe25519 ss;
fe25519 u1, u2;
fe25519 u1u1, u2u2;
fe25519 v;
fe25519 v_u2u2;
int was_square;
if (ristretto255_is_canonical(s) == 0) {
return -1;
}
fe25519_frombytes(s_, s);
fe25519_sq(ss, s_); /* ss = s^2 */
fe25519_1(u1);
fe25519_sub(u1, u1, ss); /* u1 = 1-ss */
fe25519_sq(u1u1, u1); /* u1u1 = u1^2 */
fe25519_1(u2);
fe25519_add(u2, u2, ss); /* u2 = 1+ss */
fe25519_sq(u2u2, u2); /* u2u2 = u2^2 */
fe25519_mul(v, d, u1u1); /* v = d*u1^2 */
fe25519_neg(v, v); /* v = -d*u1^2 */
fe25519_sub(v, v, u2u2); /* v = -(d*u1^2)-u2^2 */
fe25519_mul(v_u2u2, v, u2u2); /* v_u2u2 = v*u2^2 */
fe25519_1(one);
was_square = ristretto255_sqrt_ratio_m1(inv_sqrt, one, v_u2u2);
fe25519_mul(h->X, inv_sqrt, u2);
fe25519_mul(h->Y, inv_sqrt, h->X);
fe25519_mul(h->Y, h->Y, v);
fe25519_mul(h->X, h->X, s_);
fe25519_add(h->X, h->X, h->X);
fe25519_abs(h->X, h->X);
fe25519_mul(h->Y, u1, h->Y);
fe25519_1(h->Z);
fe25519_mul(h->T, h->X, h->Y);
return - ((1 - was_square) |
fe25519_isnegative(h->T) | fe25519_iszero(h->Y));
}
void
ristretto255_p3_tobytes(unsigned char *s, const ge25519_p3 *h)
{
fe25519 den1, den2;
fe25519 den_inv;
fe25519 eden;
fe25519 inv_sqrt;
fe25519 ix, iy;
fe25519 one;
fe25519 s_;
fe25519 t_z_inv;
fe25519 u1, u2;
fe25519 u1_u2u2;
fe25519 x_, y_;
fe25519 x_z_inv;
fe25519 z_inv;
fe25519 zmy;
int rotate;
fe25519_add(u1, h->Z, h->Y); /* u1 = Z+Y */
fe25519_sub(zmy, h->Z, h->Y); /* zmy = Z-Y */
fe25519_mul(u1, u1, zmy); /* u1 = (Z+Y)*(Z-Y) */
fe25519_mul(u2, h->X, h->Y); /* u2 = X*Y */
fe25519_sq(u1_u2u2, u2); /* u1_u2u2 = u2^2 */
fe25519_mul(u1_u2u2, u1, u1_u2u2); /* u1_u2u2 = u1*u2^2 */
fe25519_1(one);
(void) ristretto255_sqrt_ratio_m1(inv_sqrt, one, u1_u2u2);
fe25519_mul(den1, inv_sqrt, u1); /* den1 = inv_sqrt*u1 */
fe25519_mul(den2, inv_sqrt, u2); /* den2 = inv_sqrt*u2 */
fe25519_mul(z_inv, den1, den2); /* z_inv = den1*den2 */
fe25519_mul(z_inv, z_inv, h->T); /* z_inv = den1*den2*T */
fe25519_mul(ix, h->X, sqrtm1); /* ix = X*sqrt(-1) */
fe25519_mul(iy, h->Y, sqrtm1); /* iy = Y*sqrt(-1) */
fe25519_mul(eden, den1, invsqrtamd); /* eden = den1*sqrt(a-d) */
fe25519_mul(t_z_inv, h->T, z_inv); /* t_z_inv = T*z_inv */
rotate = fe25519_isnegative(t_z_inv);
fe25519_copy(x_, h->X);
fe25519_copy(y_, h->Y);
fe25519_copy(den_inv, den2);
fe25519_cmov(x_, iy, rotate);
fe25519_cmov(y_, ix, rotate);
fe25519_cmov(den_inv, eden, rotate);
fe25519_mul(x_z_inv, x_, z_inv);
fe25519_cneg(y_, y_, fe25519_isnegative(x_z_inv));
fe25519_sub(s_, h->Z, y_);
fe25519_mul(s_, den_inv, s_);
fe25519_abs(s_, s_);
fe25519_tobytes(s, s_);
}
static void
ristretto255_elligator(ge25519_p3 *p, const fe25519 t)
{
fe25519 c;
fe25519 n;
fe25519 one;
fe25519 r;
fe25519 rpd;
fe25519 s, s_prime;
fe25519 ss;
fe25519 u, v;
fe25519 w0, w1, w2, w3;
int wasnt_square;
fe25519_1(one);
fe25519_sq(r, t); /* r = t^2 */
fe25519_mul(r, sqrtm1, r); /* r = sqrt(-1)*t^2 */
fe25519_add(u, r, one); /* u = r+1 */
fe25519_mul(u, u, onemsqd); /* u = (r+1)*(1-d^2) */
fe25519_1(c);
fe25519_neg(c, c); /* c = -1 */
fe25519_add(rpd, r, d); /* rpd = r*d */
fe25519_mul(v, r, d); /* v = r*d */
fe25519_sub(v, c, v); /* v = c-r*d */
fe25519_mul(v, v, rpd); /* v = (c-r*d)*(r+d) */
wasnt_square = 1 - ristretto255_sqrt_ratio_m1(s, u, v);
fe25519_mul(s_prime, s, t);
fe25519_abs(s_prime, s_prime);
fe25519_neg(s_prime, s_prime); /* s_prime = -|s*t| */
fe25519_cmov(s, s_prime, wasnt_square);
fe25519_cmov(c, r, wasnt_square);
fe25519_sub(n, r, one); /* n = r-1 */
fe25519_mul(n, n, c); /* n = c*(r-1) */
fe25519_mul(n, n, sqdmone); /* n = c*(r-1)*(d-1)^2 */
fe25519_sub(n, n, v); /* n = c*(r-1)*(d-1)^2-v */
fe25519_add(w0, s, s); /* w0 = 2s */
fe25519_mul(w0, w0, v); /* w0 = 2s*v */
fe25519_mul(w1, n, sqrtadm1); /* w1 = n*sqrt(ad-1) */
fe25519_sq(ss, s); /* ss = s^2 */
fe25519_sub(w2, one, ss); /* w2 = 1-s^2 */
fe25519_add(w3, one, ss); /* w3 = 1+s^2 */
fe25519_mul(p->X, w0, w3);
fe25519_mul(p->Y, w2, w1);
fe25519_mul(p->Z, w1, w3);
fe25519_mul(p->T, w0, w2);
}
void
ristretto255_from_hash(unsigned char s[32], const unsigned char h[64])
{
fe25519 r0, r1;
ge25519_cached p1_cached;
ge25519_p1p1 p_p1p1;
ge25519_p3 p0, p1;
ge25519_p3 p;
fe25519_frombytes(r0, h);
fe25519_frombytes(r1, h + 32);
ristretto255_elligator(&p0, r0);
ristretto255_elligator(&p1, r1);
ge25519_p3_to_cached(&p1_cached, &p1);
ge25519_add(&p_p1p1, &p0, &p1_cached);
ge25519_p1p1_to_p3(&p, &p_p1p1);
ristretto255_p3_tobytes(s, &p);
}
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