/*
* Copyright 2017-2019 The OpenSSL Project Authors. All Rights Reserved.
* Copyright 2015-2016 Cryptography Research, Inc.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*
* Originally written by Mike Hamburg
*/
#include <openssl/crypto.h>
#include "word.h"
#include "point_448.h"
static const c448_word_t MONTGOMERY_FACTOR = (c448_word_t) 0x3bd440fae918bc5ULL;
static const curve448_scalar_t sc_p = {
{
{
SC_LIMB(0x2378c292ab5844f3ULL), SC_LIMB(0x216cc2728dc58f55ULL),
SC_LIMB(0xc44edb49aed63690ULL), SC_LIMB(0xffffffff7cca23e9ULL),
SC_LIMB(0xffffffffffffffffULL), SC_LIMB(0xffffffffffffffffULL),
SC_LIMB(0x3fffffffffffffffULL)
}
}
}, sc_r2 = {
{
{
SC_LIMB(0xe3539257049b9b60ULL), SC_LIMB(0x7af32c4bc1b195d9ULL),
SC_LIMB(0x0d66de2388ea1859ULL), SC_LIMB(0xae17cf725ee4d838ULL),
SC_LIMB(0x1a9cc14ba3c47c44ULL), SC_LIMB(0x2052bcb7e4d070afULL),
SC_LIMB(0x3402a939f823b729ULL)
}
}
};
#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
const curve448_scalar_t curve448_scalar_one = {{{1}}};
const curve448_scalar_t curve448_scalar_zero = {{{0}}};
/*
* {extra,accum} - sub +? p
* Must have extra <= 1
*/
static void sc_subx(curve448_scalar_t out,
const c448_word_t accum[C448_SCALAR_LIMBS],
const curve448_scalar_t sub,
const curve448_scalar_t p, c448_word_t extra)
{
c448_dsword_t chain = 0;
unsigned int i;
c448_word_t borrow;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + accum[i]) - sub->limb[i];
out->limb[i] = (c448_word_t)chain;
chain >>= WBITS;
}
borrow = (c448_word_t)chain + extra; /* = 0 or -1 */
chain = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + out->limb[i]) + (p->limb[i] & borrow);
out->limb[i] = (c448_word_t)chain;
chain >>= WBITS;
}
}
static void sc_montmul(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
unsigned int i, j;
c448_word_t accum[C448_SCALAR_LIMBS + 1] = { 0 };
c448_word_t hi_carry = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
c448_word_t mand = a->limb[i];
const c448_word_t *mier = b->limb;
c448_dword_t chain = 0;
for (j = 0; j < C448_SCALAR_LIMBS; j++) {
chain += ((c448_dword_t) mand) * mier[j] + accum[j];
accum[j] = (c448_word_t)chain;
chain >>= WBITS;
}
accum[j] = (c448_word_t)chain;
mand = accum[0] * MONTGOMERY_FACTOR;
chain = 0;
mier = sc_p->limb;
for (j = 0; j < C448_SCALAR_LIMBS; j++) {
chain += (c448_dword_t) mand *mier[j] + accum[j];
if (j)
accum[j - 1] = (c448_word_t)chain;
chain >>= WBITS;
}
chain += accum[j];
chain += hi_carry;
accum[j - 1] = (c448_word_t)chain;
hi_carry = chain >> WBITS;
}
sc_subx(out, accum, sc_p, sc_p, hi_carry);
}
void curve448_scalar_mul(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
sc_montmul(out, a, b);
sc_montmul(out, out, sc_r2);
}
void curve448_scalar_sub(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
sc_subx(out, a->limb, b, sc_p, 0);
}
void curve448_scalar_add(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
c448_dword_t chain = 0;
unsigned int i;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + a->limb[i]) + b->limb[i];
out->limb[i] = (c448_word_t)chain;
chain >>= WBITS;
}
sc_subx(out, out->limb, sc_p, sc_p, (c448_word_t)chain);
}
static ossl_inline void scalar_decode_short(curve448_scalar_t s,
const unsigned char *ser,
size_t nbytes)
{
size_t i, j, k = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
c448_word_t out = 0;
for (j = 0; j < sizeof(c448_word_t) && k < nbytes; j++, k++)
out |= ((c448_word_t) ser[k]) << (8 * j);
s->limb[i] = out;
}
}
c448_error_t curve448_scalar_decode(
curve448_scalar_t s,
const unsigned char ser[C448_SCALAR_BYTES])
{
unsigned int i;
c448_dsword_t accum = 0;
scalar_decode_short(s, ser, C448_SCALAR_BYTES);
for (i = 0; i < C448_SCALAR_LIMBS; i++)
accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS;
/* Here accum == 0 or -1 */
curve448_scalar_mul(s, s, curve448_scalar_one); /* ham-handed reduce */
return c448_succeed_if(~word_is_zero((uint32_t)accum));
}
void curve448_scalar_destroy(curve448_scalar_t scalar)
{
OPENSSL_cleanse(scalar, sizeof(curve448_scalar_t));
}
void curve448_scalar_decode_long(curve448_scalar_t s,
const unsigned char *ser, size_t ser_len)
{
size_t i;
curve448_scalar_t t1, t2;
if (ser_len == 0) {
curve448_scalar_copy(s, curve448_scalar_zero);
return;
}
i = ser_len - (ser_len % C448_SCALAR_BYTES);
if (i == ser_len)
i -= C448_SCALAR_BYTES;
scalar_decode_short(t1, &ser[i], ser_len - i);
if (ser_len == sizeof(curve448_scalar_t)) {
assert(i == 0);
/* ham-handed reduce */
curve448_scalar_mul(s, t1, curve448_scalar_one);
curve448_scalar_destroy(t1);
return;
}
while (i) {
i -= C448_SCALAR_BYTES;
sc_montmul(t1, t1, sc_r2);
(void)curve448_scalar_decode(t2, ser + i);
curve448_scalar_add(t1, t1, t2);
}
curve448_scalar_copy(s, t1);
curve448_scalar_destroy(t1);
curve448_scalar_destroy(t2);
}
void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
const curve448_scalar_t s)
{
unsigned int i, j, k = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
for (j = 0; j < sizeof(c448_word_t); j++, k++)
ser[k] = s->limb[i] >> (8 * j);
}
}
void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a)
{
c448_word_t mask = 0 - (a->limb[0] & 1);
c448_dword_t chain = 0;
unsigned int i;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask);
out->limb[i] = (c448_word_t)chain;
chain >>= C448_WORD_BITS;
}
for (i = 0; i < C448_SCALAR_LIMBS - 1; i++)
out->limb[i] = out->limb[i] >> 1 | out->limb[i + 1] << (WBITS - 1);
out->limb[i] = out->limb[i] >> 1 | (c448_word_t)(chain << (WBITS - 1));
}