mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-15 20:19:23 +00:00
588 lines
13 KiB
C
588 lines
13 KiB
C
/**
|
|
* Copyright (c) 2013-2014 Tomas Dzetkulic
|
|
* Copyright (c) 2013-2014 Pavol Rusnak
|
|
*
|
|
* Permission is hereby granted, free of charge, to any person obtaining
|
|
* a copy of this software and associated documentation files (the "Software"),
|
|
* to deal in the Software without restriction, including without limitation
|
|
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
|
|
* and/or sell copies of the Software, and to permit persons to whom the
|
|
* Software is furnished to do so, subject to the following conditions:
|
|
*
|
|
* The above copyright notice and this permission notice shall be included
|
|
* in all copies or substantial portions of the Software.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
|
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
|
|
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES
|
|
* OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
|
|
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
|
* OTHER DEALINGS IN THE SOFTWARE.
|
|
*/
|
|
|
|
#include <stdio.h>
|
|
#include <string.h>
|
|
#include "bignum.h"
|
|
#include "secp256k1.h"
|
|
|
|
inline uint32_t read_be(const uint8_t *data)
|
|
{
|
|
return (((uint32_t)data[0]) << 24) |
|
|
(((uint32_t)data[1]) << 16) |
|
|
(((uint32_t)data[2]) << 8) |
|
|
(((uint32_t)data[3]));
|
|
}
|
|
|
|
inline void write_be(uint8_t *data, uint32_t x)
|
|
{
|
|
data[0] = x >> 24;
|
|
data[1] = x >> 16;
|
|
data[2] = x >> 8;
|
|
data[3] = x;
|
|
}
|
|
|
|
void bn_read_be(const uint8_t *in_number, bignum256 *out_number)
|
|
{
|
|
int i;
|
|
uint64_t temp = 0;
|
|
for (i = 0; i < 8; i++) {
|
|
temp += (((uint64_t)read_be(in_number + (7 - i) * 4)) << (2 * i));
|
|
out_number->val[i]= temp & 0x3FFFFFFF;
|
|
temp >>= 30;
|
|
}
|
|
out_number->val[8] = temp;
|
|
}
|
|
|
|
void bn_write_be(const bignum256 *in_number, uint8_t *out_number)
|
|
{
|
|
int i, shift = 30 + 16 - 32;
|
|
uint64_t temp = in_number->val[8];
|
|
for (i = 0; i < 8; i++) {
|
|
temp <<= 30;
|
|
temp |= in_number->val[7 - i];
|
|
write_be(out_number + i * 4, temp >> shift);
|
|
shift -= 2;
|
|
}
|
|
}
|
|
|
|
void bn_zero(bignum256 *a)
|
|
{
|
|
int i;
|
|
for (i = 0; i < 9; i++) {
|
|
a->val[i] = 0;
|
|
}
|
|
}
|
|
|
|
int bn_is_zero(const bignum256 *a)
|
|
{
|
|
int i;
|
|
for (i = 0; i < 9; i++) {
|
|
if (a->val[i] != 0) return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
int bn_is_less(const bignum256 *a, const bignum256 *b)
|
|
{
|
|
int i;
|
|
for (i = 8; i >= 0; i--) {
|
|
if (a->val[i] < b->val[i]) return 1;
|
|
if (a->val[i] > b->val[i]) return 0;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
int bn_is_equal(const bignum256 *a, const bignum256 *b) {
|
|
int i;
|
|
for (i = 0; i < 9; i++) {
|
|
if (a->val[i] != b->val[i]) return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
int bn_bitlen(const bignum256 *a) {
|
|
int i = 8, j;
|
|
while (i >= 0 && a->val[i] == 0) i--;
|
|
if (i == -1) return 0;
|
|
j = 29;
|
|
while ((a->val[i] & (1 << j)) == 0) j--;
|
|
return i * 30 + j + 1;
|
|
}
|
|
|
|
void bn_lshift(bignum256 *a)
|
|
{
|
|
int i;
|
|
for (i = 8; i > 0; i--) {
|
|
a->val[i] = ((a->val[i] << 1) & 0x3FFFFFFF) | ((a->val[i - 1] & 0x20000000) >> 29);
|
|
}
|
|
a->val[0] = (a->val[0] << 1) & 0x3FFFFFFF;
|
|
}
|
|
|
|
void bn_rshift(bignum256 *a)
|
|
{
|
|
int i;
|
|
for (i = 0; i < 8; i++) {
|
|
a->val[i] = (a->val[i] >> 1) | ((a->val[i + 1] & 1) << 29);
|
|
}
|
|
a->val[8] >>= 1;
|
|
}
|
|
|
|
// assumes x < 2*prime, result < prime
|
|
void bn_mod(bignum256 *x, const bignum256 *prime)
|
|
{
|
|
int i = 8;
|
|
uint32_t temp;
|
|
// compare numbers
|
|
while (i >= 0 && prime->val[i] == x->val[i]) i--;
|
|
// if equal
|
|
if (i == -1) {
|
|
// set x to zero
|
|
bn_zero(x);
|
|
} else {
|
|
// if x is greater
|
|
if (x->val[i] > prime->val[i]) {
|
|
// substract p from x
|
|
temp = 0x40000000u;
|
|
for (i = 0; i < 9; i++) {
|
|
temp += x->val[i] - prime->val[i];
|
|
x->val[i] = temp & 0x3FFFFFFF;
|
|
temp >>= 30;
|
|
temp += 0x3FFFFFFFu;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// a = a + b
|
|
void bn_addi(bignum256 *a, uint32_t b)
|
|
{
|
|
uint64_t t = a->val[0];
|
|
t += b;
|
|
a->val[0] = t & 0x3FFFFFFFu;
|
|
t >>= 30;
|
|
a->val[1] += t;
|
|
}
|
|
|
|
// a = a * b
|
|
void bn_muli(bignum256 *a, uint32_t b)
|
|
{
|
|
uint64_t t = 0;
|
|
int i;
|
|
for (i = 0; i < 8; i++) {
|
|
t = (uint64_t)(a->val[i]) * b + t;
|
|
a->val[i] = t & 0x3FFFFFFFu;
|
|
t >>= 30;
|
|
}
|
|
a->val[8] += t;
|
|
}
|
|
|
|
// x = k * x
|
|
// both inputs and result may be bigger than prime but not bigger than 2 * prime
|
|
void bn_multiply(const bignum256 *k, bignum256 *x, const bignum256 *prime)
|
|
{
|
|
int i, j;
|
|
uint64_t temp = 0;
|
|
uint32_t res[18], coef;
|
|
|
|
// compute lower half of long multiplication
|
|
for (i = 0; i < 9; i++)
|
|
{
|
|
for (j = 0; j <= i; j++) {
|
|
temp += k->val[j] * (uint64_t)x->val[i - j];
|
|
}
|
|
res[i] = temp & 0x3FFFFFFFu;
|
|
temp >>= 30;
|
|
}
|
|
// compute upper half
|
|
for (; i < 17; i++)
|
|
{
|
|
for (j = i - 8; j < 9 ; j++) {
|
|
temp += k->val[j] * (uint64_t)x->val[i - j];
|
|
}
|
|
res[i] = temp & 0x3FFFFFFFu;
|
|
temp >>= 30;
|
|
}
|
|
res[17] = temp;
|
|
// compute modulo p division is only estimated so this may give result greater than prime but not bigger than 2 * prime
|
|
for (i = 16; i >= 8; i--) {
|
|
// estimate (res / prime)
|
|
coef = (res[i] >> 16) + (res[i + 1] << 14);
|
|
// substract (coef * prime) from res
|
|
temp = 0x1000000000000000ull + res[i - 8] - prime->val[0] * (uint64_t)coef;
|
|
res[i - 8] = temp & 0x3FFFFFFF;
|
|
for (j = 1; j < 9; j++) {
|
|
temp >>= 30;
|
|
temp += 0xFFFFFFFC0000000ull + res[i - 8 + j] - prime->val[j] * (uint64_t)coef;
|
|
res[i - 8 + j] = temp & 0x3FFFFFFF;
|
|
}
|
|
}
|
|
// store the result
|
|
for (i = 0; i < 9; i++) {
|
|
x->val[i] = res[i];
|
|
}
|
|
}
|
|
|
|
// result is smaller than 2*prime
|
|
void bn_fast_mod(bignum256 *x, const bignum256 *prime)
|
|
{
|
|
int j;
|
|
uint32_t coef;
|
|
uint64_t temp;
|
|
|
|
coef = x->val[8] >> 16;
|
|
if (!coef) return;
|
|
// substract (coef * prime) from x
|
|
temp = 0x1000000000000000ull + x->val[0] - prime->val[0] * (uint64_t)coef;
|
|
x->val[0] = temp & 0x3FFFFFFF;
|
|
for (j = 1; j < 9; j++) {
|
|
temp >>= 30;
|
|
temp += 0xFFFFFFFC0000000ull + x->val[j] - prime->val[j] * (uint64_t)coef;
|
|
x->val[j] = temp & 0x3FFFFFFF;
|
|
}
|
|
}
|
|
|
|
// square root of x = x^((p+1)/4)
|
|
// http://en.wikipedia.org/wiki/Quadratic_residue#Prime_or_prime_power_modulus
|
|
void bn_sqrt(bignum256 *x, const bignum256 *prime)
|
|
{
|
|
uint32_t i, j, limb;
|
|
bignum256 res, p;
|
|
bn_zero(&res); res.val[0] = 1;
|
|
memcpy(&p, prime, sizeof(bignum256));
|
|
p.val[0] += 1;
|
|
bn_rshift(&p);
|
|
bn_rshift(&p);
|
|
for (i = 0; i < 9; i++) {
|
|
limb = p.val[i];
|
|
for (j = 0; j < 30; j++) {
|
|
if (i == 8 && limb == 0) break;
|
|
if (limb & 1) {
|
|
bn_multiply(x, &res, prime);
|
|
}
|
|
limb >>= 1;
|
|
bn_multiply(x, x, prime);
|
|
}
|
|
}
|
|
bn_mod(&res, prime);
|
|
memcpy(x, &res, sizeof(bignum256));
|
|
}
|
|
|
|
#if ! USE_INVERSE_FAST
|
|
|
|
#if USE_PRECOMPUTED_IV
|
|
#warning USE_PRECOMPUTED_IV will not be used
|
|
#endif
|
|
|
|
// in field G_prime, small but slow
|
|
void bn_inverse(bignum256 *x, const bignum256 *prime)
|
|
{
|
|
uint32_t i, j, limb;
|
|
bignum256 res;
|
|
bn_zero(&res); res.val[0] = 1;
|
|
for (i = 0; i < 9; i++) {
|
|
limb = prime->val[i];
|
|
// this is not enough in general but fine for secp256k1 because prime->val[0] > 1
|
|
if (i == 0) limb -= 2;
|
|
for (j = 0; j < 30; j++) {
|
|
if (i == 8 && limb == 0) break;
|
|
if (limb & 1) {
|
|
bn_multiply(x, &res, prime);
|
|
}
|
|
limb >>= 1;
|
|
bn_multiply(x, x, prime);
|
|
}
|
|
}
|
|
bn_mod(&res, prime);
|
|
memcpy(x, &res, sizeof(bignum256));
|
|
}
|
|
|
|
#else
|
|
|
|
// in field G_prime, big but fast
|
|
void bn_inverse(bignum256 *x, const bignum256 *prime)
|
|
{
|
|
int i, j, k, len1, len2, mask;
|
|
uint8_t buf[32];
|
|
uint32_t u[8], v[8], s[9], r[10], temp32;
|
|
uint64_t temp, temp2;
|
|
bn_fast_mod(x, prime);
|
|
bn_mod(x, prime);
|
|
bn_write_be(prime, buf);
|
|
for (i = 0; i < 8; i++) {
|
|
u[i] = read_be(buf + 28 - i * 4);
|
|
}
|
|
bn_write_be(x, buf);
|
|
for (i = 0; i < 8; i++) {
|
|
v[i] = read_be(buf + 28 - i * 4);
|
|
}
|
|
len1 = 8;
|
|
s[0] = 1;
|
|
r[0] = 0;
|
|
len2 = 1;
|
|
k = 0;
|
|
for (;;) {
|
|
for (i = 0; i < len1; i++) {
|
|
if (v[i]) break;
|
|
}
|
|
if (i == len1) break;
|
|
for (;;) {
|
|
for (i = 0; i < 30; i++) {
|
|
if (u[0] & (1 << i)) break;
|
|
}
|
|
if (i == 0) break;
|
|
mask = (1 << i) - 1;
|
|
for (j = 0; j + 1 < len1; j++) {
|
|
u[j] = (u[j] >> i) | ((u[j + 1] & mask) << (32 - i));
|
|
}
|
|
u[j] = (u[j] >> i);
|
|
mask = (1 << (32 - i)) - 1;
|
|
s[len2] = s[len2 - 1] >> (32 - i);
|
|
for (j = len2 - 1; j > 0; j--) {
|
|
s[j] = (s[j - 1] >> (32 - i)) | ((s[j] & mask) << i);
|
|
}
|
|
s[0] = (s[0] & mask) << i;
|
|
if (s[len2]) {
|
|
r[len2] = 0;
|
|
len2++;
|
|
}
|
|
k += i;
|
|
}
|
|
for (;;) {
|
|
for (i = 0; i < 30; i++) {
|
|
if (v[0] & (1 << i)) break;
|
|
}
|
|
if (i == 0) break;
|
|
mask = (1 << i) - 1;
|
|
for (j = 0; j + 1 < len1; j++) {
|
|
v[j] = (v[j] >> i) | ((v[j + 1] & mask) << (32 - i));
|
|
}
|
|
v[j] = (v[j] >> i);
|
|
mask = (1 << (32 - i)) - 1;
|
|
r[len2] = r[len2 - 1] >> (32 - i);
|
|
for (j = len2 - 1; j > 0; j--) {
|
|
r[j] = (r[j - 1] >> (32 - i)) | ((r[j] & mask) << i);
|
|
}
|
|
r[0] = (r[0] & mask) << i;
|
|
if (r[len2]) {
|
|
s[len2] = 0;
|
|
len2++;
|
|
}
|
|
k += i;
|
|
}
|
|
|
|
i = len1 - 1;
|
|
while (i > 0 && u[i] == v[i]) i--;
|
|
if (u[i] > v[i]) {
|
|
temp = 0x100000000ull + u[0] - v[0];
|
|
u[0] = (temp >> 1) & 0x7FFFFFFF;
|
|
temp >>= 32;
|
|
for (i = 1; i < len1; i++) {
|
|
temp += 0xFFFFFFFFull + u[i] - v[i];
|
|
u[i - 1] += (temp & 1) << 31;
|
|
u[i] = (temp >> 1) & 0x7FFFFFFF;
|
|
temp >>= 32;
|
|
}
|
|
temp = temp2 = 0;
|
|
for (i = 0; i < len2; i++) {
|
|
temp += s[i];
|
|
temp += r[i];
|
|
temp2 += s[i];
|
|
temp2 += s[i];
|
|
r[i] = temp;
|
|
s[i] = temp2;
|
|
temp >>= 32;
|
|
temp2 >>= 32;
|
|
}
|
|
if (temp != 0 || temp2 != 0) {
|
|
r[len2] = temp;
|
|
s[len2] = temp2;
|
|
len2++;
|
|
}
|
|
} else {
|
|
temp = 0x100000000ull + v[0] - u[0];
|
|
v[0] = (temp >> 1) & 0x7FFFFFFF;
|
|
temp >>= 32;
|
|
for (i = 1; i < len1; i++) {
|
|
temp += 0xFFFFFFFFull + v[i] - u[i];
|
|
v[i - 1] += (temp & 1) << 31;
|
|
v[i] = (temp >> 1) & 0x7FFFFFFF;
|
|
temp >>= 32;
|
|
}
|
|
temp = temp2 = 0;
|
|
for (i = 0; i < len2; i++) {
|
|
temp += s[i];
|
|
temp += r[i];
|
|
temp2 += r[i];
|
|
temp2 += r[i];
|
|
s[i] = temp;
|
|
r[i] = temp2;
|
|
temp >>= 32;
|
|
temp2 >>= 32;
|
|
}
|
|
if (temp != 0 || temp2 != 0) {
|
|
s[len2] = temp;
|
|
r[len2] = temp2;
|
|
len2++;
|
|
}
|
|
}
|
|
if (u[len1 - 1] == 0 && v[len1 - 1] == 0) len1--;
|
|
k++;
|
|
}
|
|
|
|
j = r[0] >> 30;
|
|
r[0] = r[0] & 0x3FFFFFFFu;
|
|
for (i = 1; i < len2; i++) {
|
|
uint32_t q = r[i] >> (30 - 2 * i);
|
|
r[i] = ((r[i] << (2 * i)) & 0x3FFFFFFFu) + j;
|
|
j=q;
|
|
}
|
|
r[i] = j;
|
|
i++;
|
|
for (; i < 9; i++) r[i] = 0;
|
|
|
|
i = 8;
|
|
while (i > 0 && r[i] == prime->val[i]) i--;
|
|
if (r[i] >= prime->val[i]) {
|
|
temp32 = 1;
|
|
for (i = 0; i < 9; i++) {
|
|
temp32 += 0x3FFFFFFF + r[i] - prime->val[i];
|
|
r[i] = temp32 & 0x3FFFFFFF;
|
|
temp32 >>= 30;
|
|
}
|
|
}
|
|
temp32 = 1;
|
|
for (i = 0; i < 9; i++) {
|
|
temp32 += 0x3FFFFFFF + prime->val[i] - r[i];
|
|
r[i] = temp32 & 0x3FFFFFFF;
|
|
temp32 >>= 30;
|
|
}
|
|
int done = 0;
|
|
#if USE_PRECOMPUTED_IV
|
|
if (prime == &prime256k1) {
|
|
for (j = 0; j < 9; j++) {
|
|
x->val[j] = r[j];
|
|
}
|
|
bn_multiply(secp256k1_iv + k - 256, x, prime);
|
|
bn_fast_mod(x, prime);
|
|
done = 1;
|
|
}
|
|
#endif
|
|
if (!done) {
|
|
for (j = 0; j < k; j++) {
|
|
if (r[0] & 1) {
|
|
temp32 = r[0] + prime->val[0];
|
|
r[0] = (temp32 >> 1) & 0x1FFFFFFF;
|
|
temp32 >>= 30;
|
|
for (i = 1; i < 9; i++) {
|
|
temp32 += r[i] + prime->val[i];
|
|
r[i - 1] += (temp32 & 1) << 29;
|
|
r[i] = (temp32 >> 1) & 0x1FFFFFFF;
|
|
temp32 >>= 30;
|
|
}
|
|
} else {
|
|
for (i = 0; i < 8; i++) {
|
|
r[i] = (r[i] >> 1) | ((r[i + 1] & 1) << 29);
|
|
}
|
|
r[8] = r[8] >> 1;
|
|
}
|
|
}
|
|
for (j = 0; j < 9; j++) {
|
|
x->val[j] = r[j];
|
|
}
|
|
}
|
|
}
|
|
#endif
|
|
|
|
void bn_normalize(bignum256 *a) {
|
|
int i;
|
|
uint32_t tmp = 0;
|
|
for (i = 0; i < 9; i++) {
|
|
tmp += a->val[i];
|
|
a->val[i] = tmp & 0x3FFFFFFF;
|
|
tmp >>= 30;
|
|
}
|
|
}
|
|
|
|
void bn_addmod(bignum256 *a, const bignum256 *b, const bignum256 *prime)
|
|
{
|
|
int i;
|
|
for (i = 0; i < 9; i++) {
|
|
a->val[i] += b->val[i];
|
|
}
|
|
bn_normalize(a);
|
|
bn_fast_mod(a, prime);
|
|
bn_mod(a, prime);
|
|
}
|
|
|
|
void bn_addmodi(bignum256 *a, uint32_t b, const bignum256 *prime) {
|
|
a->val[0] += b;
|
|
bn_normalize(a);
|
|
bn_fast_mod(a, prime);
|
|
bn_mod(a, prime);
|
|
}
|
|
|
|
// res = a - b
|
|
// b < 2*prime; result not normalized
|
|
void bn_substract(const bignum256 *a, const bignum256 *b, bignum256 *res)
|
|
{
|
|
int i;
|
|
uint32_t temp = 0;
|
|
for (i = 0; i < 9; i++) {
|
|
temp += a->val[i] + 2u * prime256k1.val[i] - b->val[i];
|
|
res->val[i] = temp & 0x3FFFFFFF;
|
|
temp >>= 30;
|
|
}
|
|
}
|
|
|
|
// res = a - b ; a > b
|
|
void bn_substract_noprime(const bignum256 *a, const bignum256 *b, bignum256 *res)
|
|
{
|
|
int i;
|
|
uint32_t tmp = 1;
|
|
for (i = 0; i < 9; i++) {
|
|
tmp += 0x3FFFFFFF + a->val[i] - b->val[i];
|
|
res->val[i] = tmp & 0x3FFFFFFF;
|
|
tmp >>= 30;
|
|
}
|
|
}
|
|
|
|
// a / 58 = a (+r)
|
|
void bn_divmod58(bignum256 *a, uint32_t *r)
|
|
{
|
|
int i;
|
|
uint32_t rem, tmp;
|
|
rem = a->val[8] % 58;
|
|
a->val[8] /= 58;
|
|
for (i = 7; i >= 0; i--) {
|
|
// 2^30 == 18512790*58 + 4
|
|
tmp = rem * 4 + a->val[i];
|
|
a->val[i] = rem * 18512790 + (tmp / 58);
|
|
rem = tmp % 58;
|
|
}
|
|
*r = rem;
|
|
}
|
|
|
|
#if BN_PRINT
|
|
void bn_print(const bignum256 *a)
|
|
{
|
|
printf("%04x", a->val[8] & 0x0000FFFF);
|
|
printf("%08x", (a->val[7] << 2) | ((a->val[6] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[6] & 0x0FFFFFFF);
|
|
printf("%08x", (a->val[5] << 2) | ((a->val[4] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[4] & 0x0FFFFFFF);
|
|
printf("%08x", (a->val[3] << 2) | ((a->val[2] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[2] & 0x0FFFFFFF);
|
|
printf("%08x", (a->val[1] << 2) | ((a->val[0] & 0x30000000) >> 28));
|
|
printf("%07x", a->val[0] & 0x0FFFFFFF);
|
|
}
|
|
|
|
void bn_print_raw(const bignum256 *a)
|
|
{
|
|
int i;
|
|
for (i = 0; i <= 8; i++) {
|
|
printf("0x%08x, ", a->val[i]);
|
|
}
|
|
}
|
|
#endif
|