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trezor-firmware/ecdsa.c
Pavol Rusnak ee09a6a7b2 param names cleanup
2013-08-19 12:40:58 +02:00

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/**
* Copyright (c) 2013 Tomas Dzetkulic
* Copyright (c) 2013 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 <stdint.h>
#include <stdlib.h>
#include <string.h>
#include "rand.h"
#include "sha256.h"
#include "ecdsa.h"
#include "secp256k1.h"
#include "aux.h"
// assumes x < 2*prime
void mod(bignum256 *x, bignum256 const *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
for (i = 0; i < 9; i++) {
x->val[i] = 0;
}
} 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;
}
}
}
}
// x = k * x
// both inputs and result may be bigger than prime but not bigger than 2 * prime
void multiply(const bignum256 *k, bignum256 *x, bignum256 const *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 = 0x1000000000000000llu + res[i-8] - prime->val[0] * (uint64_t)coef;
res[i-8] = temp & 0x3FFFFFFF;
for (j = 1; j < 9; j++) {
temp >>= 30;
temp += 0xFFFFFFFC0000000llu + 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];
}
}
void fast_mod(bignum256 *x, bignum256 const *prime)
{
int j;
uint32_t coef;
uint64_t temp;
coef = x->val[8] >> 16;
if (!coef) return;
// substract (coef * prime) from x
temp = 0x1000000000000000llu + x->val[0] - prime->val[0] * (uint64_t)coef;
x->val[0] = temp & 0x3FFFFFFF;
for (j = 1; j < 9; j++) {
temp >>= 30;
temp += 0xFFFFFFFC0000000llu + x->val[j] - prime->val[j] * (uint64_t)coef;
x->val[j] = temp & 0x3FFFFFFF;
}
}
// in field G_prime
void inverse(bignum256 *x, bignum256 const *prime)
{
int i, j, k, len1, len2, mask;
uint32_t u[9], v[9], s[10], r[10], temp, temp2;
fast_mod(x, prime);
mod(x, prime);
for (i = 0; i < 9; i++) {
u[i] = prime->val[i];
v[i] = x->val[i];
}
len1 = 9;
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) << (30 - i));
}
u[j] = (u[j] >> i);
mask = (1 << (30 - i)) - 1;
s[len2] = s[len2 - 1] >> (30 - i);
for (j = len2 - 1; j > 0; j--) {
s[j] = (s[j - 1] >> (30 - 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) << (30 - i));
}
v[j] = (v[j] >> i);
mask = (1 << (30 - i)) - 1;
r[len2] = r[len2 - 1] >> (30 - i);
for (j = len2 - 1; j > 0; j--) {
r[j] = (r[j - 1] >> (30 - 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 = 0x40000000u + u[0] - v[0];
u[0] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
for (i = 1; i < len1; i++) {
temp += 0x3FFFFFFFu + u[i] - v[i];
u[i-1] += (temp & 1) << 29;
u[i] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
}
temp = temp2 = 0;
for (i = 0; i < len2; i++) {
temp += s[i] + r[i];
temp2 += s[i] << 1;
r[i] = temp & 0x3FFFFFFF;
s[i] = temp2 & 0x3FFFFFFF;
temp >>= 30;
temp2 >>= 30;
}
if (temp != 0 || temp2 != 0) {
r[len2] = temp;
s[len2] = temp2;
len2++;
}
} else {
temp = 0x40000000u + v[0] - u[0];
v[0] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
for (i = 1; i < len1; i++) {
temp += 0x3FFFFFFFu + v[i] - u[i];
v[i-1] += (temp & 1) << 29;
v[i] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
}
temp = temp2 = 0;
for (i = 0; i < len2; i++) {
temp += s[i] + r[i];
temp2 += r[i] << 1;
s[i] = temp & 0x3FFFFFFF;
r[i] = temp2 & 0x3FFFFFFF;
temp >>= 30;
temp2 >>= 30;
}
if (temp != 0 || temp2 != 0) {
s[len2] = temp;
r[len2] = temp2;
len2++;
}
}
if (u[len1 - 1] == 0 && v[len1 - 1] == 0) len1--;
k++;
}
i = 8;
while (i>0 && r[i] == prime->val[i]) i--;
if (r[i] >= prime->val[i]) {
temp = 1;
for (i = 0; i < 9; i++) {
temp += 0x3FFFFFFF + r[i] - prime->val[i];
r[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
}
temp = 1;
for (i = 0; i < 9; i++) {
temp += 0x3FFFFFFF + prime->val[i] - r[i];
r[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
int done = 0;
#ifdef USE_PRECOMPUTED_IV
if (prime == &prime256k1) {
for (j = 0; j < 9; j++) {
x->val[j] = r[j];
}
multiply(secp256k1_iv + k - 256, x, prime);
fast_mod(x, prime);
done = 1;
}
#endif
if (!done) {
for (j = 0; j < k; j++) {
if (r[0] & 1) {
temp = r[0] + prime->val[0];
r[0] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
for (i = 1; i < 9; i++) {
temp += r[i] + prime->val[i];
r[i-1] += (temp & 1) << 29;
r[i] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 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];
}
}
}
// res = a - b
// b < 2*prime; result not normalized
void fast_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;
}
}
// cp2 = cp1 + cp2
void point_add(const curve_point *cp1, curve_point *cp2)
{
int i;
uint32_t temp;
bignum256 lambda, inv, xr, yr;
fast_substract(&(cp2->x), &(cp1->x), &inv);
inverse(&inv, &prime256k1);
fast_substract(&(cp2->y), &(cp1->y), &lambda);
multiply(&inv, &lambda, &prime256k1);
memcpy(&xr, &lambda, sizeof(bignum256));
multiply(&xr, &xr, &prime256k1);
temp = 0;
for (i = 0; i < 9; i++) {
temp += xr.val[i] + 3u * prime256k1.val[i] - cp1->x.val[i] - cp2->x.val[i];
xr.val[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
fast_mod(&xr, &prime256k1);
fast_substract(&(cp1->x), &xr, &yr);
// no need to fast_mod here
// fast_mod(&yr);
multiply(&lambda, &yr, &prime256k1);
fast_substract(&yr, &(cp1->y), &yr);
fast_mod(&yr, &prime256k1);
memcpy(&(cp2->x), &xr, sizeof(bignum256));
memcpy(&(cp2->y), &yr, sizeof(bignum256));
}
#ifndef USE_PRECOMPUTED_CP
// cp = cp + cp
void point_double(curve_point *cp)
{
int i;
uint32_t temp;
bignum256 lambda, inverse_y, xr, yr;
memcpy(&inverse_y, &(cp->y), sizeof(bignum256));
inverse(&inverse_y, &prime256k1);
memcpy(&lambda, &three_over_two256k1, sizeof(bignum256));
multiply(&inverse_y, &lambda, &prime256k1);
multiply(&(cp->x), &lambda, &prime256k1);
multiply(&(cp->x), &lambda, &prime256k1);
memcpy(&xr, &lambda, sizeof(bignum256));
multiply(&xr, &xr, &prime256k1);
temp = 0;
for (i = 0; i < 9; i++) {
temp += xr.val[i] + 3u * prime256k1.val[i] - 2u * cp->x.val[i];
xr.val[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
fast_mod(&xr, &prime256k1);
fast_substract(&(cp->x), &xr, &yr);
// no need to fast_mod here
// fast_mod(&yr);
multiply(&lambda, &yr, &prime256k1);
fast_substract(&yr, &(cp->y), &yr);
fast_mod(&yr, &prime256k1);
memcpy(&(cp->x), &xr, sizeof(bignum256));
memcpy(&(cp->y), &yr, sizeof(bignum256));
}
#endif
// res = k * G
void scalar_multiply(bignum256 *k, curve_point *res)
{
int i, j;
// result is zero
int is_zero = 1;
#ifdef USE_PRECOMPUTED_CP
int exp = 0;
#else
curve_point curr;
// initial res
memcpy(&curr, &G256k1, sizeof(curve_point));
#endif
for (i = 0; i < 9; i++) {
for (j = 0; j < 30; j++) {
if (i == 8 && (k->val[i] >> j) == 0) break;
if (k->val[i] & (1u<<j)) {
if (is_zero) {
#ifdef USE_PRECOMPUTED_CP
memcpy(res, secp256k1_cp + exp, sizeof(curve_point));
#else
memcpy(res, &curr, sizeof(curve_point));
#endif
is_zero = 0;
} else {
#ifdef USE_PRECOMPUTED_CP
point_add(secp256k1_cp + exp, res);
#else
point_add(&curr, res);
#endif
}
}
#ifdef USE_PRECOMPUTED_CP
exp++;
#else
point_double(&curr);
#endif
}
}
mod(&(res->x), &prime256k1);
mod(&(res->y), &prime256k1);
}
// write DER encoding of number to buffer
void write_der(const bignum256 *x, uint8_t *buf)
{
int i, j = 8, k = 8, len = 0;
uint8_t r = 0, temp;
buf[0] = 2;
for (i = 0; i < 32; i++) {
temp = (x->val[j] >> k) + r;
k -= 8;
if (k < 0) {
r = (x->val[j]) << (-k);
k += 30;
j--;
} else {
r = 0;
}
if (len || temp) {
buf[2 + len] = temp;
len++;
}
}
buf[1] = len;
}
// uses secp256k1 curve
// priv_key is a 32 byte big endian stored number
// msg is a data to be signed
// msg_len is the message length
// sig is at least 70 bytes long array for the signature
// sig_len is the pointer to a uint that will contain resulting signature length. note that ((*sig_len) == sig[1]+2)
void ecdsa_sign(uint8_t *priv_key, uint8_t *msg, uint32_t msg_len, uint8_t *sig, uint32_t *sig_len)
{
uint32_t i;
uint64_t temp;
uint8_t hash[32];
curve_point R;
bignum256 k, z;
bignum256 *da = &R.y;
// compute hash function of message
sha256(msg, msg_len, hash);
// if double hash is required uncomment the following line:
// sha256(hash, 32, hash);
temp = 0;
for (i = 0; i < 8; i++) {
temp += (((uint64_t)read_be(hash + (7 - i) * 4)) << (2 * i));
z.val[i]= temp & 0x3FFFFFFF;
temp >>= 30;
}
z.val[8] = temp;
for (;;) {
// generate random number k
for (i = 0; i < 8; i++) {
k.val[i] = random32() & 0x3FFFFFFF;
}
k.val[8] = random32() & 0xFFFF;
// if k is too big or too small, we don't like it
if (k.val[5] == 0x3FFFFFFF && k.val[6] == 0x3FFFFFFF && k.val[7] == 0x3FFFFFFF && k.val[8] == 0xFFFF) continue;
if (k.val[5] == 0x0 && k.val[6] == 0x0 && k.val[7] == 0x0 && k.val[8] == 0x0) continue;
// compute k*G
scalar_multiply(&k, &R);
// r = (rx mod n)
mod(&R.x, &order256k1);
// if r is zero, we try different k
for (i = 0; i < 9; i++) {
if (R.x.val[i] != 0) break;
}
if (i == 9) continue;
inverse(&k, &order256k1);
temp = 0;
for (i = 0; i < 8; i++) {
temp += (((uint64_t)read_be(priv_key + (7 - i) * 4)) << (2 * i));
da->val[i] = temp & 0x3FFFFFFF;
temp >>= 30;
}
da->val[8] = temp;
multiply(&R.x, da, &order256k1);
for (i = 0; i < 8; i++) {
da->val[i] += z.val[i];
da->val[i+1] += (da->val[i] >> 30);
da->val[i] &= 0x3FFFFFFF;
}
da->val[8] += z.val[8];
multiply(da, &k, &order256k1);
mod(&k, &order256k1);
for (i = 0; i < 9; i++) {
if (k.val[i] != 0) break;
}
if (i == 9) continue;
// we are done, R.x and k is the result signature
break;
}
write_der(&R.x, sig + 2);
i = sig[3] + 2;
write_der(&k, sig + 2 + i);
i += sig[3+i] + 2;
sig[0] = 0x30;
sig[1] = i;
*sig_len = i + 2;
}
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