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trezor-firmware/ecdsa.c
Pavol Rusnak 0fe1857513 normalize y^2 in pubkey validation 
fix last commit
2014-07-07 21:11:25 +02:00

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/**
* 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 <stdint.h>
#include <stdlib.h>
#include <string.h>
#include "bignum.h"
#include "rand.h"
#include "sha2.h"
#include "ripemd160.h"
#include "hmac.h"
#include "ecdsa.h"
#include "base58.h"
// Set cp2 = cp1
void point_copy(const curve_point *cp1, curve_point *cp2)
{
memcpy(&(cp2->x), &(cp1->x), sizeof(bignum256));
memcpy(&(cp2->y), &(cp1->y), sizeof(bignum256));
}
// cp2 = cp1 + cp2
void point_add(const curve_point *cp1, curve_point *cp2)
{
int i;
uint32_t temp;
bignum256 lambda, inv, xr, yr;
if (point_is_infinity(cp1)) {
return;
}
if (point_is_infinity(cp2)) {
point_copy(cp1, cp2);
return;
}
if (point_is_equal(cp1, cp2)) {
point_double(cp2);
return;
}
if (point_is_negative_of(cp1, cp2)) {
point_set_infinity(cp2);
return;
}
bn_substract(&(cp2->x), &(cp1->x), &inv);
bn_inverse(&inv, &prime256k1);
bn_substract(&(cp2->y), &(cp1->y), &lambda);
bn_multiply(&inv, &lambda, &prime256k1);
memcpy(&xr, &lambda, sizeof(bignum256));
bn_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;
}
bn_fast_mod(&xr, &prime256k1);
bn_substract(&(cp1->x), &xr, &yr);
// no need to fast_mod here
// bn_fast_mod(&yr);
bn_multiply(&lambda, &yr, &prime256k1);
bn_substract(&yr, &(cp1->y), &yr);
bn_fast_mod(&yr, &prime256k1);
memcpy(&(cp2->x), &xr, sizeof(bignum256));
memcpy(&(cp2->y), &yr, sizeof(bignum256));
bn_mod(&(cp2->x), &prime256k1);
bn_mod(&(cp2->y), &prime256k1);
}
// cp = cp + cp
void point_double(curve_point *cp)
{
int i;
uint32_t temp;
bignum256 lambda, inverse_y, xr, yr;
if (point_is_infinity(cp)) {
return;
}
if (bn_is_zero(&(cp->y))) {
point_set_infinity(cp);
return;
}
memcpy(&inverse_y, &(cp->y), sizeof(bignum256));
bn_inverse(&inverse_y, &prime256k1);
memcpy(&lambda, &three_over_two256k1, sizeof(bignum256));
bn_multiply(&inverse_y, &lambda, &prime256k1);
bn_multiply(&(cp->x), &lambda, &prime256k1);
bn_multiply(&(cp->x), &lambda, &prime256k1);
memcpy(&xr, &lambda, sizeof(bignum256));
bn_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;
}
bn_fast_mod(&xr, &prime256k1);
bn_substract(&(cp->x), &xr, &yr);
// no need to fast_mod here
// bn_fast_mod(&yr);
bn_multiply(&lambda, &yr, &prime256k1);
bn_substract(&yr, &(cp->y), &yr);
bn_fast_mod(&yr, &prime256k1);
memcpy(&(cp->x), &xr, sizeof(bignum256));
memcpy(&(cp->y), &yr, sizeof(bignum256));
bn_mod(&(cp->x), &prime256k1);
bn_mod(&(cp->y), &prime256k1);
}
// res = k * p
void point_multiply(const bignum256 *k, const curve_point *p, curve_point *res)
{
int i, j;
// result is zero
int is_zero = 1;
curve_point curr;
// initial res
memcpy(&curr, p, sizeof(curve_point));
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) {
memcpy(res, &curr, sizeof(curve_point));
is_zero = 0;
} else {
point_add(&curr, res);
}
}
point_double(&curr);
}
}
}
// set point to internal representation of point at infinity
void point_set_infinity(curve_point *p)
{
bn_zero(&(p->x));
bn_zero(&(p->y));
}
// return true iff p represent point at infinity
// both coords are zero in internal representation
int point_is_infinity(const curve_point *p)
{
return bn_is_zero(&(p->x)) && bn_is_zero(&(p->y));
}
// return true iff both points are equal
int point_is_equal(const curve_point *p, const curve_point *q)
{
return bn_is_equal(&(p->x), &(q->x)) && bn_is_equal(&(p->y), &(q->y));
}
// returns true iff p == -q
// expects p and q be valid points on curve other than point at infinity
int point_is_negative_of(const curve_point *p, const curve_point *q)
{
// if P == (x, y), then -P would be (x, -y) on this curve
if (!bn_is_equal(&(p->x), &(q->x))) {
return 0;
}
// we shouldn't hit this for a valid point
if (bn_is_zero(&(p->y))) {
return 0;
}
return !bn_is_equal(&(p->y), &(q->y));
}
// res = k * G
void scalar_multiply(const bignum256 *k, curve_point *res)
{
int i;
// result is zero
int is_zero = 1;
curve_point curr;
// initial res
memcpy(&curr, &G256k1, sizeof(curve_point));
for (i = 0; i < 256; i++) {
if (k->val[i / 30] & (1u << (i % 30))) {
if (is_zero) {
#if USE_PRECOMPUTED_CP
if (i < 255 && (k->val[(i + 1) / 30] & (1u << ((i + 1) % 30)))) {
memcpy(res, secp256k1_cp2 + i, sizeof(curve_point));
i++;
} else {
memcpy(res, secp256k1_cp + i, sizeof(curve_point));
}
#else
memcpy(res, &curr, sizeof(curve_point));
#endif
is_zero = 0;
} else {
#if USE_PRECOMPUTED_CP
if (i < 255 && (k->val[(i + 1) / 30] & (1u << ((i + 1) % 30)))) {
point_add(secp256k1_cp2 + i, res);
i++;
} else {
point_add(secp256k1_cp + i, res);
}
#else
point_add(&curr, res);
#endif
}
}
#if ! USE_PRECOMPUTED_CP
point_double(&curr);
#endif
}
}
// generate random K for signing
int generate_k_random(bignum256 *k) {
int i, j;
for (j = 0; j < 10000; j++) {
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 ( !bn_is_zero(k) && bn_is_less(k, &order256k1) ) {
return 0; // good number - no error
}
}
// we generated 10000 numbers, none of them is good -> fail
return 1;
}
// generate K in a deterministic way, according to RFC6979
// http://tools.ietf.org/html/rfc6979
int generate_k_rfc6979(bignum256 *secret, const uint8_t *priv_key, const uint8_t *hash)
{
int i;
uint8_t v[32], k[32], bx[2*32], buf[32 + 1 + sizeof(bx)], t[32];
bignum256 z1;
memcpy(bx, priv_key, 32);
bn_read_be(hash, &z1);
bn_mod(&z1, &order256k1);
bn_write_be(&z1, bx + 32);
memset(v, 1, sizeof(v));
memset(k, 0, sizeof(k));
memcpy(buf, v, sizeof(v));
buf[sizeof(v)] = 0x00;
memcpy(buf + sizeof(v) + 1, bx, 64);
hmac_sha256(k, sizeof(k), buf, sizeof(buf), k);
hmac_sha256(k, sizeof(k), v, sizeof(v), v);
memcpy(buf, v, sizeof(v));
buf[sizeof(v)] = 0x01;
memcpy(buf + sizeof(v) + 1, bx, 64);
hmac_sha256(k, sizeof(k), buf, sizeof(buf), k);
hmac_sha256(k, sizeof(k), v, sizeof(k), v);
for (i = 0; i < 10000; i++) {
hmac_sha256(k, sizeof(k), v, sizeof(v), t);
bn_read_be(t, secret);
if ( !bn_is_zero(secret) && bn_is_less(secret, &order256k1) ) {
return 0; // good number -> no error
}
memcpy(buf, v, sizeof(v));
buf[sizeof(v)] = 0x00;
hmac_sha256(k, sizeof(k), buf, sizeof(v) + 1, k);
hmac_sha256(k, sizeof(k), v, sizeof(v), v);
}
// we generated 10000 numbers, none of them is good -> fail
return 1;
}
// msg is a data to be signed
// msg_len is the message length
int ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig)
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
return ecdsa_sign_digest(priv_key, hash, sig);
}
// msg is a data to be signed
// msg_len is the message length
int ecdsa_sign_double(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig)
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
sha256_Raw(hash, 32, hash);
return ecdsa_sign_digest(priv_key, hash, sig);
}
// uses secp256k1 curve
// priv_key is a 32 byte big endian stored number
// sig is 64 bytes long array for the signature
// digest is 32 bytes of digest
int ecdsa_sign_digest(const uint8_t *priv_key, const uint8_t *digest, uint8_t *sig)
{
uint32_t i;
curve_point R;
bignum256 k, z;
bignum256 *da = &R.y;
bn_read_be(digest, &z);
#if USE_RFC6979
// generate K deterministically
if (generate_k_rfc6979(&k, priv_key, digest) != 0) {
return 1;
}
#else
// generate random number k
if (generate_k_random(&k) != 0) {
return 1;
}
#endif
// compute k*G
scalar_multiply(&k, &R);
// r = (rx mod n)
bn_mod(&R.x, &order256k1);
// if r is zero, we fail
for (i = 0; i < 9; i++) {
if (R.x.val[i] != 0) break;
}
if (i == 9) {
return 2;
}
bn_inverse(&k, &order256k1);
bn_read_be(priv_key, da);
bn_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];
bn_multiply(da, &k, &order256k1);
bn_mod(&k, &order256k1);
for (i = 0; i < 9; i++) {
if (k.val[i] != 0) break;
}
// if k is zero, we fail
if (i == 9) {
return 3;
}
// if S > order/2 => S = -S
if (bn_is_less(&order256k1_half, &k)) {
bn_substract_noprime(&order256k1, &k, &k);
}
// we are done, R.x and k is the result signature
bn_write_be(&R.x, sig);
bn_write_be(&k, sig + 32);
return 0;
}
void ecdsa_get_public_key33(const uint8_t *priv_key, uint8_t *pub_key)
{
curve_point R;
bignum256 k;
bn_read_be(priv_key, &k);
// compute k*G
scalar_multiply(&k, &R);
pub_key[0] = 0x02 | (R.y.val[0] & 0x01);
bn_write_be(&R.x, pub_key + 1);
}
void ecdsa_get_public_key65(const uint8_t *priv_key, uint8_t *pub_key)
{
curve_point R;
bignum256 k;
bn_read_be(priv_key, &k);
// compute k*G
scalar_multiply(&k, &R);
pub_key[0] = 0x04;
bn_write_be(&R.x, pub_key + 1);
bn_write_be(&R.y, pub_key + 33);
}
void ecdsa_get_pubkeyhash(const uint8_t *pub_key, uint8_t *pubkeyhash)
{
uint8_t h[32];
if (pub_key[0] == 0x04) { // uncompressed format
sha256_Raw(pub_key, 65, h);
} else if (pub_key[0] == 0x00) { // point at infinity
sha256_Raw(pub_key, 1, h);
} else {
sha256_Raw(pub_key, 33, h); // expecting compressed format
}
ripemd160(h, 32, pubkeyhash);
}
void ecdsa_get_address(const uint8_t *pub_key, uint8_t version, char *addr)
{
uint8_t data[21];
data[0] = version;
ecdsa_get_pubkeyhash(pub_key, data + 1);
base58_encode_check(data, 21, addr);
}
void ecdsa_get_wif(const uint8_t *priv_key, uint8_t version, char *wif)
{
uint8_t data[34];
data[0] = version;
memcpy(data + 1, priv_key, 32);
data[33 ] = 0x01;
base58_encode_check(data, 34, wif);
}
int ecdsa_address_decode(const char *addr, uint8_t *out)
{
if (!addr) return 0;
return base58_decode_check(addr, out) == 21;
}
void uncompress_coords(uint8_t odd, const bignum256 *x, bignum256 *y)
{
// y^2 = x^3 + 0*x + 7
memcpy(y, x, sizeof(bignum256)); // y is x
bn_multiply(x, y, &prime256k1); // y is x^2
bn_multiply(x, y, &prime256k1); // y is x^3
bn_addmodi(y, 7, &prime256k1); // y is x^3 + 7
bn_sqrt(y, &prime256k1); // y = sqrt(y)
if ((odd & 0x01) != (y->val[0] & 1)) {
bn_substract_noprime(&prime256k1, y, y); // y = -y
}
}
int ecdsa_read_pubkey(const uint8_t *pub_key, curve_point *pub)
{
if (pub_key[0] == 0x04) {
bn_read_be(pub_key + 1, &(pub->x));
bn_read_be(pub_key + 33, &(pub->y));
#if USE_PUBKEY_VALIDATE
return ecdsa_validate_pubkey(pub);
#else
return 1;
#endif
}
if (pub_key[0] == 0x02 || pub_key[0] == 0x03) { // compute missing y coords
bn_read_be(pub_key + 1, &(pub->x));
uncompress_coords(pub_key[0], &(pub->x), &(pub->y));
#if USE_PUBKEY_VALIDATE
return ecdsa_validate_pubkey(pub);
#else
return 1;
#endif
}
// error
return 0;
}
// Verifies that:
// - pub is not the point at infinity.
// - pub->x and pub->y are in range [0,p-1].
// - pub is on the curve.
// - n*pub is the point at infinity.
int ecdsa_validate_pubkey(const curve_point *pub)
{
bignum256 y_2, x_3_b;
curve_point temp;
if (point_is_infinity(pub)) {
return 0;
}
if (!bn_is_less(&(pub->x), &prime256k1) || !bn_is_less(&(pub->y), &prime256k1)) {
return 0;
}
memcpy(&y_2, &(pub->y), sizeof(bignum256));
memcpy(&x_3_b, &(pub->x), sizeof(bignum256));
// y^2
bn_multiply(&(pub->y), &y_2, &prime256k1);
bn_mod(&y_2, &prime256k1);
// x^3 + b
bn_multiply(&(pub->x), &x_3_b, &prime256k1);
bn_multiply(&(pub->x), &x_3_b, &prime256k1);
bn_addmodi(&x_3_b, 7, &prime256k1);
if (!bn_is_equal(&x_3_b, &y_2)) {
return 0;
}
point_multiply(&order256k1, pub, &temp);
if (!point_is_infinity(&temp)) {
return 0;
}
return 1;
}
// uses secp256k1 curve
// pub_key - 65 bytes uncompressed key
// signature - 64 bytes signature
// msg is a data that was signed
// msg_len is the message length
int ecdsa_verify(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
return ecdsa_verify_digest(pub_key, sig, hash);
}
int ecdsa_verify_double(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
{
uint8_t hash[32];
sha256_Raw(msg, msg_len, hash);
sha256_Raw(hash, 32, hash);
return ecdsa_verify_digest(pub_key, sig, hash);
}
// returns 0 if verification succeeded
int ecdsa_verify_digest(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *digest)
{
int i, j;
curve_point pub, res;
bignum256 r, s, z;
if (!ecdsa_read_pubkey(pub_key, &pub)) {
return 1;
}
bn_read_be(sig, &r);
bn_read_be(sig + 32, &s);
bn_read_be(digest, &z);
if (bn_is_zero(&r) || bn_is_zero(&s) ||
(!bn_is_less(&r, &order256k1)) ||
(!bn_is_less(&s, &order256k1))) return 2;
bn_inverse(&s, &order256k1); // s^-1
bn_multiply(&s, &z, &order256k1); // z*s^-1
bn_mod(&z, &order256k1);
bn_multiply(&r, &s, &order256k1); // r*s^-1
bn_mod(&s, &order256k1);
if (bn_is_zero(&z)) {
// our message hashes to zero
// I don't expect this to happen any time soon
return 3;
} else {
scalar_multiply(&z, &res);
}
// both pub and res can be infinity, can have y = 0 OR can be equal -> false negative
for (i = 0; i < 9; i++) {
for (j = 0; j < 30; j++) {
if (i == 8 && (s.val[i] >> j) == 0) break;
if (s.val[i] & (1u << j)) {
point_add(&pub, &res);
}
point_double(&pub);
}
}
bn_mod(&(res.x), &order256k1);
// signature does not match
for (i = 0; i < 9; i++) {
if (res.x.val[i] != r.val[i]) {
return 5;
}
}
// all OK
return 0;
}
int ecdsa_sig_to_der(const uint8_t *sig, uint8_t *der)
{
int i;
uint8_t *p = der, *len, *len1, *len2;
*p = 0x30; p++; // sequence
*p = 0x00; len = p; p++; // len(sequence)
*p = 0x02; p++; // integer
*p = 0x00; len1 = p; p++; // len(integer)
// process R
i = 0;
while (sig[i] == 0 && i < 32) { i++; } // skip leading zeroes
if (sig[i] >= 0x80) { // put zero in output if MSB set
*p = 0x00; p++; *len1 = *len1 + 1;
}
while (i < 32) { // copy bytes to output
*p = sig[i]; p++; *len1 = *len1 + 1; i++;
}
*p = 0x02; p++; // integer
*p = 0x00; len2 = p; p++; // len(integer)
// process S
i = 32;
while (sig[i] == 0 && i < 64) { i++; } // skip leading zeroes
if (sig[i] >= 0x80) { // put zero in output if MSB set
*p = 0x00; p++; *len2 = *len2 + 1;
}
while (i < 64) { // copy bytes to output
*p = sig[i]; p++; *len2 = *len2 + 1; i++;
}
*len = *len1 + *len2 + 4;
return *len + 2;
}
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