You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
447 lines
11 KiB
447 lines
11 KiB
/**
|
|
* 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 "bignum.h"
|
|
#include "rand.h"
|
|
#include "sha2.h"
|
|
#include "ripemd160.h"
|
|
#include "hmac.h"
|
|
#include "ecdsa.h"
|
|
|
|
// cp2 = cp1 + cp2
|
|
void point_add(const curve_point *cp1, curve_point *cp2)
|
|
{
|
|
int i;
|
|
uint32_t temp;
|
|
bignum256 lambda, inv, xr, yr;
|
|
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));
|
|
}
|
|
|
|
// 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));
|
|
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));
|
|
}
|
|
|
|
// res = k * G
|
|
void scalar_multiply(bignum256 *k, curve_point *res)
|
|
{
|
|
int i, j;
|
|
// result is zero
|
|
int is_zero = 1;
|
|
#if 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) {
|
|
#if USE_PRECOMPUTED_CP
|
|
memcpy(res, secp256k1_cp + exp, sizeof(curve_point));
|
|
#else
|
|
memcpy(res, &curr, sizeof(curve_point));
|
|
#endif
|
|
is_zero = 0;
|
|
} else {
|
|
#if USE_PRECOMPUTED_CP
|
|
point_add(secp256k1_cp + exp, res);
|
|
#else
|
|
point_add(&curr, res);
|
|
#endif
|
|
}
|
|
}
|
|
#if USE_PRECOMPUTED_CP
|
|
exp++;
|
|
#else
|
|
point_double(&curr);
|
|
#endif
|
|
}
|
|
}
|
|
bn_mod(&(res->x), &prime256k1);
|
|
bn_mod(&(res->y), &prime256k1);
|
|
}
|
|
|
|
// 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;
|
|
}
|
|
|
|
// 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 64 bytes long array for the signature
|
|
int ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig)
|
|
{
|
|
uint32_t i;
|
|
uint8_t hash[32];
|
|
curve_point R;
|
|
bignum256 k, z;
|
|
bignum256 *da = &R.y;
|
|
// compute hash function of message
|
|
SHA256_Raw(msg, msg_len, hash);
|
|
// if double hash is required uncomment the following line:
|
|
// SHA256_Raw(hash, 32, hash);
|
|
|
|
bn_read_be(hash, &z);
|
|
|
|
#if USE_RFC6979
|
|
// generate K deterministically
|
|
if (generate_k_rfc6979(&k, priv_key, hash) != 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_address(const uint8_t *pub_key, uint8_t version, char *addr)
|
|
{
|
|
const char code[] = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz";
|
|
char *p = addr, s;
|
|
uint8_t a[32], b[21];
|
|
uint32_t r;
|
|
bignum256 c;
|
|
int i, l;
|
|
|
|
if (pub_key[0] == 0x04) {
|
|
SHA256_Raw(pub_key, 65, a);
|
|
} else {
|
|
SHA256_Raw(pub_key, 33, a);
|
|
}
|
|
b[0] = version;
|
|
ripemd160(a, 32, b + 1);
|
|
|
|
SHA256_Raw(b, 21, a);
|
|
SHA256_Raw(a, 32, a);
|
|
|
|
memcpy(a + 28, a, 4); // checksum
|
|
memset(a, 0, 7); // zeroes
|
|
memcpy(a + 7, b, 21); // ripemd160(sha256(version + pubkey)
|
|
|
|
bn_read_be(a, &c);
|
|
|
|
while (!bn_is_zero(&c)) {
|
|
bn_divmod58(&c, &r);
|
|
*p = code[r];
|
|
p++;
|
|
}
|
|
|
|
i = 7;
|
|
while (a[i] == 0) {
|
|
*p = code[0];
|
|
p++; i++;
|
|
}
|
|
|
|
*p = 0;
|
|
|
|
l = strlen(addr);
|
|
|
|
for (i = 0; i < l / 2; i++) {
|
|
s = addr[i];
|
|
addr[i] = addr[l - 1 - i];
|
|
addr[l - 1 - i] = s;
|
|
}
|
|
}
|
|
|
|
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));
|
|
return 1;
|
|
}
|
|
|
|
if (pub_key[0] == 0x02 || pub_key[0] == 0x03) { // compute missing y coords
|
|
// y^2 = x^3 + 0*x + 7
|
|
bn_read_be(pub_key + 1, &(pub->x));
|
|
bn_read_be(pub_key + 1, &(pub->y)); // y is x
|
|
bn_multiply(&(pub->x), &(pub->y), &prime256k1); // y is x^2
|
|
bn_multiply(&(pub->x), &(pub->y), &prime256k1); // y is x^3
|
|
bn_addmodi(&(pub->y), 7, &prime256k1); // y is x^3 + 7
|
|
bn_sqrt(&(pub->y), &prime256k1); // y = sqrt(y)
|
|
if ((pub_key[0] & 0x01) != (pub->y.val[0] & 1)) {
|
|
bn_substract(&prime256k1, &(pub->y), &(pub->y)); // y = -y
|
|
bn_mod(&(pub->y), &prime256k1);
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
// error
|
|
return 0;
|
|
}
|
|
|
|
// 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
|
|
// returns 0 if verification succeeded
|
|
// it is assumed that public key is valid otherwise calling this does not make much sense
|
|
int ecdsa_verify(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
|
|
{
|
|
int i, j;
|
|
uint8_t hash[32];
|
|
curve_point pub, res;
|
|
bignum256 r, s, z;
|
|
// compute hash function of message
|
|
SHA256_Raw(msg, msg_len, hash);
|
|
// if double hash is required uncomment the following line:
|
|
// SHA256_Raw(hash, 32, hash);
|
|
|
|
if (!ecdsa_read_pubkey(pub_key, &pub)) {
|
|
return 1;
|
|
}
|
|
|
|
bn_read_be(sig, &r);
|
|
bn_read_be(sig + 32, &s);
|
|
|
|
bn_read_be(hash, &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)) {
|
|
bn_mod(&(pub.y), &prime256k1);
|
|
bn_mod(&(res.y), &prime256k1);
|
|
if (bn_is_equal(&(pub.y), &(res.y))) {
|
|
// this is not a failure, but a very inprobable case
|
|
// that we don't handle because of its inprobability
|
|
return 4;
|
|
}
|
|
point_add(&pub, &res);
|
|
}
|
|
point_double(&pub);
|
|
}
|
|
}
|
|
|
|
bn_mod(&(res.x), &prime256k1);
|
|
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;
|
|
}
|