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trezor-firmware/crypto/schnorr.c
Fabien 9ef26c347e Add support for Schnorr crypto (BCH variant)
Support Schnorr signature and verification defined in
https://github.com/bitcoincashorg/bitcoincash.org/blob/master/spec/2019-05-15-schnorr.md.

The implementation is based on https://github.com/Bitcoin-ABC/secp256k1
as well as the test vectors.
2021-03-09 14:22:56 +01:00

214 lines
5.8 KiB
C

/**
* Copyright (c) 2021 The Bitcoin ABC developers
*
* 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 "schnorr.h"
#include "hmac_drbg.h"
#include "memzero.h"
#include "rfc6979.h"
#include <assert.h>
#include <stdio.h>
#include <string.h>
static int jacobi(const bignum256 *_n, const bignum256 *_k) {
assert(!bn_is_zero(_k) && bn_is_odd(_k));
bignum256 n_copy = {0};
bignum256 *n = &n_copy;
bn_copy(_n, n);
bignum256 k_copy = {0};
bignum256 *k = &k_copy;
bn_copy(_k, k);
int t = 0;
while (!bn_is_zero(n)) {
while (bn_is_even(n)) {
// jacobi(2 * n, k) = jacobi(n, k) if k = 1 (mod 8) or k = 7 (mod 8)
// jacobi(2 * n, k) = -jacobi(n, k) if k = 3 (mod 8) or k = 5 (mod 8)
uint32_t r = k->val[0] & 0x07;
t ^= (r == 3 || r == 5);
bn_rshift(n);
}
if (bn_is_less(n, k)) {
// jacobi(n, k) = jacobi(k, n) if k = n = 1 (mod 4)
// jacobi(n, k) = -jacobi(k, n) if k = n = 3 (mod 4)
t ^= ((n->val[0] & k->val[0] & 3) == 3);
bignum256 *temp = n;
n = k;
k = temp;
}
// jacobi(n, k) = jacobi(n - k, k)
bn_subtract(n, k, n);
}
int k_is_one = bn_is_one(k);
// Cleanup
memzero(&n_copy, sizeof(n_copy));
memzero(&k_copy, sizeof(k_copy));
// Map t: [0] => 1, [1] => -1
t = -2 * t + 1;
return k_is_one * t;
}
static int is_non_quad_residue(const bignum256 *n, const bignum256 *prime) {
return jacobi(n, prime) == -1;
}
static int generate_k_schnorr(const ecdsa_curve *curve, const uint8_t *priv_key,
const uint8_t *hash, bignum256 *k) {
rfc6979_state rng = {0};
uint8_t hmac_data[SHA256_DIGEST_LENGTH + 16] = {0};
/*
* Init the HMAC with additional data specific to Schnorr. This prevents from
* leaking the private key in the case the same message is signed with both
* Schnorr and ECDSA.
*/
memcpy(hmac_data, hash, SHA256_DIGEST_LENGTH);
memcpy(hmac_data + SHA256_DIGEST_LENGTH, "Schnorr+SHA256 ", 16);
hmac_drbg_init(&rng, priv_key, 32, hmac_data, SHA256_DIGEST_LENGTH + 16);
for (int i = 0; i < 10000; i++) {
generate_k_rfc6979(k, &rng);
// If k is too big or too small, we don't like it
if (bn_is_zero(k) || !bn_is_less(k, &curve->order)) {
continue;
}
memzero(&rng, sizeof(rng));
return 0;
}
memzero(&rng, sizeof(rng));
return 1;
}
// e = H(Rx, pub_key, msg_hash)
static void calc_e(const ecdsa_curve *curve, const bignum256 *Rx,
const uint8_t pub_key[33], const uint8_t *msg_hash,
bignum256 *e) {
uint8_t Rxbuf[32] = {0};
SHA256_CTX ctx = {0};
uint8_t digest[SHA256_DIGEST_LENGTH] = {0};
bn_write_be(Rx, Rxbuf);
sha256_Init(&ctx);
sha256_Update(&ctx, Rxbuf, sizeof(Rxbuf));
sha256_Update(&ctx, pub_key, 33);
sha256_Update(&ctx, msg_hash, SHA256_DIGEST_LENGTH);
sha256_Final(&ctx, digest);
bn_read_be(digest, e);
bn_fast_mod(e, &curve->order);
bn_mod(e, &curve->order);
}
int schnorr_sign_digest(const ecdsa_curve *curve, const uint8_t *priv_key,
const uint8_t *digest, uint8_t *sign) {
uint8_t pub_key[33] = {0};
curve_point R = {0};
bignum256 e = {0}, s = {0}, k = {0};
ecdsa_get_public_key33(curve, priv_key, pub_key);
// Compute k
if (generate_k_schnorr(curve, priv_key, digest, &k) != 0) {
memzero(&k, sizeof(k));
return 1;
}
// Compute R = k * G
scalar_multiply(curve, &k, &R);
// If R.y is not a quadratic residue, negate the nonce
bn_cnegate(is_non_quad_residue(&R.y, &curve->prime), &k, &curve->order);
bn_write_be(&R.x, sign);
// Compute e = H(Rx, pub_key, msg_hash)
calc_e(curve, &R.x, pub_key, digest, &e);
// Compute s = k + e * priv_key
bn_read_be(priv_key, &s);
bn_multiply(&e, &s, &curve->order);
bn_addmod(&s, &k, &curve->order);
memzero(&k, sizeof(k));
bn_mod(&s, &curve->order);
bn_write_be(&s, sign + 32);
return 0;
}
int schnorr_verify_digest(const ecdsa_curve *curve, const uint8_t *pub_key,
const uint8_t *digest, const uint8_t *sign) {
curve_point P = {0}, sG = {0}, R = {0};
bignum256 r = {0}, s = {0}, e = {0};
bn_read_be(sign, &r);
bn_read_be(sign + 32, &s);
// Signature is invalid if s >= n or r >= p.
if (!bn_is_less(&r, &curve->prime) || !bn_is_less(&s, &curve->order)) {
return 1;
}
if (!ecdsa_read_pubkey(curve, pub_key, &P)) {
return 2;
}
// Compute e
calc_e(curve, &r, pub_key, digest, &e);
if (bn_is_zero(&e)) {
return 3;
}
// Compute R = sG - eP
bn_subtract(&curve->order, &e, &e);
scalar_multiply(curve, &s, &sG);
point_multiply(curve, &e, &P, &R);
point_add(curve, &sG, &R);
if (point_is_infinity(&R)) {
return 4;
}
// Check r == Rx
if (!bn_is_equal(&r, &R.x)) {
return 5;
}
// Check Ry is a quadratic residue
if (is_non_quad_residue(&R.y, &curve->prime)) {
return 6;
}
return 0;
}