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.
414 lines
11 KiB
414 lines
11 KiB
/**
|
|
* 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 <assert.h>
|
|
#include <stdint.h>
|
|
#include <string.h>
|
|
|
|
#include "bignum.h"
|
|
#include "ecdsa.h"
|
|
#include "memzero.h"
|
|
#include "nist256p1.h"
|
|
#include "sha2.h"
|
|
|
|
#include "hash_to_curve.h"
|
|
|
|
// https://www.rfc-editor.org/rfc/rfc9380.html#name-hash_to_field-implementatio
|
|
static bool hash_to_field(const uint8_t *msg, size_t msg_len,
|
|
const uint8_t *dst, // domain separation tag
|
|
const size_t dst_len, size_t expansion_len,
|
|
const bignum256 *prime,
|
|
bool expand(const uint8_t *, size_t, const uint8_t *,
|
|
size_t, uint8_t *, size_t),
|
|
bignum256 *out, size_t out_len) {
|
|
const size_t max_expansion_len = 64;
|
|
if (expansion_len > max_expansion_len) {
|
|
// Not supported by this implementation
|
|
return false;
|
|
}
|
|
|
|
const size_t expanded_msg_length = out_len * expansion_len;
|
|
uint8_t expanded_msg[expanded_msg_length];
|
|
memzero(expanded_msg, sizeof(expanded_msg));
|
|
|
|
if (!expand(msg, msg_len, dst, dst_len, expanded_msg, expanded_msg_length)) {
|
|
return false;
|
|
}
|
|
|
|
uint8_t raw_number[max_expansion_len];
|
|
memzero(raw_number, sizeof(raw_number));
|
|
bignum512 bn_number = {0};
|
|
|
|
for (size_t i = 0; i < out_len; i++) {
|
|
memcpy(raw_number + (max_expansion_len - expansion_len),
|
|
expanded_msg + i * expansion_len, expansion_len);
|
|
|
|
bn_read_be_512(raw_number, &bn_number);
|
|
bn_reduce(&bn_number, prime);
|
|
bn_copy_lower(&bn_number, &out[i]);
|
|
bn_mod(&out[i], prime);
|
|
}
|
|
|
|
memzero(expanded_msg, sizeof(expanded_msg));
|
|
memzero(raw_number, sizeof(raw_number));
|
|
memzero(&bn_number, sizeof(bn_number));
|
|
|
|
return true;
|
|
}
|
|
|
|
// Simplified Shallue-van de Woestijne-Ulas Method
|
|
// https://www.rfc-editor.org/rfc/rfc9380.html#name-simplified-shallue-van-de-w
|
|
// Algorithm assumptions:
|
|
// * z is a non-square modulo p
|
|
// * z != -1 modulo p
|
|
// * x^2 + a * x + b - z is an irreducible polynomial modulo p
|
|
// * (b/(z*a))^2 + a * (b/(z*a)) + b is a square modulo p
|
|
// * z is not zero
|
|
// * a is not zero
|
|
// * b is not zero
|
|
// * p is at least 6
|
|
// Implementation assumptions:
|
|
// * p is a prime
|
|
// * 2**256 - 2**224 <= prime <= 2**256
|
|
// * p % 4 == 3
|
|
static bool simple_swu(const bignum256 *u, const bignum256 *a,
|
|
const bignum256 *b, const bignum256 *p,
|
|
const bignum256 *z, int sign_function(const bignum256 *),
|
|
curve_point *point) {
|
|
if (bn_is_zero(a) || bn_is_zero(b) || (p->val[0] % 4 != 3)) {
|
|
return false;
|
|
}
|
|
|
|
// c1 = -b / a
|
|
bignum256 c1 = {0};
|
|
bn_copy(a, &c1);
|
|
bn_subtract(p, &c1, &c1);
|
|
bn_inverse(&c1, p);
|
|
bn_multiply(b, &c1, p);
|
|
bn_mod(&c1, p);
|
|
|
|
// c2 = -1 / z
|
|
bignum256 c2 = {0};
|
|
bn_copy(z, &c2);
|
|
bn_subtract(p, &c2, &c2);
|
|
bn_inverse(&c2, p);
|
|
bn_mod(&c2, p);
|
|
|
|
// t1 = z * u^2
|
|
bignum256 t1 = {0};
|
|
bn_copy(u, &t1);
|
|
bn_multiply(&t1, &t1, p);
|
|
bn_mod(&t1, p);
|
|
bn_multiply(z, &t1, p);
|
|
bn_mod(&t1, p);
|
|
|
|
// t2 = t1^2
|
|
bignum256 t2 = {0};
|
|
bn_copy(&t1, &t2);
|
|
bn_multiply(&t2, &t2, p);
|
|
bn_mod(&t2, p);
|
|
|
|
// x1 = t1 + t2
|
|
bignum256 x1 = {0};
|
|
bn_copy(&t1, &x1);
|
|
bn_add(&x1, &t2);
|
|
bn_mod(&x1, p);
|
|
|
|
// x1 = inv0(1)
|
|
bn_inverse(&x1, p);
|
|
|
|
// e1 = x1 == 0
|
|
int e1 = bn_is_zero(&x1);
|
|
|
|
// x1 = x1 + 1
|
|
bn_addi(&x1, 1);
|
|
bn_mod(&x1, p);
|
|
|
|
// x1 = CMOV(x1, c2, e1)
|
|
bn_cmov(&x1, e1, &c2, &x1);
|
|
memzero(&c2, sizeof(c2));
|
|
|
|
// x1 = x1 * c1
|
|
bn_multiply(&c1, &x1, p);
|
|
memzero(&c1, sizeof(c1));
|
|
bn_mod(&x1, p);
|
|
|
|
// gx1 = x1^2
|
|
bignum256 gx1 = {0};
|
|
bn_copy(&x1, &gx1);
|
|
bn_multiply(&x1, &gx1, p);
|
|
bn_mod(&gx1, p);
|
|
|
|
// gx1 = gx1 + A
|
|
bn_add(&gx1, a);
|
|
bn_mod(&gx1, p);
|
|
|
|
// gx1 = gx1 * x1
|
|
bn_multiply(&x1, &gx1, p);
|
|
bn_mod(&gx1, p);
|
|
|
|
// gx1 = gx1 + B
|
|
bn_add(&gx1, b);
|
|
bn_mod(&gx1, p);
|
|
|
|
// x2 = t1 * x1
|
|
bignum256 x2 = {0};
|
|
bn_copy(&t1, &x2);
|
|
bn_multiply(&x1, &x2, p);
|
|
bn_mod(&x2, p);
|
|
|
|
// t2 = t1 * t2
|
|
bn_multiply(&t1, &t2, p);
|
|
memzero(&t1, sizeof(t1));
|
|
bn_mod(&t2, p);
|
|
|
|
// gx2 = gx1 * t2
|
|
bignum256 gx2 = {0};
|
|
bn_copy(&gx1, &gx2);
|
|
bn_multiply(&t2, &gx2, p);
|
|
memzero(&t2, sizeof(t2));
|
|
bn_mod(&gx2, p);
|
|
|
|
// e2 = is_square(gx1)
|
|
int e2 = bn_legendre(&gx1, p) >= 0;
|
|
|
|
// x = CMOV(x2, x1, e2)
|
|
bignum256 x = {0};
|
|
bn_cmov(&x, e2, &x1, &x2);
|
|
memzero(&x1, sizeof(x1));
|
|
memzero(&x2, sizeof(x2));
|
|
|
|
// y2 = CMOV(gx2, gx1, e2)
|
|
bignum256 y2 = {0};
|
|
bn_cmov(&y2, e2, &gx1, &gx2);
|
|
memzero(&gx1, sizeof(gx1));
|
|
memzero(&gx2, sizeof(gx2));
|
|
|
|
// y = sqrt(y2)
|
|
bignum256 y = {0};
|
|
bn_copy(&y2, &y);
|
|
memzero(&y2, sizeof(y2));
|
|
bn_sqrt(&y, p); // This is the slowest operation
|
|
|
|
// e3 = sgn0(u) == sgn0(y)
|
|
int e3 = sign_function(u) == sign_function(&y);
|
|
|
|
bignum256 minus_y = {0};
|
|
bn_subtract(p, &y, &minus_y);
|
|
|
|
// y = CMOV(-y, y, e3)
|
|
bn_cmov(&y, e3, &y, &minus_y);
|
|
memzero(&minus_y, sizeof(minus_y));
|
|
|
|
bn_copy(&x, &point->x);
|
|
bn_copy(&y, &point->y);
|
|
memzero(&x, sizeof(x));
|
|
memzero(&y, sizeof(y));
|
|
|
|
return true;
|
|
}
|
|
|
|
static void bn_read_int32(int32_t in_number, const bignum256 *prime,
|
|
bignum256 *out_number) {
|
|
if (in_number < 0) {
|
|
bn_read_uint32(-in_number, out_number);
|
|
bn_subtract(prime, out_number, out_number);
|
|
} else {
|
|
bn_read_uint32(in_number, out_number);
|
|
}
|
|
}
|
|
|
|
// https://www.rfc-editor.org/rfc/rfc9380.html#name-encoding-byte-strings-to-el
|
|
static bool hash_to_curve(const uint8_t *msg, size_t msg_len,
|
|
const ecdsa_curve *curve, const uint8_t *suite_id,
|
|
const uint8_t suite_id_len, int z, int cofactor,
|
|
bool expand_function(const uint8_t *, size_t,
|
|
const uint8_t *, size_t,
|
|
uint8_t *, size_t),
|
|
int sign_function(const bignum256 *),
|
|
curve_point *point) {
|
|
if (cofactor != 1) {
|
|
// Not supported by this implementation
|
|
return false;
|
|
}
|
|
|
|
bignum256 bn_z = {0};
|
|
bn_read_int32(z, &curve->prime, &bn_z);
|
|
|
|
bignum256 bn_a = {0};
|
|
bn_read_int32(curve->a, &curve->prime, &bn_a);
|
|
|
|
bignum256 u[2] = {0};
|
|
|
|
if (!hash_to_field(msg, msg_len, suite_id, suite_id_len, 48, &curve->prime,
|
|
expand_function, u, 2)) {
|
|
return false;
|
|
}
|
|
|
|
curve_point point1 = {0}, point2 = {0};
|
|
|
|
if (!simple_swu(&u[0], &bn_a, &curve->b, &curve->prime, &bn_z, sign_function,
|
|
&point1)) {
|
|
memzero(&u[0], sizeof(u[0]));
|
|
return false;
|
|
}
|
|
memzero(&u[0], sizeof(u[0]));
|
|
|
|
if (!simple_swu(&u[1], &bn_a, &curve->b, &curve->prime, &bn_z, sign_function,
|
|
&point2)) {
|
|
memzero(&u[1], sizeof(u[1]));
|
|
return false;
|
|
}
|
|
memzero(&u[1], sizeof(u[1]));
|
|
|
|
point_add(curve, &point1, &point2);
|
|
|
|
point->x = point2.x;
|
|
point->y = point2.y;
|
|
|
|
memzero(&point1, sizeof(point1));
|
|
memzero(&point2, sizeof(point2));
|
|
|
|
return true;
|
|
}
|
|
|
|
static int sgn0(const bignum256 *a) {
|
|
// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-05#section-4.1.2
|
|
if (bn_is_even(a)) {
|
|
return 1;
|
|
}
|
|
|
|
return -1;
|
|
}
|
|
|
|
// https://www.rfc-editor.org/rfc/rfc9380.html#hashtofield-expand-xmd
|
|
bool expand_message_xmd_sha256(const uint8_t *msg, size_t msg_len,
|
|
const uint8_t *dst, // domain separation tag
|
|
size_t dst_len, uint8_t *output,
|
|
size_t output_len) {
|
|
if (dst_len > 255) {
|
|
return false;
|
|
}
|
|
|
|
if ((output_len > 65535) || (output_len > 255 * SHA256_DIGEST_LENGTH)) {
|
|
return false;
|
|
}
|
|
|
|
const uint8_t zero_block[SHA256_BLOCK_LENGTH] = {0};
|
|
const uint8_t output_len_bytes[2] = {(output_len >> 8) & 255,
|
|
output_len & 255};
|
|
const uint8_t dst_len_bytes[1] = {dst_len & 255};
|
|
const uint8_t zero[1] = {0};
|
|
|
|
SHA256_CTX ctx = {0};
|
|
sha256_Init(&ctx);
|
|
|
|
// Z_pad = I2OSP(0, s_in_bytes)
|
|
sha256_Update(&ctx, zero_block, sizeof(zero_block));
|
|
|
|
// msg
|
|
sha256_Update(&ctx, msg, msg_len);
|
|
|
|
// l_i_b_str = I2OSP(len_in_bytes, 2)
|
|
sha256_Update(&ctx, output_len_bytes, sizeof(output_len_bytes));
|
|
|
|
// I2OSP(0, 1)
|
|
sha256_Update(&ctx, zero, sizeof(zero));
|
|
|
|
// DST_prime = DST || I2OSP(len(DST), 1)
|
|
sha256_Update(&ctx, dst, dst_len);
|
|
sha256_Update(&ctx, dst_len_bytes, sizeof(dst_len_bytes));
|
|
|
|
uint8_t first_digest[SHA256_DIGEST_LENGTH] = {0}; // b_0
|
|
sha256_Final(&ctx, first_digest);
|
|
|
|
uint8_t current_digest[SHA256_DIGEST_LENGTH] = {0}; // b_i
|
|
|
|
size_t output_position = 0;
|
|
size_t remaining_output_length = output_len;
|
|
int i = 1;
|
|
|
|
while (remaining_output_length > 0) {
|
|
const uint8_t i_bytes[1] = {i & 255};
|
|
|
|
// strxor(b_0, b_(i - 1))
|
|
for (size_t j = 0; j < sizeof(current_digest); j++) {
|
|
current_digest[j] ^= first_digest[j];
|
|
}
|
|
|
|
sha256_Init(&ctx);
|
|
|
|
// strxor(b_0, b_(i - 1))
|
|
sha256_Update(&ctx, current_digest, sizeof(current_digest));
|
|
|
|
// I2OSP(i, 1)
|
|
sha256_Update(&ctx, i_bytes, sizeof(i_bytes));
|
|
|
|
// DST_prime = DST || I2OSP(len(DST), 1)
|
|
sha256_Update(&ctx, dst, dst_len);
|
|
sha256_Update(&ctx, dst_len_bytes, sizeof(dst_len_bytes));
|
|
|
|
sha256_Final(&ctx, current_digest);
|
|
|
|
const size_t copy_length = remaining_output_length > SHA256_DIGEST_LENGTH
|
|
? SHA256_DIGEST_LENGTH
|
|
: remaining_output_length;
|
|
memcpy(output + output_position, current_digest, copy_length);
|
|
|
|
output_position += copy_length;
|
|
remaining_output_length -= copy_length;
|
|
i++;
|
|
}
|
|
|
|
memzero(&ctx, sizeof(ctx));
|
|
memzero(first_digest, sizeof(first_digest));
|
|
memzero(current_digest, sizeof(current_digest));
|
|
|
|
return true;
|
|
}
|
|
|
|
bool hash_to_curve_p256(const uint8_t *msg, size_t msg_len, const uint8_t *dst,
|
|
size_t dst_len, curve_point *point) {
|
|
// https://www.rfc-editor.org/rfc/rfc9380.html#suites-p256
|
|
// P256_XMD:SHA-256_SSWU_RO_
|
|
if (!hash_to_curve(msg, msg_len, &nist256p1, dst, dst_len, -10, 1,
|
|
expand_message_xmd_sha256, sgn0, point)) {
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool hash_to_curve_optiga(const uint8_t input[32], uint8_t public_key[65]) {
|
|
char dst[] = "OPTIGA-SECRET-V0-P256_XMD:SHA-256_SSWU_RO_";
|
|
curve_point point = {0};
|
|
|
|
if (!hash_to_curve_p256(input, 32, (uint8_t *)dst, sizeof(dst) - 1, &point)) {
|
|
return false;
|
|
}
|
|
|
|
public_key[0] = 0x04;
|
|
bn_write_be(&point.x, public_key + 1);
|
|
bn_write_be(&point.y, public_key + 33);
|
|
|
|
memzero(&point, sizeof(point));
|
|
|
|
return true;
|
|
}
|