mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-17 21:22:10 +00:00
414 lines
11 KiB
C
414 lines
11 KiB
C
/**
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
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* and/or sell copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
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* in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES
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* OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
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* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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* OTHER DEALINGS IN THE SOFTWARE.
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*/
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#include <assert.h>
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#include <stdint.h>
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#include <string.h>
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#include "bignum.h"
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#include "ecdsa.h"
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#include "memzero.h"
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#include "nist256p1.h"
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#include "sha2.h"
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#include "hash_to_curve.h"
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// https://www.rfc-editor.org/rfc/rfc9380.html#name-hash_to_field-implementatio
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static bool hash_to_field(const uint8_t *msg, size_t msg_len,
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const uint8_t *dst, // domain separation tag
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const size_t dst_len, size_t expansion_len,
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const bignum256 *prime,
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bool expand(const uint8_t *, size_t, const uint8_t *,
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size_t, uint8_t *, size_t),
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bignum256 *out, size_t out_len) {
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const size_t max_expansion_len = 64;
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if (expansion_len > max_expansion_len) {
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// Not supported by this implementation
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return false;
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}
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const size_t expanded_msg_length = out_len * expansion_len;
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uint8_t expanded_msg[expanded_msg_length];
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memzero(expanded_msg, sizeof(expanded_msg));
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if (!expand(msg, msg_len, dst, dst_len, expanded_msg, expanded_msg_length)) {
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return false;
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}
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uint8_t raw_number[max_expansion_len];
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memzero(raw_number, sizeof(raw_number));
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bignum512 bn_number = {0};
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for (size_t i = 0; i < out_len; i++) {
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memcpy(raw_number + (max_expansion_len - expansion_len),
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expanded_msg + i * expansion_len, expansion_len);
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bn_read_be_512(raw_number, &bn_number);
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bn_reduce(&bn_number, prime);
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bn_copy_lower(&bn_number, &out[i]);
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bn_mod(&out[i], prime);
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}
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memzero(expanded_msg, sizeof(expanded_msg));
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memzero(raw_number, sizeof(raw_number));
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memzero(&bn_number, sizeof(bn_number));
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return true;
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}
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// Simplified Shallue-van de Woestijne-Ulas Method
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// https://www.rfc-editor.org/rfc/rfc9380.html#name-simplified-shallue-van-de-w
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// Algorithm assumptions:
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// * z is a non-square modulo p
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// * z != -1 modulo p
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// * x^2 + a * x + b - z is an irreducible polynomial modulo p
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// * (b/(z*a))^2 + a * (b/(z*a)) + b is a square modulo p
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// * z is not zero
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// * a is not zero
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// * b is not zero
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// * p is at least 6
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// Implementation assumptions:
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// * p is a prime
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// * 2**256 - 2**224 <= prime <= 2**256
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// * p % 4 == 3
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static bool simple_swu(const bignum256 *u, const bignum256 *a,
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const bignum256 *b, const bignum256 *p,
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const bignum256 *z, int sign_function(const bignum256 *),
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curve_point *point) {
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if (bn_is_zero(a) || bn_is_zero(b) || (p->val[0] % 4 != 3)) {
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return false;
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}
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// c1 = -b / a
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bignum256 c1 = {0};
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bn_copy(a, &c1);
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bn_subtract(p, &c1, &c1);
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bn_inverse(&c1, p);
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bn_multiply(b, &c1, p);
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bn_mod(&c1, p);
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// c2 = -1 / z
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bignum256 c2 = {0};
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bn_copy(z, &c2);
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bn_subtract(p, &c2, &c2);
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bn_inverse(&c2, p);
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bn_mod(&c2, p);
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// t1 = z * u^2
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bignum256 t1 = {0};
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bn_copy(u, &t1);
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bn_multiply(&t1, &t1, p);
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bn_mod(&t1, p);
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bn_multiply(z, &t1, p);
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bn_mod(&t1, p);
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// t2 = t1^2
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bignum256 t2 = {0};
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bn_copy(&t1, &t2);
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bn_multiply(&t2, &t2, p);
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bn_mod(&t2, p);
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// x1 = t1 + t2
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bignum256 x1 = {0};
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bn_copy(&t1, &x1);
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bn_add(&x1, &t2);
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bn_mod(&x1, p);
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// x1 = inv0(1)
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bn_inverse(&x1, p);
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// e1 = x1 == 0
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int e1 = bn_is_zero(&x1);
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// x1 = x1 + 1
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bn_addi(&x1, 1);
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bn_mod(&x1, p);
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// x1 = CMOV(x1, c2, e1)
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bn_cmov(&x1, e1, &c2, &x1);
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memzero(&c2, sizeof(c2));
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// x1 = x1 * c1
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bn_multiply(&c1, &x1, p);
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memzero(&c1, sizeof(c1));
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bn_mod(&x1, p);
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// gx1 = x1^2
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bignum256 gx1 = {0};
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bn_copy(&x1, &gx1);
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bn_multiply(&x1, &gx1, p);
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bn_mod(&gx1, p);
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// gx1 = gx1 + A
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bn_add(&gx1, a);
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bn_mod(&gx1, p);
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// gx1 = gx1 * x1
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bn_multiply(&x1, &gx1, p);
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bn_mod(&gx1, p);
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// gx1 = gx1 + B
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bn_add(&gx1, b);
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bn_mod(&gx1, p);
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// x2 = t1 * x1
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bignum256 x2 = {0};
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bn_copy(&t1, &x2);
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bn_multiply(&x1, &x2, p);
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bn_mod(&x2, p);
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// t2 = t1 * t2
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bn_multiply(&t1, &t2, p);
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memzero(&t1, sizeof(t1));
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bn_mod(&t2, p);
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// gx2 = gx1 * t2
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bignum256 gx2 = {0};
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bn_copy(&gx1, &gx2);
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bn_multiply(&t2, &gx2, p);
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memzero(&t2, sizeof(t2));
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bn_mod(&gx2, p);
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// e2 = is_square(gx1)
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int e2 = bn_legendre(&gx1, p) >= 0;
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// x = CMOV(x2, x1, e2)
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bignum256 x = {0};
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bn_cmov(&x, e2, &x1, &x2);
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memzero(&x1, sizeof(x1));
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memzero(&x2, sizeof(x2));
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// y2 = CMOV(gx2, gx1, e2)
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bignum256 y2 = {0};
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bn_cmov(&y2, e2, &gx1, &gx2);
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memzero(&gx1, sizeof(gx1));
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memzero(&gx2, sizeof(gx2));
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// y = sqrt(y2)
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bignum256 y = {0};
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bn_copy(&y2, &y);
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memzero(&y2, sizeof(y2));
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bn_sqrt(&y, p); // This is the slowest operation
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// e3 = sgn0(u) == sgn0(y)
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int e3 = sign_function(u) == sign_function(&y);
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bignum256 minus_y = {0};
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bn_subtract(p, &y, &minus_y);
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// y = CMOV(-y, y, e3)
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bn_cmov(&y, e3, &y, &minus_y);
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memzero(&minus_y, sizeof(minus_y));
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bn_copy(&x, &point->x);
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bn_copy(&y, &point->y);
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memzero(&x, sizeof(x));
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memzero(&y, sizeof(y));
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return true;
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}
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static void bn_read_int32(int32_t in_number, const bignum256 *prime,
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bignum256 *out_number) {
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if (in_number < 0) {
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bn_read_uint32(-in_number, out_number);
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bn_subtract(prime, out_number, out_number);
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} else {
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bn_read_uint32(in_number, out_number);
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}
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}
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// https://www.rfc-editor.org/rfc/rfc9380.html#name-encoding-byte-strings-to-el
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static bool hash_to_curve(const uint8_t *msg, size_t msg_len,
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const ecdsa_curve *curve, const uint8_t *suite_id,
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const uint8_t suite_id_len, int z, int cofactor,
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bool expand_function(const uint8_t *, size_t,
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const uint8_t *, size_t,
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uint8_t *, size_t),
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int sign_function(const bignum256 *),
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curve_point *point) {
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if (cofactor != 1) {
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// Not supported by this implementation
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return false;
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}
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bignum256 bn_z = {0};
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bn_read_int32(z, &curve->prime, &bn_z);
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bignum256 bn_a = {0};
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bn_read_int32(curve->a, &curve->prime, &bn_a);
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bignum256 u[2] = {0};
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if (!hash_to_field(msg, msg_len, suite_id, suite_id_len, 48, &curve->prime,
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expand_function, u, 2)) {
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return false;
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}
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curve_point point1 = {0}, point2 = {0};
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if (!simple_swu(&u[0], &bn_a, &curve->b, &curve->prime, &bn_z, sign_function,
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&point1)) {
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memzero(&u[0], sizeof(u[0]));
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return false;
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}
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memzero(&u[0], sizeof(u[0]));
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if (!simple_swu(&u[1], &bn_a, &curve->b, &curve->prime, &bn_z, sign_function,
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&point2)) {
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memzero(&u[1], sizeof(u[1]));
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return false;
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}
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memzero(&u[1], sizeof(u[1]));
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point_add(curve, &point1, &point2);
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point->x = point2.x;
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point->y = point2.y;
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memzero(&point1, sizeof(point1));
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memzero(&point2, sizeof(point2));
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return true;
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}
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static int sgn0(const bignum256 *a) {
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// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-05#section-4.1.2
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if (bn_is_even(a)) {
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return 1;
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}
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return -1;
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}
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// https://www.rfc-editor.org/rfc/rfc9380.html#hashtofield-expand-xmd
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bool expand_message_xmd_sha256(const uint8_t *msg, size_t msg_len,
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const uint8_t *dst, // domain separation tag
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size_t dst_len, uint8_t *output,
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size_t output_len) {
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if (dst_len > 255) {
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return false;
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}
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if ((output_len > 65535) || (output_len > 255 * SHA256_DIGEST_LENGTH)) {
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return false;
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}
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const uint8_t zero_block[SHA256_BLOCK_LENGTH] = {0};
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const uint8_t output_len_bytes[2] = {(output_len >> 8) & 255,
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output_len & 255};
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const uint8_t dst_len_bytes[1] = {dst_len & 255};
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const uint8_t zero[1] = {0};
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SHA256_CTX ctx = {0};
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sha256_Init(&ctx);
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// Z_pad = I2OSP(0, s_in_bytes)
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sha256_Update(&ctx, zero_block, sizeof(zero_block));
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// msg
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sha256_Update(&ctx, msg, msg_len);
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// l_i_b_str = I2OSP(len_in_bytes, 2)
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sha256_Update(&ctx, output_len_bytes, sizeof(output_len_bytes));
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// I2OSP(0, 1)
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sha256_Update(&ctx, zero, sizeof(zero));
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// DST_prime = DST || I2OSP(len(DST), 1)
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sha256_Update(&ctx, dst, dst_len);
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sha256_Update(&ctx, dst_len_bytes, sizeof(dst_len_bytes));
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uint8_t first_digest[SHA256_DIGEST_LENGTH] = {0}; // b_0
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sha256_Final(&ctx, first_digest);
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uint8_t current_digest[SHA256_DIGEST_LENGTH] = {0}; // b_i
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size_t output_position = 0;
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size_t remaining_output_length = output_len;
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int i = 1;
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while (remaining_output_length > 0) {
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const uint8_t i_bytes[1] = {i & 255};
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// strxor(b_0, b_(i - 1))
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for (size_t j = 0; j < sizeof(current_digest); j++) {
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current_digest[j] ^= first_digest[j];
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}
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sha256_Init(&ctx);
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// strxor(b_0, b_(i - 1))
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sha256_Update(&ctx, current_digest, sizeof(current_digest));
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// I2OSP(i, 1)
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sha256_Update(&ctx, i_bytes, sizeof(i_bytes));
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// DST_prime = DST || I2OSP(len(DST), 1)
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sha256_Update(&ctx, dst, dst_len);
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sha256_Update(&ctx, dst_len_bytes, sizeof(dst_len_bytes));
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sha256_Final(&ctx, current_digest);
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const size_t copy_length = remaining_output_length > SHA256_DIGEST_LENGTH
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? SHA256_DIGEST_LENGTH
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: remaining_output_length;
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memcpy(output + output_position, current_digest, copy_length);
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output_position += copy_length;
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remaining_output_length -= copy_length;
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i++;
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}
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memzero(&ctx, sizeof(ctx));
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memzero(first_digest, sizeof(first_digest));
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memzero(current_digest, sizeof(current_digest));
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return true;
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}
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bool hash_to_curve_p256(const uint8_t *msg, size_t msg_len, const uint8_t *dst,
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size_t dst_len, curve_point *point) {
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// https://www.rfc-editor.org/rfc/rfc9380.html#suites-p256
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// P256_XMD:SHA-256_SSWU_RO_
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if (!hash_to_curve(msg, msg_len, &nist256p1, dst, dst_len, -10, 1,
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expand_message_xmd_sha256, sgn0, point)) {
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return false;
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}
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return true;
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}
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bool hash_to_curve_optiga(const uint8_t input[32], uint8_t public_key[65]) {
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char dst[] = "OPTIGA-SECRET-V0-P256_XMD:SHA-256_SSWU_RO_";
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curve_point point = {0};
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if (!hash_to_curve_p256(input, 32, (uint8_t *)dst, sizeof(dst) - 1, &point)) {
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return false;
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}
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public_key[0] = 0x04;
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bn_write_be(&point.x, public_key + 1);
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bn_write_be(&point.y, public_key + 33);
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memzero(&point, sizeof(point));
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return true;
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}
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