2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
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9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
27 #define I15_LEN ((BR_MAX_EC_SIZE + 29) / 15)
28 #define POINT_LEN (1 + (((BR_MAX_EC_SIZE + 7) >> 3) << 1))
29 #define ORDER_LEN ((BR_MAX_EC_SIZE + 7) >> 3)
31 /* see bearssl_ec.h */
33 br_ecdsa_i15_sign_raw(const br_ec_impl *impl,
34 const br_hash_class *hf, const void *hash_value,
35 const br_ec_private_key *sk, void *sig)
38 * IMPORTANT: this code is fit only for curves with a prime
39 * order. This is needed so that modular reduction of the X
40 * coordinate of a point can be done with a simple subtraction.
41 * We also rely on the last byte of the curve order to be distinct
44 const br_ec_curve_def *cd;
45 uint16_t n[I15_LEN], r[I15_LEN], s[I15_LEN], x[I15_LEN];
46 uint16_t m[I15_LEN], k[I15_LEN], t1[I15_LEN], t2[I15_LEN];
47 unsigned char tt[ORDER_LEN << 1];
48 unsigned char eU[POINT_LEN];
49 size_t hash_len, nlen, ulen;
52 br_hmac_drbg_context drbg;
55 * If the curve is not supported, then exit with an error.
57 if (((impl->supported_curves >> sk->curve) & 1) == 0) {
62 * Get the curve parameters (generator and order).
82 br_i15_decode(n, cd->order, nlen);
83 n0i = br_i15_ninv15(n[1]);
86 * Get private key as an i15 integer. This also checks that the
87 * private key is well-defined (not zero, and less than the
90 if (!br_i15_decode_mod(x, sk->x, sk->xlen, n)) {
93 if (br_i15_iszero(x)) {
100 hash_len = (hf->desc >> BR_HASHDESC_OUT_OFF) & BR_HASHDESC_OUT_MASK;
103 * Truncate and reduce the hash value modulo the curve order.
105 br_ecdsa_i15_bits2int(m, hash_value, hash_len, n[0]);
106 br_i15_sub(m, n, br_i15_sub(m, n, 0) ^ 1);
109 * RFC 6979 generation of the "k" value.
111 * The process uses HMAC_DRBG (with the hash function used to
112 * process the message that is to be signed). The seed is the
113 * concatenation of the encodings of the private key and
114 * the hash value (after truncation and modular reduction).
116 br_i15_encode(tt, nlen, x);
117 br_i15_encode(tt + nlen, nlen, m);
118 br_hmac_drbg_init(&drbg, hf, tt, nlen << 1);
120 br_hmac_drbg_generate(&drbg, tt, nlen);
121 br_ecdsa_i15_bits2int(k, tt, nlen, n[0]);
122 if (br_i15_iszero(k)) {
125 if (br_i15_sub(k, n, 0)) {
131 * Compute k*G and extract the X coordinate, then reduce it
132 * modulo the curve order. Since we support only curves with
133 * prime order, that reduction is only a matter of computing
136 br_i15_encode(tt, nlen, k);
137 ulen = impl->mulgen(eU, tt, nlen, sk->curve);
138 br_i15_zero(r, n[0]);
139 br_i15_decode(r, &eU[1], ulen >> 1);
141 br_i15_sub(r, n, br_i15_sub(r, n, 0) ^ 1);
144 * Compute 1/k in double-Montgomery representation. We do so by
145 * first converting _from_ Montgomery representation (twice),
146 * then using a modular exponentiation.
148 br_i15_from_monty(k, n, n0i);
149 br_i15_from_monty(k, n, n0i);
150 memcpy(tt, cd->order, nlen);
152 br_i15_modpow(k, tt, nlen, n, n0i, t1, t2);
155 * Compute s = (m+xr)/k (mod n).
156 * The k[] array contains R^2/k (double-Montgomery representation);
157 * we thus can use direct Montgomery multiplications and conversions
158 * from Montgomery, avoiding any call to br_i15_to_monty() (which
161 br_i15_from_monty(m, n, n0i);
162 br_i15_montymul(t1, x, r, n, n0i);
163 ctl = br_i15_add(t1, m, 1);
164 ctl |= br_i15_sub(t1, n, 0) ^ 1;
165 br_i15_sub(t1, n, ctl);
166 br_i15_montymul(s, t1, k, n, n0i);
169 * Encode r and s in the signature.
171 br_i15_encode(sig, nlen, r);
172 br_i15_encode((unsigned char *)sig + nlen, nlen, s);