1/*
2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
3 *
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,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
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
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25#include "inner.h"
26
27#define I31_LEN     ((BR_MAX_EC_SIZE + 61) / 31)
28#define POINT_LEN   (1 + (((BR_MAX_EC_SIZE + 7) >> 3) << 1))
29#define ORDER_LEN   ((BR_MAX_EC_SIZE + 7) >> 3)
30
31/* see bearssl_ec.h */
32size_t
33br_ecdsa_i31_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)
36{
37	/*
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
42	 * from 0 and 1.
43	 */
44	const br_ec_curve_def *cd;
45	uint32_t n[I31_LEN], r[I31_LEN], s[I31_LEN], x[I31_LEN];
46	uint32_t m[I31_LEN], k[I31_LEN], t1[I31_LEN], t2[I31_LEN];
47	unsigned char tt[ORDER_LEN << 1];
48	unsigned char eU[POINT_LEN];
49	size_t hash_len, nlen, ulen;
50	uint32_t n0i, ctl;
51	br_hmac_drbg_context drbg;
52
53	/*
54	 * If the curve is not supported, then exit with an error.
55	 */
56	if (((impl->supported_curves >> sk->curve) & 1) == 0) {
57		return 0;
58	}
59
60	/*
61	 * Get the curve parameters (generator and order).
62	 */
63	switch (sk->curve) {
64	case BR_EC_secp256r1:
65		cd = &br_secp256r1;
66		break;
67	case BR_EC_secp384r1:
68		cd = &br_secp384r1;
69		break;
70	case BR_EC_secp521r1:
71		cd = &br_secp521r1;
72		break;
73	default:
74		return 0;
75	}
76
77	/*
78	 * Get modulus.
79	 */
80	nlen = cd->order_len;
81	br_i31_decode(n, cd->order, nlen);
82	n0i = br_i31_ninv31(n[1]);
83
84	/*
85	 * Get private key as an i31 integer. This also checks that the
86	 * private key is well-defined (not zero, and less than the
87	 * curve order).
88	 */
89	if (!br_i31_decode_mod(x, sk->x, sk->xlen, n)) {
90		return 0;
91	}
92	if (br_i31_iszero(x)) {
93		return 0;
94	}
95
96	/*
97	 * Get hash length.
98	 */
99	hash_len = (hf->desc >> BR_HASHDESC_OUT_OFF) & BR_HASHDESC_OUT_MASK;
100
101	/*
102	 * Truncate and reduce the hash value modulo the curve order.
103	 */
104	br_ecdsa_i31_bits2int(m, hash_value, hash_len, n[0]);
105	br_i31_sub(m, n, br_i31_sub(m, n, 0) ^ 1);
106
107	/*
108	 * RFC 6979 generation of the "k" value.
109	 *
110	 * The process uses HMAC_DRBG (with the hash function used to
111	 * process the message that is to be signed). The seed is the
112	 * concatenation of the encodings of the private key and
113	 * the hash value (after truncation and modular reduction).
114	 */
115	br_i31_encode(tt, nlen, x);
116	br_i31_encode(tt + nlen, nlen, m);
117	br_hmac_drbg_init(&drbg, hf, tt, nlen << 1);
118	for (;;) {
119		br_hmac_drbg_generate(&drbg, tt, nlen);
120		br_ecdsa_i31_bits2int(k, tt, nlen, n[0]);
121		if (br_i31_iszero(k)) {
122			continue;
123		}
124		if (br_i31_sub(k, n, 0)) {
125			break;
126		}
127	}
128
129	/*
130	 * Compute k*G and extract the X coordinate, then reduce it
131	 * modulo the curve order. Since we support only curves with
132	 * prime order, that reduction is only a matter of computing
133	 * a subtraction.
134	 */
135	br_i31_encode(tt, nlen, k);
136	ulen = impl->mulgen(eU, tt, nlen, sk->curve);
137	br_i31_zero(r, n[0]);
138	br_i31_decode(r, &eU[1], ulen >> 1);
139	r[0] = n[0];
140	br_i31_sub(r, n, br_i31_sub(r, n, 0) ^ 1);
141
142	/*
143	 * Compute 1/k in double-Montgomery representation. We do so by
144	 * first converting _from_ Montgomery representation (twice),
145	 * then using a modular exponentiation.
146	 */
147	br_i31_from_monty(k, n, n0i);
148	br_i31_from_monty(k, n, n0i);
149	memcpy(tt, cd->order, nlen);
150	tt[nlen - 1] -= 2;
151	br_i31_modpow(k, tt, nlen, n, n0i, t1, t2);
152
153	/*
154	 * Compute s = (m+xr)/k (mod n).
155	 * The k[] array contains R^2/k (double-Montgomery representation);
156	 * we thus can use direct Montgomery multiplications and conversions
157	 * from Montgomery, avoiding any call to br_i31_to_monty() (which
158	 * is slower).
159	 */
160	br_i31_from_monty(m, n, n0i);
161	br_i31_montymul(t1, x, r, n, n0i);
162	ctl = br_i31_add(t1, m, 1);
163	ctl |= br_i31_sub(t1, n, 0) ^ 1;
164	br_i31_sub(t1, n, ctl);
165	br_i31_montymul(s, t1, k, n, n0i);
166
167	/*
168	 * Encode r and s in the signature.
169	 */
170	br_i31_encode(sig, nlen, r);
171	br_i31_encode((unsigned char *)sig + nlen, nlen, s);
172	return nlen << 1;
173}
174