New "i15" implementation of big integers (faster, and constant-time, on ARM Cortex...
[BearSSL] / src / ec / ecdsa_i31_sign_raw.c
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 */
32 size_t
33 br_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 ulen = cd->generator_len;
136 memcpy(eU, cd->generator, ulen);
137 br_i31_encode(tt, nlen, k);
138 if (!impl->mul(eU, ulen, tt, nlen, sk->curve)) {
139 /*
140 * Point multiplication may fail here only if the
141 * EC implementation does not support the curve, or the
142 * private key is incorrect (x is a multiple of the curve
143 * order).
144 */
145 return 0;
146 }
147 br_i31_zero(r, n[0]);
148 br_i31_decode(r, &eU[1], ulen >> 1);
149 r[0] = n[0];
150 br_i31_sub(r, n, br_i31_sub(r, n, 0) ^ 1);
151
152 /*
153 * Compute 1/k in double-Montgomery representation. We do so by
154 * first converting _from_ Montgomery representation (twice),
155 * then using a modular exponentiation.
156 */
157 br_i31_from_monty(k, n, n0i);
158 br_i31_from_monty(k, n, n0i);
159 memcpy(tt, cd->order, nlen);
160 tt[nlen - 1] -= 2;
161 br_i31_modpow(k, tt, nlen, n, n0i, t1, t2);
162
163 /*
164 * Compute s = (m+xr)/k (mod n).
165 * The k[] array contains R^2/k (double-Montgomery representation);
166 * we thus can use direct Montgomery multiplications and conversions
167 * from Montgomery, avoiding any call to br_i31_to_monty() (which
168 * is slower).
169 */
170 br_i31_from_monty(m, n, n0i);
171 br_i31_montymul(t1, x, r, n, n0i);
172 ctl = br_i31_add(t1, m, 1);
173 ctl |= br_i31_sub(t1, n, 0) ^ 1;
174 br_i31_sub(t1, n, ctl);
175 br_i31_montymul(s, t1, k, n, n0i);
176
177 /*
178 * Encode r and s in the signature.
179 */
180 br_i31_encode(sig, nlen, r);
181 br_i31_encode((unsigned char *)sig + nlen, nlen, s);
182 return nlen << 1;
183 }