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
30 /* see bearssl_ec.h */
31 uint32_t
br_ecdsa_i31_vrfy_raw(const br_ec_impl * impl,const void * hash,size_t hash_len,const br_ec_public_key * pk,const void * sig,size_t sig_len)32 br_ecdsa_i31_vrfy_raw(const br_ec_impl *impl,
33 const void *hash, size_t hash_len,
34 const br_ec_public_key *pk,
35 const void *sig, size_t sig_len)
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 */
42 const br_ec_curve_def *cd;
43 uint32_t n[I31_LEN], r[I31_LEN], s[I31_LEN], t1[I31_LEN], t2[I31_LEN];
44 unsigned char tx[(BR_MAX_EC_SIZE + 7) >> 3];
45 unsigned char ty[(BR_MAX_EC_SIZE + 7) >> 3];
46 unsigned char eU[POINT_LEN];
47 size_t nlen, rlen, ulen;
48 uint32_t n0i, res;
49
50 /*
51 * If the curve is not supported, then report an error.
52 */
53 if (((impl->supported_curves >> pk->curve) & 1) == 0) {
54 return 0;
55 }
56
57 /*
58 * Get the curve parameters (generator and order).
59 */
60 switch (pk->curve) {
61 case BR_EC_secp256r1:
62 cd = &br_secp256r1;
63 break;
64 case BR_EC_secp384r1:
65 cd = &br_secp384r1;
66 break;
67 case BR_EC_secp521r1:
68 cd = &br_secp521r1;
69 break;
70 default:
71 return 0;
72 }
73
74 /*
75 * Signature length must be even.
76 */
77 if (sig_len & 1) {
78 return 0;
79 }
80 rlen = sig_len >> 1;
81
82 /*
83 * Public key point must have the proper size for this curve.
84 */
85 if (pk->qlen != cd->generator_len) {
86 return 0;
87 }
88
89 /*
90 * Get modulus; then decode the r and s values. They must be
91 * lower than the modulus, and s must not be null.
92 */
93 nlen = cd->order_len;
94 br_i31_decode(n, cd->order, nlen);
95 n0i = br_i31_ninv31(n[1]);
96 if (!br_i31_decode_mod(r, sig, rlen, n)) {
97 return 0;
98 }
99 if (!br_i31_decode_mod(s, (const unsigned char *)sig + rlen, rlen, n)) {
100 return 0;
101 }
102 if (br_i31_iszero(s)) {
103 return 0;
104 }
105
106 /*
107 * Invert s. We do that with a modular exponentiation; we use
108 * the fact that for all the curves we support, the least
109 * significant byte is not 0 or 1, so we can subtract 2 without
110 * any carry to process.
111 * We also want 1/s in Montgomery representation, which can be
112 * done by converting _from_ Montgomery representation before
113 * the inversion (because (1/s)*R = 1/(s/R)).
114 */
115 br_i31_from_monty(s, n, n0i);
116 memcpy(tx, cd->order, nlen);
117 tx[nlen - 1] -= 2;
118 br_i31_modpow(s, tx, nlen, n, n0i, t1, t2);
119
120 /*
121 * Truncate the hash to the modulus length (in bits) and reduce
122 * it modulo the curve order. The modular reduction can be done
123 * with a subtraction since the truncation already reduced the
124 * value to the modulus bit length.
125 */
126 br_ecdsa_i31_bits2int(t1, hash, hash_len, n[0]);
127 br_i31_sub(t1, n, br_i31_sub(t1, n, 0) ^ 1);
128
129 /*
130 * Multiply the (truncated, reduced) hash value with 1/s, result in
131 * t2, encoded in ty.
132 */
133 br_i31_montymul(t2, t1, s, n, n0i);
134 br_i31_encode(ty, nlen, t2);
135
136 /*
137 * Multiply r with 1/s, result in t1, encoded in tx.
138 */
139 br_i31_montymul(t1, r, s, n, n0i);
140 br_i31_encode(tx, nlen, t1);
141
142 /*
143 * Compute the point x*Q + y*G.
144 */
145 ulen = cd->generator_len;
146 memcpy(eU, pk->q, ulen);
147 res = impl->muladd(eU, NULL, ulen,
148 tx, nlen, ty, nlen, cd->curve);
149
150 /*
151 * Get the X coordinate, reduce modulo the curve order, and
152 * compare with the 'r' value.
153 *
154 * The modular reduction can be done with subtractions because
155 * we work with curves of prime order, so the curve order is
156 * close to the field order (Hasse's theorem).
157 */
158 br_i31_zero(t1, n[0]);
159 br_i31_decode(t1, &eU[1], ulen >> 1);
160 t1[0] = n[0];
161 br_i31_sub(t1, n, br_i31_sub(t1, n, 0) ^ 1);
162 res &= ~br_i31_sub(t1, r, 1);
163 res &= br_i31_iszero(t1);
164 return res;
165 }
166