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  	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  }