_ Git - BearSSL/blob - 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          * Get the curve parameters (generator and order).
  55          */
  56         switch (sk->curve) {
  57         case BR_EC_secp256r1:
  58                 cd = &br_secp256r1;
  59                 break;
  60         case BR_EC_secp384r1:
  61                 cd = &br_secp384r1;
  62                 break;
  63         case BR_EC_secp521r1:
  64                 cd = &br_secp521r1;
  65                 break;
  66         default:
  67                 return 0;
  68         }
  69
  70         /*
  71          * Get modulus.
  72          */
  73         nlen = cd->order_len;
  74         br_i31_decode(n, cd->order, nlen);
  75         n0i = br_i31_ninv31(n[1]);
  76
  77         /*
  78          * Get private key as an i31 integer. This also checks that the
  79          * private key is well-defined (not zero, and less than the
  80          * curve order).
  81          */
  82         if (!br_i31_decode_mod(x, sk->x, sk->xlen, n)) {
  83                 return 0;
  84         }
  85         if (br_i31_iszero(x)) {
  86                 return 0;
  87         }
  88
  89         /*
  90          * Get hash length.
  91          */
  92         hash_len = (hf->desc >> BR_HASHDESC_OUT_OFF) & BR_HASHDESC_OUT_MASK;
  93
  94         /*
  95          * Truncate and reduce the hash value modulo the curve order.
  96          */
  97         br_ecdsa_i31_bits2int(m, hash_value, hash_len, n[0]);
  98         br_i31_sub(m, n, br_i31_sub(m, n, 0) ^ 1);
  99
 100         /*
 101          * RFC 6979 generation of the "k" value.
 102          *
 103          * The process uses HMAC_DRBG (with the hash function used to
 104          * process the message that is to be signed). The seed is the
 105          * concatenation of the encodings of the private key and
 106          * the hash value (after truncation and modular reduction).
 107          */
 108         br_i31_encode(tt, nlen, x);
 109         br_i31_encode(tt + nlen, nlen, m);
 110         br_hmac_drbg_init(&drbg, hf, tt, nlen << 1);
 111         for (;;) {
 112                 br_hmac_drbg_generate(&drbg, tt, nlen);
 113                 br_ecdsa_i31_bits2int(k, tt, nlen, n[0]);
 114                 if (br_i31_iszero(k)) {
 115                         continue;
 116                 }
 117                 if (br_i31_sub(k, n, 0)) {
 118                         break;
 119                 }
 120         }
 121
 122         /*
 123          * Compute k*G and extract the X coordinate, then reduce it
 124          * modulo the curve order. Since we support only curves with
 125          * prime order, that reduction is only a matter of computing
 126          * a subtraction.
 127          */
 128         ulen = cd->generator_len;
 129         memcpy(eU, cd->generator, ulen);
 130         br_i31_encode(tt, nlen, k);
 131         if (!impl->mul(eU, ulen, tt, nlen, sk->curve)) {
 132                 /*
 133                  * Point multiplication may fail here only if the
 134                  * EC implementation does not support the curve, or the
 135                  * private key is incorrect (x is a multiple of the curve
 136                  * order).
 137                  */
 138                 return 0;
 139         }
 140         br_i31_zero(r, n[0]);
 141         br_i31_decode(r, &eU[1], ulen >> 1);
 142         r[0] = n[0];
 143         br_i31_sub(r, n, br_i31_sub(r, n, 0) ^ 1);
 144
 145         /*
 146          * Compute 1/k in double-Montgomery representation. We do so by
 147          * first converting _from_ Montgomery representation (twice),
 148          * then using a modular exponentiation.
 149          */
 150         br_i31_from_monty(k, n, n0i);
 151         br_i31_from_monty(k, n, n0i);
 152         memcpy(tt, cd->order, nlen);
 153         tt[nlen - 1] -= 2;
 154         br_i31_modpow(k, tt, nlen, n, n0i, t1, t2);
 155
 156         /*
 157          * Compute s = (m+xr)/k (mod n).
 158          * The k[] array contains R^2/k (double-Montgomery representation);
 159          * we thus can use direct Montgomery multiplications and conversions
 160          * from Montgomery, avoiding any call to br_i31_to_monty() (which
 161          * is slower).
 162          */
 163         br_i31_from_monty(m, n, n0i);
 164         br_i31_montymul(t1, x, r, n, n0i);
 165         ctl = br_i31_add(t1, m, 1);
 166         ctl |= br_i31_sub(t1, n, 0) ^ 1;
 167         br_i31_sub(t1, n, ctl);
 168         br_i31_montymul(s, t1, k, n, n0i);
 169
 170         /*
 171          * Encode r and s in the signature.
 172          */
 173         br_i31_encode(sig, nlen, r);
 174         br_i31_encode((unsigned char *)sig + nlen, nlen, s);
 175         return nlen << 1;
 176 }