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 U (2 + ((BR_MAX_RSA_FACTOR + 30) / 31)) 28 #define TLEN (8 * U) 29 30 /* see bearssl_rsa.h */ 31 uint32_t 32 br_rsa_i31_private(unsigned char *x, const br_rsa_private_key *sk) 33 { 34 const unsigned char *p, *q; 35 size_t plen, qlen; 36 size_t fwlen; 37 uint32_t p0i, q0i; 38 size_t xlen, u; 39 uint32_t tmp[1 + TLEN]; 40 long z; 41 uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3; 42 uint32_t r; 43 44 /* 45 * Compute the actual lengths of p and q, in bytes. 46 * These lengths are not considered secret (we cannot really hide 47 * them anyway in constant-time code). 48 */ 49 p = sk->p; 50 plen = sk->plen; 51 while (plen > 0 && *p == 0) { 52 p ++; 53 plen --; 54 } 55 q = sk->q; 56 qlen = sk->qlen; 57 while (qlen > 0 && *q == 0) { 58 q ++; 59 qlen --; 60 } 61 62 /* 63 * Compute the maximum factor length, in words. 64 */ 65 z = (long)(plen > qlen ? plen : qlen) << 3; 66 fwlen = 1; 67 while (z > 0) { 68 z -= 31; 69 fwlen ++; 70 } 71 72 /* 73 * Round up the word length to an even number. 74 */ 75 fwlen += (fwlen & 1); 76 77 /* 78 * We need to fit at least 6 values in the stack buffer. 79 */ 80 if (6 * fwlen > TLEN) { 81 return 0; 82 } 83 84 /* 85 * Compute modulus length (in bytes). 86 */ 87 xlen = (sk->n_bitlen + 7) >> 3; 88 89 /* 90 * Decode q. 91 */ 92 mq = tmp; 93 br_i31_decode(mq, q, qlen); 94 95 /* 96 * Decode p. 97 */ 98 t1 = mq + fwlen; 99 br_i31_decode(t1, p, plen); 100 101 /* 102 * Compute the modulus (product of the two factors), to compare 103 * it with the source value. We use br_i31_mulacc(), since it's 104 * already used later on. 105 */ 106 t2 = mq + 2 * fwlen; 107 br_i31_zero(t2, mq[0]); 108 br_i31_mulacc(t2, mq, t1); 109 110 /* 111 * We encode the modulus into bytes, to perform the comparison 112 * with bytes. We know that the product length, in bytes, is 113 * exactly xlen. 114 * The comparison actually computes the carry when subtracting 115 * the modulus from the source value; that carry must be 1 for 116 * a value in the correct range. We keep it in r, which is our 117 * accumulator for the error code. 118 */ 119 t3 = mq + 4 * fwlen; 120 br_i31_encode(t3, xlen, t2); 121 u = xlen; 122 r = 0; 123 while (u > 0) { 124 uint32_t wn, wx; 125 126 u --; 127 wn = ((unsigned char *)t3)[u]; 128 wx = x[u]; 129 r = ((wx - (wn + r)) >> 8) & 1; 130 } 131 132 /* 133 * Move the decoded p to another temporary buffer. 134 */ 135 mp = mq + 2 * fwlen; 136 memmove(mp, t1, fwlen * sizeof *t1); 137 138 /* 139 * Compute s2 = x^dq mod q. 140 */ 141 q0i = br_i31_ninv31(mq[1]); 142 s2 = mq + fwlen; 143 br_i31_decode_reduce(s2, x, xlen, mq); 144 r &= br_i31_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i, 145 mq + 3 * fwlen, TLEN - 3 * fwlen); 146 147 /* 148 * Compute s1 = x^dp mod p. 149 */ 150 p0i = br_i31_ninv31(mp[1]); 151 s1 = mq + 3 * fwlen; 152 br_i31_decode_reduce(s1, x, xlen, mp); 153 r &= br_i31_modpow_opt(s1, sk->dp, sk->dplen, mp, p0i, 154 mq + 4 * fwlen, TLEN - 4 * fwlen); 155 156 /* 157 * Compute: 158 * h = (s1 - s2)*(1/q) mod p 159 * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is 160 * unclear about whether p may be lower than q (some existing, 161 * widely deployed implementations of RSA don't tolerate p < q), 162 * but we want to support that occurrence, so we need to use the 163 * reduction function. 164 * 165 * Since we use br_i31_decode_reduce() for iq (purportedly, the 166 * inverse of q modulo p), we also tolerate improperly large 167 * values for this parameter. 168 */ 169 t1 = mq + 4 * fwlen; 170 t2 = mq + 5 * fwlen; 171 br_i31_reduce(t2, s2, mp); 172 br_i31_add(s1, mp, br_i31_sub(s1, t2, 1)); 173 br_i31_to_monty(s1, mp); 174 br_i31_decode_reduce(t1, sk->iq, sk->iqlen, mp); 175 br_i31_montymul(t2, s1, t1, mp, p0i); 176 177 /* 178 * h is now in t2. We compute the final result: 179 * s = s2 + q*h 180 * All these operations are non-modular. 181 * 182 * We need mq, s2 and t2. We use the t3 buffer as destination. 183 * The buffers mp, s1 and t1 are no longer needed, so we can 184 * reuse them for t3. Moreover, the first step of the computation 185 * is to copy s2 into t3, after which s2 is not needed. Right 186 * now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5. 187 * Therefore, we have ample room for t3 by simply using s2. 188 */ 189 t3 = s2; 190 br_i31_mulacc(t3, mq, t2); 191 192 /* 193 * Encode the result. Since we already checked the value of xlen, 194 * we can just use it right away. 195 */ 196 br_i31_encode(x, xlen, t3); 197 198 /* 199 * The only error conditions remaining at that point are invalid 200 * values for p and q (even integers). 201 */ 202 return p0i & q0i & r; 203 } 204