_ Git - BearSSL/blob - src/rsa/rsa_i31_priv.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 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 }