_ 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;
  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 signature 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          * Compute s2 = x^dq mod q.
  97          */
  98         q0i = br_i31_ninv31(mq[1]);
  99         s2 = mq + fwlen;
 100         br_i31_decode_reduce(s2, x, xlen, mq);
 101         r = br_i31_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
 102                 mq + 2 * fwlen, TLEN - 2 * fwlen);
 103
 104         /*
 105          * Decode p.
 106          */
 107         mp = mq + 2 * fwlen;
 108         br_i31_decode(mp, p, plen);
 109
 110         /*
 111          * Compute s1 = x^dp mod p.
 112          */
 113         p0i = br_i31_ninv31(mp[1]);
 114         s1 = mq + 3 * fwlen;
 115         br_i31_decode_reduce(s1, x, xlen, mp);
 116         r &= br_i31_modpow_opt(s1, sk->dp, sk->dplen, mp, p0i,
 117                 mq + 4 * fwlen, TLEN - 4 * fwlen);
 118
 119         /*
 120          * Compute:
 121          *   h = (s1 - s2)*(1/q) mod p
 122          * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
 123          * unclear about whether p may be lower than q (some existing,
 124          * widely deployed implementations of RSA don't tolerate p < q),
 125          * but we want to support that occurrence, so we need to use the
 126          * reduction function.
 127          *
 128          * Since we use br_i31_decode_reduce() for iq (purportedly, the
 129          * inverse of q modulo p), we also tolerate improperly large
 130          * values for this parameter.
 131          */
 132         t1 = mq + 4 * fwlen;
 133         t2 = mq + 5 * fwlen;
 134         br_i31_reduce(t2, s2, mp);
 135         br_i31_add(s1, mp, br_i31_sub(s1, t2, 1));
 136         br_i31_to_monty(s1, mp);
 137         br_i31_decode_reduce(t1, sk->iq, sk->iqlen, mp);
 138         br_i31_montymul(t2, s1, t1, mp, p0i);
 139
 140         /*
 141          * h is now in t2. We compute the final result:
 142          *   s = s2 + q*h
 143          * All these operations are non-modular.
 144          *
 145          * We need mq, s2 and t2. We use the t3 buffer as destination.
 146          * The buffers mp, s1 and t1 are no longer needed, so we can
 147          * reuse them for t3. Moreover, the first step of the computation
 148          * is to copy s2 into t3, after which s2 is not needed. Right
 149          * now, mq is in slot 0, s2 is in slot 1, and t2 is in slot 5.
 150          * Therefore, we have ample room for t3 by simply using s2.
 151          */
 152         t3 = s2;
 153         br_i31_mulacc(t3, mq, t2);
 154
 155         /*
 156          * Encode the result. Since we already checked the value of xlen,
 157          * we can just use it right away.
 158          */
 159         br_i31_encode(x, xlen, t3);
 160
 161         /*
 162          * The only error conditions remaining at that point are invalid
 163          * values for p and q (even integers).
 164          */
 165         return p0i & q0i & r;
 166 }