_ 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   (1 + ((BR_MAX_RSA_FACTOR + 30) / 31))
  28
  29 /* see bearssl_rsa.h */
  30 uint32_t
  31 br_rsa_i31_private(unsigned char *x, const br_rsa_private_key *sk)
  32 {
  33         const unsigned char *p, *q;
  34         size_t plen, qlen;
  35         uint32_t tmp[6 * U];
  36         uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
  37         uint32_t p0i, q0i;
  38         size_t xlen;
  39
  40         /*
  41          * All our temporary buffers are from the tmp[] array.
  42          *
  43          * The mp, mq, s1, s2, t1 and t2 buffers are large enough to
  44          * contain a RSA factor. The t3 buffer can contain a complete
  45          * RSA modulus. t3 shares its storage space with s2, s1 and t1,
  46          * in that order (this is important, see below).
  47          */
  48         mq = tmp;
  49         mp = tmp + U;
  50         t2 = tmp + 2 * U;
  51         s2 = tmp + 3 * U;
  52         s1 = tmp + 4 * U;
  53         t1 = tmp + 5 * U;
  54         t3 = s2;
  55
  56         /*
  57          * Compute the actual lengths (in bytes) of p and q, and check
  58          * that they fit within our stack buffers.
  59          */
  60         p = sk->p;
  61         plen = sk->plen;
  62         while (plen > 0 && *p == 0) {
  63                 p ++;
  64                 plen --;
  65         }
  66         q = sk->q;
  67         qlen = sk->qlen;
  68         while (qlen > 0 && *q == 0) {
  69                 q ++;
  70                 qlen --;
  71         }
  72         if (plen > (BR_MAX_RSA_FACTOR >> 3)
  73                 || qlen > (BR_MAX_RSA_FACTOR >> 3))
  74         {
  75                 return 0;
  76         }
  77
  78         /*
  79          * Decode p and q.
  80          */
  81         br_i31_decode(mp, p, plen);
  82         br_i31_decode(mq, q, qlen);
  83
  84         /*
  85          * Compute signature length (in bytes).
  86          */
  87         xlen = (sk->n_bitlen + 7) >> 3;
  88
  89         /*
  90          * Compute s1 = x^dp mod p.
  91          */
  92         p0i = br_i31_ninv31(mp[1]);
  93         br_i31_decode_reduce(s1, x, xlen, mp);
  94         br_i31_modpow(s1, sk->dp, sk->dplen, mp, p0i, t1, t2);
  95
  96         /*
  97          * Compute s2 = x^dq mod q.
  98          */
  99         q0i = br_i31_ninv31(mq[1]);
 100         br_i31_decode_reduce(s2, x, xlen, mq);
 101         br_i31_modpow(s2, sk->dq, sk->dqlen, mq, q0i, t1, t2);
 102
 103         /*
 104          * Compute:
 105          *   h = (s1 - s2)*(1/q) mod p
 106          * s1 is an integer modulo p, but s2 is modulo q. PKCS#1 is
 107          * unclear about whether p may be lower than q (some existing,
 108          * widely deployed implementations of RSA don't tolerate p < q),
 109          * but we want to support that occurrence, so we need to use the
 110          * reduction function.
 111          *
 112          * Since we use br_i31_decode_reduce() for iq (purportedly, the
 113          * inverse of q modulo p), we also tolerate improperly large
 114          * values for this parameter.
 115          */
 116         br_i31_reduce(t2, s2, mp);
 117         br_i31_add(s1, mp, br_i31_sub(s1, t2, 1));
 118         br_i31_to_monty(s1, mp);
 119         br_i31_decode_reduce(t1, sk->iq, sk->iqlen, mp);
 120         br_i31_montymul(t2, s1, t1, mp, p0i);
 121
 122         /*
 123          * h is now in t2. We compute the final result:
 124          *   s = s2 + q*h
 125          * All these operations are non-modular.
 126          *
 127          * We need mq, s2 and t2. We use the t3 buffer as destination.
 128          * The buffers mp, s1 and t1 are no longer needed. Moreover,
 129          * the first step is to copy s2 into the destination buffer t3.
 130          * We thus arranged for t3 to actually share space with s2, and
 131          * to be followed by the space formerly used by s1 and t1.
 132          */
 133         br_i31_mulacc(t3, mq, t2);
 134
 135         /*
 136          * Encode the result. Since we already checked the value of xlen,
 137          * we can just use it right away.
 138          */
 139         br_i31_encode(x, xlen, t3);
 140
 141         /*
 142          * The only error conditions remaining at that point are invalid
 143          * values for p and q (even integers).
 144          */
 145         return p0i & q0i & 1;
 146 }