crypto/bn/bn_x931p.c

   1 /* bn_x931p.c */
   2 /*
   3  * Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL project
   4  * 2005.
   5  */
   6 /* ====================================================================
   7  * Copyright (c) 2005 The OpenSSL Project.  All rights reserved.
   8  *
   9  * Redistribution and use in source and binary forms, with or without
  10  * modification, are permitted provided that the following conditions
  11  * are met:
  12  *
  13  * 1. Redistributions of source code must retain the above copyright
  14  *    notice, this list of conditions and the following disclaimer.
  15  *
  16  * 2. Redistributions in binary form must reproduce the above copyright
  17  *    notice, this list of conditions and the following disclaimer in
  18  *    the documentation and/or other materials provided with the
  19  *    distribution.
  20  *
  21  * 3. All advertising materials mentioning features or use of this
  22  *    software must display the following acknowledgment:
  23  *    "This product includes software developed by the OpenSSL Project
  24  *    for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
  25  *
  26  * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
  27  *    endorse or promote products derived from this software without
  28  *    prior written permission. For written permission, please contact
  29  *    licensing@OpenSSL.org.
  30  *
  31  * 5. Products derived from this software may not be called "OpenSSL"
  32  *    nor may "OpenSSL" appear in their names without prior written
  33  *    permission of the OpenSSL Project.
  34  *
  35  * 6. Redistributions of any form whatsoever must retain the following
  36  *    acknowledgment:
  37  *    "This product includes software developed by the OpenSSL Project
  38  *    for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
  39  *
  40  * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
  41  * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  42  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  43  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
  44  * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  45  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  46  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  47  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  49  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  50  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  51  * OF THE POSSIBILITY OF SUCH DAMAGE.
  52  * ====================================================================
  53  *
  54  * This product includes cryptographic software written by Eric Young
  55  * (eay@cryptsoft.com).  This product includes software written by Tim
  56  * Hudson (tjh@cryptsoft.com).
  57  *
  58  */
  59
  60 #include <stdio.h>
  61 #include <openssl/bn.h>
  62
  63 /* X9.31 routines for prime derivation */
  64
  65 /*
  66  * X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
  67  * q1, q2) from a parameter Xpi by checking successive odd integers.
  68  */
  69
  70 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
  71                              BN_GENCB *cb)
  72 {
  73     int i = 0;
  74     if (!BN_copy(pi, Xpi))
  75         return 0;
  76     if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
  77         return 0;
  78     for (;;) {
  79         i++;
  80         BN_GENCB_call(cb, 0, i);
  81         /* NB 27 MR is specificed in X9.31 */
  82         if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
  83             break;
  84         if (!BN_add_word(pi, 2))
  85             return 0;
  86     }
  87     BN_GENCB_call(cb, 2, i);
  88     return 1;
  89 }
  90
  91 /*
  92  * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
  93  * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
  94  * will be returned too: this is needed for testing.
  95  */
  96
  97 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
  98                             const BIGNUM *Xp, const BIGNUM *Xp1,
  99                             const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
 100                             BN_GENCB *cb)
 101 {
 102     int ret = 0;
 103
 104     BIGNUM *t, *p1p2, *pm1;
 105
 106     /* Only even e supported */
 107     if (!BN_is_odd(e))
 108         return 0;
 109
 110     BN_CTX_start(ctx);
 111     if (!p1)
 112         p1 = BN_CTX_get(ctx);
 113
 114     if (!p2)
 115         p2 = BN_CTX_get(ctx);
 116
 117     t = BN_CTX_get(ctx);
 118
 119     p1p2 = BN_CTX_get(ctx);
 120
 121     pm1 = BN_CTX_get(ctx);
 122
 123     if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
 124         goto err;
 125
 126     if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
 127         goto err;
 128
 129     if (!BN_mul(p1p2, p1, p2, ctx))
 130         goto err;
 131
 132     /* First set p to value of Rp */
 133
 134     if (!BN_mod_inverse(p, p2, p1, ctx))
 135         goto err;
 136
 137     if (!BN_mul(p, p, p2, ctx))
 138         goto err;
 139
 140     if (!BN_mod_inverse(t, p1, p2, ctx))
 141         goto err;
 142
 143     if (!BN_mul(t, t, p1, ctx))
 144         goto err;
 145
 146     if (!BN_sub(p, p, t))
 147         goto err;
 148
 149     if (p->neg && !BN_add(p, p, p1p2))
 150         goto err;
 151
 152     /* p now equals Rp */
 153
 154     if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
 155         goto err;
 156
 157     if (!BN_add(p, p, Xp))
 158         goto err;
 159
 160     /* p now equals Yp0 */
 161
 162     for (;;) {
 163         int i = 1;
 164         BN_GENCB_call(cb, 0, i++);
 165         if (!BN_copy(pm1, p))
 166             goto err;
 167         if (!BN_sub_word(pm1, 1))
 168             goto err;
 169         if (!BN_gcd(t, pm1, e, ctx))
 170             goto err;
 171         if (BN_is_one(t)
 172             /*
 173              * X9.31 specifies 8 MR and 1 Lucas test or any prime test
 174              * offering similar or better guarantees 50 MR is considerably
 175              * better.
 176              */
 177             && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
 178             break;
 179         if (!BN_add(p, p, p1p2))
 180             goto err;
 181     }
 182
 183     BN_GENCB_call(cb, 3, 0);
 184
 185     ret = 1;
 186
 187  err:
 188
 189     BN_CTX_end(ctx);
 190
 191     return ret;
 192 }
 193
 194 /*
 195  * Generate pair of paramters Xp, Xq for X9.31 prime generation. Note: nbits
 196  * paramter is sum of number of bits in both.
 197  */
 198
 199 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
 200 {
 201     BIGNUM *t;
 202     int i;
 203     /*
 204      * Number of bits for each prime is of the form 512+128s for s = 0, 1,
 205      * ...
 206      */
 207     if ((nbits < 1024) || (nbits & 0xff))
 208         return 0;
 209     nbits >>= 1;
 210     /*
 211      * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
 212      * - 1. By setting the top two bits we ensure that the lower bound is
 213      * exceeded.
 214      */
 215     if (!BN_rand(Xp, nbits, 1, 0))
 216         return 0;
 217
 218     BN_CTX_start(ctx);
 219     t = BN_CTX_get(ctx);
 220
 221     for (i = 0; i < 1000; i++) {
 222         if (!BN_rand(Xq, nbits, 1, 0))
 223             return 0;
 224         /* Check that |Xp - Xq| > 2^(nbits - 100) */
 225         BN_sub(t, Xp, Xq);
 226         if (BN_num_bits(t) > (nbits - 100))
 227             break;
 228     }
 229
 230     BN_CTX_end(ctx);
 231
 232     if (i < 1000)
 233         return 1;
 234
 235     return 0;
 236
 237 }
 238
 239 /*
 240  * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
 241  * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
 242  * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
 243  * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
 244  * previous function and supplied as input.
 245  */
 246
 247 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
 248                               BIGNUM *Xp1, BIGNUM *Xp2,
 249                               const BIGNUM *Xp,
 250                               const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
 251 {
 252     int ret = 0;
 253
 254     BN_CTX_start(ctx);
 255     if (!Xp1)
 256         Xp1 = BN_CTX_get(ctx);
 257     if (!Xp2)
 258         Xp2 = BN_CTX_get(ctx);
 259
 260     if (!BN_rand(Xp1, 101, 0, 0))
 261         goto error;
 262     if (!BN_rand(Xp2, 101, 0, 0))
 263         goto error;
 264     if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
 265         goto error;
 266
 267     ret = 1;
 268
 269  error:
 270     BN_CTX_end(ctx);
 271
 272     return ret;
 273
 274 }