bn_x931p.c revision 193645
1/* bn_x931p.c */ 2/* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL 3 * project 2005. 4 */ 5/* ==================================================================== 6 * Copyright (c) 2005 The OpenSSL Project. All rights reserved. 7 * 8 * Redistribution and use in source and binary forms, with or without 9 * modification, are permitted provided that the following conditions 10 * are met: 11 * 12 * 1. Redistributions of source code must retain the above copyright 13 * notice, this list of conditions and the following disclaimer. 14 * 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in 17 * the documentation and/or other materials provided with the 18 * distribution. 19 * 20 * 3. All advertising materials mentioning features or use of this 21 * software must display the following acknowledgment: 22 * "This product includes software developed by the OpenSSL Project 23 * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" 24 * 25 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to 26 * endorse or promote products derived from this software without 27 * prior written permission. For written permission, please contact 28 * licensing@OpenSSL.org. 29 * 30 * 5. Products derived from this software may not be called "OpenSSL" 31 * nor may "OpenSSL" appear in their names without prior written 32 * permission of the OpenSSL Project. 33 * 34 * 6. Redistributions of any form whatsoever must retain the following 35 * acknowledgment: 36 * "This product includes software developed by the OpenSSL Project 37 * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" 38 * 39 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY 40 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 41 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 42 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR 43 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 44 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 45 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 46 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 48 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 49 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED 50 * OF THE POSSIBILITY OF SUCH DAMAGE. 51 * ==================================================================== 52 * 53 * This product includes cryptographic software written by Eric Young 54 * (eay@cryptsoft.com). This product includes software written by Tim 55 * Hudson (tjh@cryptsoft.com). 56 * 57 */ 58 59#include <stdio.h> 60#include <openssl/bn.h> 61 62/* X9.31 routines for prime derivation */ 63 64/* X9.31 prime derivation. This is used to generate the primes pi 65 * (p1, p2, q1, q2) from a parameter Xpi by checking successive odd 66 * integers. 67 */ 68 69static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx, 70 BN_GENCB *cb) 71 { 72 int i = 0; 73 if (!BN_copy(pi, Xpi)) 74 return 0; 75 if (!BN_is_odd(pi) && !BN_add_word(pi, 1)) 76 return 0; 77 for(;;) 78 { 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/* This is the main X9.31 prime derivation function. From parameters 92 * Xp1, Xp2 and Xp derive the prime p. If the parameters p1 or p2 are 93 * not NULL they will be returned too: this is needed for testing. 94 */ 95 96int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 97 const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2, 98 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb) 99 { 100 int ret = 0; 101 102 BIGNUM *t, *p1p2, *pm1; 103 104 /* Only even e supported */ 105 if (!BN_is_odd(e)) 106 return 0; 107 108 BN_CTX_start(ctx); 109 if (!p1) 110 p1 = BN_CTX_get(ctx); 111 112 if (!p2) 113 p2 = BN_CTX_get(ctx); 114 115 t = BN_CTX_get(ctx); 116 117 p1p2 = BN_CTX_get(ctx); 118 119 pm1 = BN_CTX_get(ctx); 120 121 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb)) 122 goto err; 123 124 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb)) 125 goto err; 126 127 if (!BN_mul(p1p2, p1, p2, ctx)) 128 goto err; 129 130 /* First set p to value of Rp */ 131 132 if (!BN_mod_inverse(p, p2, p1, ctx)) 133 goto err; 134 135 if (!BN_mul(p, p, p2, ctx)) 136 goto err; 137 138 if (!BN_mod_inverse(t, p1, p2, ctx)) 139 goto err; 140 141 if (!BN_mul(t, t, p1, ctx)) 142 goto err; 143 144 if (!BN_sub(p, p, t)) 145 goto err; 146 147 if (p->neg && !BN_add(p, p, p1p2)) 148 goto err; 149 150 /* p now equals Rp */ 151 152 if (!BN_mod_sub(p, p, Xp, p1p2, ctx)) 153 goto err; 154 155 if (!BN_add(p, p, Xp)) 156 goto err; 157 158 /* p now equals Yp0 */ 159 160 for (;;) 161 { 162 int i = 1; 163 BN_GENCB_call(cb, 0, i++); 164 if (!BN_copy(pm1, p)) 165 goto err; 166 if (!BN_sub_word(pm1, 1)) 167 goto err; 168 if (!BN_gcd(t, pm1, e, ctx)) 169 goto err; 170 if (BN_is_one(t) 171 /* X9.31 specifies 8 MR and 1 Lucas test or any prime test 172 * offering similar or better guarantees 50 MR is considerably 173 * better. 174 */ 175 && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb)) 176 break; 177 if (!BN_add(p, p, p1p2)) 178 goto err; 179 } 180 181 BN_GENCB_call(cb, 3, 0); 182 183 ret = 1; 184 185 err: 186 187 BN_CTX_end(ctx); 188 189 return ret; 190 } 191 192/* Generate pair of paramters Xp, Xq for X9.31 prime generation. 193 * Note: nbits paramter is sum of number of bits in both. 194 */ 195 196int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx) 197 { 198 BIGNUM *t; 199 int i; 200 /* Number of bits for each prime is of the form 201 * 512+128s for s = 0, 1, ... 202 */ 203 if ((nbits < 1024) || (nbits & 0xff)) 204 return 0; 205 nbits >>= 1; 206 /* The random value Xp must be between sqrt(2) * 2^(nbits-1) and 207 * 2^nbits - 1. By setting the top two bits we ensure that the lower 208 * bound is exceeded. 209 */ 210 if (!BN_rand(Xp, nbits, 1, 0)) 211 return 0; 212 213 BN_CTX_start(ctx); 214 t = BN_CTX_get(ctx); 215 216 for (i = 0; i < 1000; i++) 217 { 218 if (!BN_rand(Xq, nbits, 1, 0)) 219 return 0; 220 /* Check that |Xp - Xq| > 2^(nbits - 100) */ 221 BN_sub(t, Xp, Xq); 222 if (BN_num_bits(t) > (nbits - 100)) 223 break; 224 } 225 226 BN_CTX_end(ctx); 227 228 if (i < 1000) 229 return 1; 230 231 return 0; 232 233 } 234 235/* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 236 * and Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL 237 * the relevant parameter will be stored in it. 238 * 239 * Due to the fact that |Xp - Xq| > 2^(nbits - 100) must be satisfied Xp and Xq 240 * are generated using the previous function and supplied as input. 241 */ 242 243int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 244 BIGNUM *Xp1, BIGNUM *Xp2, 245 const BIGNUM *Xp, 246 const BIGNUM *e, BN_CTX *ctx, 247 BN_GENCB *cb) 248 { 249 int ret = 0; 250 251 BN_CTX_start(ctx); 252 if (!Xp1) 253 Xp1 = BN_CTX_get(ctx); 254 if (!Xp2) 255 Xp2 = BN_CTX_get(ctx); 256 257 if (!BN_rand(Xp1, 101, 0, 0)) 258 goto error; 259 if (!BN_rand(Xp2, 101, 0, 0)) 260 goto error; 261 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb)) 262 goto error; 263 264 ret = 1; 265 266 error: 267 BN_CTX_end(ctx); 268 269 return ret; 270 271 } 272 273