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 goto err; 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 goto err; 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 err: 238 BN_CTX_end(ctx); 239 return 0; 240 } 241 242 /* 243 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and 244 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the 245 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| > 246 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the 247 * previous function and supplied as input. 248 */ 249 250 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 251 BIGNUM *Xp1, BIGNUM *Xp2, 252 const BIGNUM *Xp, 253 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb) 254 { 255 int ret = 0; 256 257 BN_CTX_start(ctx); 258 if (!Xp1) 259 Xp1 = BN_CTX_get(ctx); 260 if (!Xp2) 261 Xp2 = BN_CTX_get(ctx); 262 263 if (!BN_rand(Xp1, 101, 0, 0)) 264 goto error; 265 if (!BN_rand(Xp2, 101, 0, 0)) 266 goto error; 267 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb)) 268 goto error; 269 270 ret = 1; 271 272 error: 273 BN_CTX_end(ctx); 274 275 return ret; 276 277 } 278