1 /* 2 * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved. 3 * 4 * Licensed under the OpenSSL license (the "License"). You may not use 5 * this file except in compliance with the License. You can obtain a copy 6 * in the file LICENSE in the source distribution or at 7 * https://www.openssl.org/source/license.html 8 */ 9 10 #include <stdio.h> 11 #include <openssl/bn.h> 12 #include "bn_local.h" 13 14 /* X9.31 routines for prime derivation */ 15 16 /* 17 * X9.31 prime derivation. This is used to generate the primes pi (p1, p2, 18 * q1, q2) from a parameter Xpi by checking successive odd integers. 19 */ 20 21 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx, 22 BN_GENCB *cb) 23 { 24 int i = 0, is_prime; 25 if (!BN_copy(pi, Xpi)) 26 return 0; 27 if (!BN_is_odd(pi) && !BN_add_word(pi, 1)) 28 return 0; 29 for (;;) { 30 i++; 31 BN_GENCB_call(cb, 0, i); 32 /* NB 27 MR is specified in X9.31 */ 33 is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb); 34 if (is_prime < 0) 35 return 0; 36 if (is_prime) 37 break; 38 if (!BN_add_word(pi, 2)) 39 return 0; 40 } 41 BN_GENCB_call(cb, 2, i); 42 return 1; 43 } 44 45 /* 46 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2 47 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they 48 * will be returned too: this is needed for testing. 49 */ 50 51 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 52 const BIGNUM *Xp, const BIGNUM *Xp1, 53 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx, 54 BN_GENCB *cb) 55 { 56 int ret = 0; 57 58 BIGNUM *t, *p1p2, *pm1; 59 60 /* Only even e supported */ 61 if (!BN_is_odd(e)) 62 return 0; 63 64 BN_CTX_start(ctx); 65 if (p1 == NULL) 66 p1 = BN_CTX_get(ctx); 67 68 if (p2 == NULL) 69 p2 = BN_CTX_get(ctx); 70 71 t = BN_CTX_get(ctx); 72 73 p1p2 = BN_CTX_get(ctx); 74 75 pm1 = BN_CTX_get(ctx); 76 77 if (pm1 == NULL) 78 goto err; 79 80 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb)) 81 goto err; 82 83 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb)) 84 goto err; 85 86 if (!BN_mul(p1p2, p1, p2, ctx)) 87 goto err; 88 89 /* First set p to value of Rp */ 90 91 if (!BN_mod_inverse(p, p2, p1, ctx)) 92 goto err; 93 94 if (!BN_mul(p, p, p2, ctx)) 95 goto err; 96 97 if (!BN_mod_inverse(t, p1, p2, ctx)) 98 goto err; 99 100 if (!BN_mul(t, t, p1, ctx)) 101 goto err; 102 103 if (!BN_sub(p, p, t)) 104 goto err; 105 106 if (p->neg && !BN_add(p, p, p1p2)) 107 goto err; 108 109 /* p now equals Rp */ 110 111 if (!BN_mod_sub(p, p, Xp, p1p2, ctx)) 112 goto err; 113 114 if (!BN_add(p, p, Xp)) 115 goto err; 116 117 /* p now equals Yp0 */ 118 119 for (;;) { 120 int i = 1; 121 BN_GENCB_call(cb, 0, i++); 122 if (!BN_copy(pm1, p)) 123 goto err; 124 if (!BN_sub_word(pm1, 1)) 125 goto err; 126 if (!BN_gcd(t, pm1, e, ctx)) 127 goto err; 128 if (BN_is_one(t)) { 129 /* 130 * X9.31 specifies 8 MR and 1 Lucas test or any prime test 131 * offering similar or better guarantees 50 MR is considerably 132 * better. 133 */ 134 int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb); 135 if (r < 0) 136 goto err; 137 if (r) 138 break; 139 } 140 if (!BN_add(p, p, p1p2)) 141 goto err; 142 } 143 144 BN_GENCB_call(cb, 3, 0); 145 146 ret = 1; 147 148 err: 149 150 BN_CTX_end(ctx); 151 152 return ret; 153 } 154 155 /* 156 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits 157 * parameter is sum of number of bits in both. 158 */ 159 160 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx) 161 { 162 BIGNUM *t; 163 int i; 164 /* 165 * Number of bits for each prime is of the form 512+128s for s = 0, 1, 166 * ... 167 */ 168 if ((nbits < 1024) || (nbits & 0xff)) 169 return 0; 170 nbits >>= 1; 171 /* 172 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits 173 * - 1. By setting the top two bits we ensure that the lower bound is 174 * exceeded. 175 */ 176 if (!BN_priv_rand(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY)) 177 goto err; 178 179 BN_CTX_start(ctx); 180 t = BN_CTX_get(ctx); 181 if (t == NULL) 182 goto err; 183 184 for (i = 0; i < 1000; i++) { 185 if (!BN_priv_rand(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY)) 186 goto err; 187 188 /* Check that |Xp - Xq| > 2^(nbits - 100) */ 189 if (!BN_sub(t, Xp, Xq)) 190 goto err; 191 if (BN_num_bits(t) > (nbits - 100)) 192 break; 193 } 194 195 BN_CTX_end(ctx); 196 197 if (i < 1000) 198 return 1; 199 200 return 0; 201 202 err: 203 BN_CTX_end(ctx); 204 return 0; 205 } 206 207 /* 208 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and 209 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the 210 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| > 211 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the 212 * previous function and supplied as input. 213 */ 214 215 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 216 BIGNUM *Xp1, BIGNUM *Xp2, 217 const BIGNUM *Xp, 218 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb) 219 { 220 int ret = 0; 221 222 BN_CTX_start(ctx); 223 if (Xp1 == NULL) 224 Xp1 = BN_CTX_get(ctx); 225 if (Xp2 == NULL) 226 Xp2 = BN_CTX_get(ctx); 227 if (Xp1 == NULL || Xp2 == NULL) 228 goto error; 229 230 if (!BN_priv_rand(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY)) 231 goto error; 232 if (!BN_priv_rand(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY)) 233 goto error; 234 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb)) 235 goto error; 236 237 ret = 1; 238 239 error: 240 BN_CTX_end(ctx); 241 242 return ret; 243 244 } 245