1 /* 2 * Copyright 2011-2021 The OpenSSL Project Authors. All Rights Reserved. 3 * 4 * Licensed under the Apache License 2.0 (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 #define OPENSSL_SUPPRESS_DEPRECATED 11 12 #include <stdio.h> 13 #include <openssl/bn.h> 14 #include "bn_local.h" 15 16 /* X9.31 routines for prime derivation */ 17 18 /* 19 * X9.31 prime derivation. This is used to generate the primes pi (p1, p2, 20 * q1, q2) from a parameter Xpi by checking successive odd integers. 21 */ 22 23 static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx, 24 BN_GENCB *cb) 25 { 26 int i = 0, is_prime; 27 if (!BN_copy(pi, Xpi)) 28 return 0; 29 if (!BN_is_odd(pi) && !BN_add_word(pi, 1)) 30 return 0; 31 for (;;) { 32 i++; 33 BN_GENCB_call(cb, 0, i); 34 /* NB 27 MR is specified in X9.31 */ 35 is_prime = BN_check_prime(pi, ctx, cb); 36 if (is_prime < 0) 37 return 0; 38 if (is_prime) 39 break; 40 if (!BN_add_word(pi, 2)) 41 return 0; 42 } 43 BN_GENCB_call(cb, 2, i); 44 return 1; 45 } 46 47 /* 48 * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2 49 * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they 50 * will be returned too: this is needed for testing. 51 */ 52 53 int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 54 const BIGNUM *Xp, const BIGNUM *Xp1, 55 const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx, 56 BN_GENCB *cb) 57 { 58 int ret = 0; 59 60 BIGNUM *t, *p1p2, *pm1; 61 62 /* Only even e supported */ 63 if (!BN_is_odd(e)) 64 return 0; 65 66 BN_CTX_start(ctx); 67 if (p1 == NULL) 68 p1 = BN_CTX_get(ctx); 69 70 if (p2 == NULL) 71 p2 = BN_CTX_get(ctx); 72 73 t = BN_CTX_get(ctx); 74 75 p1p2 = BN_CTX_get(ctx); 76 77 pm1 = BN_CTX_get(ctx); 78 79 if (pm1 == NULL) 80 goto err; 81 82 if (!bn_x931_derive_pi(p1, Xp1, ctx, cb)) 83 goto err; 84 85 if (!bn_x931_derive_pi(p2, Xp2, ctx, cb)) 86 goto err; 87 88 if (!BN_mul(p1p2, p1, p2, ctx)) 89 goto err; 90 91 /* First set p to value of Rp */ 92 93 if (!BN_mod_inverse(p, p2, p1, ctx)) 94 goto err; 95 96 if (!BN_mul(p, p, p2, ctx)) 97 goto err; 98 99 if (!BN_mod_inverse(t, p1, p2, ctx)) 100 goto err; 101 102 if (!BN_mul(t, t, p1, ctx)) 103 goto err; 104 105 if (!BN_sub(p, p, t)) 106 goto err; 107 108 if (p->neg && !BN_add(p, p, p1p2)) 109 goto err; 110 111 /* p now equals Rp */ 112 113 if (!BN_mod_sub(p, p, Xp, p1p2, ctx)) 114 goto err; 115 116 if (!BN_add(p, p, Xp)) 117 goto err; 118 119 /* p now equals Yp0 */ 120 121 for (;;) { 122 int i = 1; 123 BN_GENCB_call(cb, 0, i++); 124 if (!BN_copy(pm1, p)) 125 goto err; 126 if (!BN_sub_word(pm1, 1)) 127 goto err; 128 if (!BN_gcd(t, pm1, e, ctx)) 129 goto err; 130 if (BN_is_one(t)) { 131 /* 132 * X9.31 specifies 8 MR and 1 Lucas test or any prime test 133 * offering similar or better guarantees 50 MR is considerably 134 * better. 135 */ 136 int r = BN_check_prime(p, ctx, cb); 137 if (r < 0) 138 goto err; 139 if (r) 140 break; 141 } 142 if (!BN_add(p, p, p1p2)) 143 goto err; 144 } 145 146 BN_GENCB_call(cb, 3, 0); 147 148 ret = 1; 149 150 err: 151 152 BN_CTX_end(ctx); 153 154 return ret; 155 } 156 157 /* 158 * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits 159 * parameter is sum of number of bits in both. 160 */ 161 162 int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx) 163 { 164 BIGNUM *t; 165 int i; 166 /* 167 * Number of bits for each prime is of the form 512+128s for s = 0, 1, 168 * ... 169 */ 170 if ((nbits < 1024) || (nbits & 0xff)) 171 return 0; 172 nbits >>= 1; 173 /* 174 * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits 175 * - 1. By setting the top two bits we ensure that the lower bound is 176 * exceeded. 177 */ 178 if (!BN_priv_rand_ex(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, 0, 179 ctx)) 180 return 0; 181 182 BN_CTX_start(ctx); 183 t = BN_CTX_get(ctx); 184 if (t == NULL) 185 goto err; 186 187 for (i = 0; i < 1000; i++) { 188 if (!BN_priv_rand_ex(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY, 0, 189 ctx)) 190 goto err; 191 192 /* Check that |Xp - Xq| > 2^(nbits - 100) */ 193 if (!BN_sub(t, Xp, Xq)) 194 goto err; 195 if (BN_num_bits(t) > (nbits - 100)) 196 break; 197 } 198 199 BN_CTX_end(ctx); 200 201 if (i < 1000) 202 return 1; 203 204 return 0; 205 206 err: 207 BN_CTX_end(ctx); 208 return 0; 209 } 210 211 /* 212 * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and 213 * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the 214 * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| > 215 * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the 216 * previous function and supplied as input. 217 */ 218 219 int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2, 220 BIGNUM *Xp1, BIGNUM *Xp2, 221 const BIGNUM *Xp, 222 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb) 223 { 224 int ret = 0; 225 226 BN_CTX_start(ctx); 227 if (Xp1 == NULL) 228 Xp1 = BN_CTX_get(ctx); 229 if (Xp2 == NULL) 230 Xp2 = BN_CTX_get(ctx); 231 if (Xp1 == NULL || Xp2 == NULL) 232 goto error; 233 234 if (!BN_priv_rand_ex(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, 0, ctx)) 235 goto error; 236 if (!BN_priv_rand_ex(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY, 0, ctx)) 237 goto error; 238 if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb)) 239 goto error; 240 241 ret = 1; 242 243 error: 244 BN_CTX_end(ctx); 245 246 return ret; 247 248 } 249