[331] | 1 | /*
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| 2 | * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved.
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| 3 | *
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| 4 | * Licensed under the OpenSSL license (the "License"). You may not use
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| 5 | * this file except in compliance with the License. You can obtain a copy
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| 6 | * in the file LICENSE in the source distribution or at
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| 7 | * https://www.openssl.org/source/license.html
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| 8 | */
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| 9 |
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| 10 | #include <stdio.h>
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| 11 | #include <openssl/bn.h>
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| 12 | #include "bn_lcl.h"
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| 13 |
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| 14 | /* X9.31 routines for prime derivation */
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| 15 |
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| 16 | /*
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| 17 | * X9.31 prime derivation. This is used to generate the primes pi (p1, p2,
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| 18 | * q1, q2) from a parameter Xpi by checking successive odd integers.
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| 19 | */
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| 20 |
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| 21 | static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
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| 22 | BN_GENCB *cb)
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| 23 | {
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| 24 | int i = 0, is_prime;
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| 25 | if (!BN_copy(pi, Xpi))
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| 26 | return 0;
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| 27 | if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
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| 28 | return 0;
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| 29 | for (;;) {
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| 30 | i++;
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| 31 | BN_GENCB_call(cb, 0, i);
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| 32 | /* NB 27 MR is specified in X9.31 */
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| 33 | is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb);
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| 34 | if (is_prime < 0)
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| 35 | return 0;
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| 36 | if (is_prime)
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| 37 | break;
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| 38 | if (!BN_add_word(pi, 2))
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| 39 | return 0;
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| 40 | }
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| 41 | BN_GENCB_call(cb, 2, i);
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| 42 | return 1;
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| 43 | }
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| 44 |
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| 45 | /*
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| 46 | * This is the main X9.31 prime derivation function. From parameters Xp1, Xp2
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| 47 | * and Xp derive the prime p. If the parameters p1 or p2 are not NULL they
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| 48 | * will be returned too: this is needed for testing.
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| 49 | */
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| 50 |
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| 51 | int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
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| 52 | const BIGNUM *Xp, const BIGNUM *Xp1,
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| 53 | const BIGNUM *Xp2, const BIGNUM *e, BN_CTX *ctx,
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| 54 | BN_GENCB *cb)
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| 55 | {
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| 56 | int ret = 0;
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| 57 |
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| 58 | BIGNUM *t, *p1p2, *pm1;
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| 59 |
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| 60 | /* Only even e supported */
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| 61 | if (!BN_is_odd(e))
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| 62 | return 0;
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| 63 |
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| 64 | BN_CTX_start(ctx);
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| 65 | if (!p1)
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| 66 | p1 = BN_CTX_get(ctx);
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| 67 |
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| 68 | if (!p2)
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| 69 | p2 = BN_CTX_get(ctx);
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| 70 |
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| 71 | t = BN_CTX_get(ctx);
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| 72 |
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| 73 | p1p2 = BN_CTX_get(ctx);
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| 74 |
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| 75 | pm1 = BN_CTX_get(ctx);
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| 76 |
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| 77 | if (pm1 == NULL)
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| 78 | goto err;
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| 79 |
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| 80 | if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
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| 81 | goto err;
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| 82 |
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| 83 | if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
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| 84 | goto err;
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| 85 |
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| 86 | if (!BN_mul(p1p2, p1, p2, ctx))
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| 87 | goto err;
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| 88 |
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| 89 | /* First set p to value of Rp */
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| 90 |
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| 91 | if (!BN_mod_inverse(p, p2, p1, ctx))
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| 92 | goto err;
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| 93 |
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| 94 | if (!BN_mul(p, p, p2, ctx))
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| 95 | goto err;
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| 96 |
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| 97 | if (!BN_mod_inverse(t, p1, p2, ctx))
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| 98 | goto err;
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| 99 |
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| 100 | if (!BN_mul(t, t, p1, ctx))
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| 101 | goto err;
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| 102 |
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| 103 | if (!BN_sub(p, p, t))
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| 104 | goto err;
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| 105 |
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| 106 | if (p->neg && !BN_add(p, p, p1p2))
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| 107 | goto err;
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| 108 |
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| 109 | /* p now equals Rp */
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| 110 |
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| 111 | if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
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| 112 | goto err;
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| 113 |
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| 114 | if (!BN_add(p, p, Xp))
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| 115 | goto err;
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| 116 |
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| 117 | /* p now equals Yp0 */
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| 118 |
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| 119 | for (;;) {
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| 120 | int i = 1;
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| 121 | BN_GENCB_call(cb, 0, i++);
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| 122 | if (!BN_copy(pm1, p))
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| 123 | goto err;
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| 124 | if (!BN_sub_word(pm1, 1))
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| 125 | goto err;
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| 126 | if (!BN_gcd(t, pm1, e, ctx))
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| 127 | goto err;
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| 128 | if (BN_is_one(t)) {
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| 129 | /*
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| 130 | * X9.31 specifies 8 MR and 1 Lucas test or any prime test
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| 131 | * offering similar or better guarantees 50 MR is considerably
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| 132 | * better.
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| 133 | */
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| 134 | int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb);
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| 135 | if (r < 0)
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| 136 | goto err;
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| 137 | if (r)
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| 138 | break;
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| 139 | }
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| 140 | if (!BN_add(p, p, p1p2))
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| 141 | goto err;
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| 142 | }
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| 143 |
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| 144 | BN_GENCB_call(cb, 3, 0);
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| 145 |
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| 146 | ret = 1;
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| 147 |
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| 148 | err:
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| 149 |
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| 150 | BN_CTX_end(ctx);
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| 151 |
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| 152 | return ret;
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| 153 | }
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| 154 |
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| 155 | /*
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| 156 | * Generate pair of parameters Xp, Xq for X9.31 prime generation. Note: nbits
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| 157 | * parameter is sum of number of bits in both.
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| 158 | */
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| 159 |
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| 160 | int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
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| 161 | {
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| 162 | BIGNUM *t;
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| 163 | int i;
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| 164 | /*
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| 165 | * Number of bits for each prime is of the form 512+128s for s = 0, 1,
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| 166 | * ...
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| 167 | */
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| 168 | if ((nbits < 1024) || (nbits & 0xff))
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| 169 | return 0;
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| 170 | nbits >>= 1;
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| 171 | /*
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| 172 | * The random value Xp must be between sqrt(2) * 2^(nbits-1) and 2^nbits
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| 173 | * - 1. By setting the top two bits we ensure that the lower bound is
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| 174 | * exceeded.
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| 175 | */
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| 176 | if (!BN_rand(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
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| 177 | goto err;
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| 178 |
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| 179 | BN_CTX_start(ctx);
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| 180 | t = BN_CTX_get(ctx);
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| 181 |
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| 182 | for (i = 0; i < 1000; i++) {
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| 183 | if (!BN_rand(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
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| 184 | goto err;
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| 185 | /* Check that |Xp - Xq| > 2^(nbits - 100) */
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| 186 | BN_sub(t, Xp, Xq);
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| 187 | if (BN_num_bits(t) > (nbits - 100))
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| 188 | break;
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| 189 | }
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| 190 |
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| 191 | BN_CTX_end(ctx);
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| 192 |
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| 193 | if (i < 1000)
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| 194 | return 1;
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| 195 |
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| 196 | return 0;
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| 197 |
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| 198 | err:
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| 199 | BN_CTX_end(ctx);
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| 200 | return 0;
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| 201 | }
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| 202 |
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| 203 | /*
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| 204 | * Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1 and
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| 205 | * Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL the
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| 206 | * relevant parameter will be stored in it. Due to the fact that |Xp - Xq| >
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| 207 | * 2^(nbits - 100) must be satisfied Xp and Xq are generated using the
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| 208 | * previous function and supplied as input.
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| 209 | */
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| 210 |
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| 211 | int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
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| 212 | BIGNUM *Xp1, BIGNUM *Xp2,
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| 213 | const BIGNUM *Xp,
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| 214 | const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
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| 215 | {
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| 216 | int ret = 0;
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| 217 |
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| 218 | BN_CTX_start(ctx);
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| 219 | if (!Xp1)
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| 220 | Xp1 = BN_CTX_get(ctx);
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| 221 | if (!Xp2)
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| 222 | Xp2 = BN_CTX_get(ctx);
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| 223 |
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| 224 | if (!BN_rand(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
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| 225 | goto error;
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| 226 | if (!BN_rand(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
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| 227 | goto error;
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| 228 | if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
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| 229 | goto error;
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| 230 |
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| 231 | ret = 1;
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| 232 |
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| 233 | error:
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| 234 | BN_CTX_end(ctx);
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| 235 |
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| 236 | return ret;
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| 237 |
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| 238 | }
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