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- /* bn_x931p.c */
- /* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL
- * project 2005.
- */
- /* ====================================================================
- * Copyright (c) 2005 The OpenSSL Project. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- *
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in
- * the documentation and/or other materials provided with the
- * distribution.
- *
- * 3. All advertising materials mentioning features or use of this
- * software must display the following acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
- *
- * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
- * endorse or promote products derived from this software without
- * prior written permission. For written permission, please contact
- * licensing@OpenSSL.org.
- *
- * 5. Products derived from this software may not be called "OpenSSL"
- * nor may "OpenSSL" appear in their names without prior written
- * permission of the OpenSSL Project.
- *
- * 6. Redistributions of any form whatsoever must retain the following
- * acknowledgment:
- * "This product includes software developed by the OpenSSL Project
- * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
- *
- * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
- * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
- * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
- * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
- * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
- * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
- * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
- * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
- * OF THE POSSIBILITY OF SUCH DAMAGE.
- * ====================================================================
- *
- * This product includes cryptographic software written by Eric Young
- * (eay@cryptsoft.com). This product includes software written by Tim
- * Hudson (tjh@cryptsoft.com).
- *
- */
- #include <stdio.h>
- #include <openssl/bn.h>
- /* X9.31 routines for prime derivation */
- /* X9.31 prime derivation. This is used to generate the primes pi
- * (p1, p2, q1, q2) from a parameter Xpi by checking successive odd
- * integers.
- */
- static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
- BN_GENCB *cb)
- {
- int i = 0;
- if (!BN_copy(pi, Xpi))
- return 0;
- if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
- return 0;
- for(;;)
- {
- i++;
- BN_GENCB_call(cb, 0, i);
- /* NB 27 MR is specificed in X9.31 */
- if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
- break;
- if (!BN_add_word(pi, 2))
- return 0;
- }
- BN_GENCB_call(cb, 2, i);
- return 1;
- }
- /* This is the main X9.31 prime derivation function. From parameters
- * Xp1, Xp2 and Xp derive the prime p. If the parameters p1 or p2 are
- * not NULL they will be returned too: this is needed for testing.
- */
- int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
- const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
- const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
- {
- int ret = 0;
- BIGNUM *t, *p1p2, *pm1;
- /* Only even e supported */
- if (!BN_is_odd(e))
- return 0;
- BN_CTX_start(ctx);
- if (!p1)
- p1 = BN_CTX_get(ctx);
- if (!p2)
- p2 = BN_CTX_get(ctx);
- t = BN_CTX_get(ctx);
- p1p2 = BN_CTX_get(ctx);
- pm1 = BN_CTX_get(ctx);
- if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
- goto err;
- if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
- goto err;
- if (!BN_mul(p1p2, p1, p2, ctx))
- goto err;
- /* First set p to value of Rp */
- if (!BN_mod_inverse(p, p2, p1, ctx))
- goto err;
- if (!BN_mul(p, p, p2, ctx))
- goto err;
- if (!BN_mod_inverse(t, p1, p2, ctx))
- goto err;
- if (!BN_mul(t, t, p1, ctx))
- goto err;
- if (!BN_sub(p, p, t))
- goto err;
- if (p->neg && !BN_add(p, p, p1p2))
- goto err;
- /* p now equals Rp */
- if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
- goto err;
- if (!BN_add(p, p, Xp))
- goto err;
- /* p now equals Yp0 */
- for (;;)
- {
- int i = 1;
- BN_GENCB_call(cb, 0, i++);
- if (!BN_copy(pm1, p))
- goto err;
- if (!BN_sub_word(pm1, 1))
- goto err;
- if (!BN_gcd(t, pm1, e, ctx))
- goto err;
- if (BN_is_one(t)
- /* X9.31 specifies 8 MR and 1 Lucas test or any prime test
- * offering similar or better guarantees 50 MR is considerably
- * better.
- */
- && BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
- break;
- if (!BN_add(p, p, p1p2))
- goto err;
- }
- BN_GENCB_call(cb, 3, 0);
- ret = 1;
- err:
- BN_CTX_end(ctx);
- return ret;
- }
- /* Generate pair of paramters Xp, Xq for X9.31 prime generation.
- * Note: nbits paramter is sum of number of bits in both.
- */
- int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
- {
- BIGNUM *t;
- int i;
- /* Number of bits for each prime is of the form
- * 512+128s for s = 0, 1, ...
- */
- if ((nbits < 1024) || (nbits & 0xff))
- return 0;
- nbits >>= 1;
- /* The random value Xp must be between sqrt(2) * 2^(nbits-1) and
- * 2^nbits - 1. By setting the top two bits we ensure that the lower
- * bound is exceeded.
- */
- if (!BN_rand(Xp, nbits, 1, 0))
- return 0;
- BN_CTX_start(ctx);
- t = BN_CTX_get(ctx);
- for (i = 0; i < 1000; i++)
- {
- if (!BN_rand(Xq, nbits, 1, 0))
- return 0;
- /* Check that |Xp - Xq| > 2^(nbits - 100) */
- BN_sub(t, Xp, Xq);
- if (BN_num_bits(t) > (nbits - 100))
- break;
- }
- BN_CTX_end(ctx);
- if (i < 1000)
- return 1;
- return 0;
- }
- /* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1
- * and Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL
- * the relevant parameter will be stored in it.
- *
- * Due to the fact that |Xp - Xq| > 2^(nbits - 100) must be satisfied Xp and Xq
- * are generated using the previous function and supplied as input.
- */
- int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
- BIGNUM *Xp1, BIGNUM *Xp2,
- const BIGNUM *Xp,
- const BIGNUM *e, BN_CTX *ctx,
- BN_GENCB *cb)
- {
- int ret = 0;
- BN_CTX_start(ctx);
- if (!Xp1)
- Xp1 = BN_CTX_get(ctx);
- if (!Xp2)
- Xp2 = BN_CTX_get(ctx);
- if (!BN_rand(Xp1, 101, 0, 0))
- goto error;
- if (!BN_rand(Xp2, 101, 0, 0))
- goto error;
- if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
- goto error;
- ret = 1;
- error:
- BN_CTX_end(ctx);
- return ret;
- }
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