/* bn_x931p.c */ /* Written by Dr Stephen N Henson (shenson@bigfoot.com) 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 #include /* 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; }