/* * Copyright (c) 2000-2001 Apple Computer, Inc. All Rights Reserved. * * The contents of this file constitute Original Code as defined in and are * subject to the Apple Public Source License Version 1.2 (the 'License'). * You may not use this file except in compliance with the License. Please obtain * a copy of the License at http://www.apple.com/publicsource and read it before * using this file. * * This Original Code and all software distributed under the License are * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS * OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, INCLUDING WITHOUT * LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR * PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. Please see the License for the * specific language governing rights and limitations under the License. */ /* crypto/bn/bn_prime.c */ /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * 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 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 acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS 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 AUTHOR OR 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. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ /* ==================================================================== * Copyright (c) 1998-2000 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 * openssl-core@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 <time.h> #include "cryptlib.h" #include "bn_lcl.h" #include <openssl/rand.h> /* The quick sieve algorithm approach to weeding out primes is * Philip Zimmermann's, as implemented in PGP. I have had a read of * his comments and implemented my own version. */ #include "bn_prime.h" static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); static int probable_prime(BIGNUM *rnd, int bits); static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem, BN_CTX *ctx); static int probable_prime_dh_safe(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem, BN_CTX *ctx); BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add, BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg) { BIGNUM *rnd=NULL; BIGNUM t; int found=0; int i,j,c1=0; BN_CTX *ctx; int checks = BN_prime_checks_for_size(bits); ctx=BN_CTX_new(); if (ctx == NULL) goto err; if (ret == NULL) { if ((rnd=BN_new()) == NULL) goto err; } else rnd=ret; BN_init(&t); loop: /* make a random number and set the top and bottom bits */ if (add == NULL) { if (!probable_prime(rnd,bits)) goto err; } else { if (safe) { if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx)) goto err; } else { if (!probable_prime_dh(rnd,bits,add,rem,ctx)) goto err; } } /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */ if (callback != NULL) callback(0,c1++,cb_arg); if (!safe) { i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0); if (i == -1) goto err; if (i == 0) goto loop; } else { /* for "safe prime" generation, * check that (p-1)/2 is prime. * Since a prime is odd, We just * need to divide by 2 */ if (!BN_rshift1(&t,rnd)) goto err; for (i=0; i<checks; i++) { j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0); if (j == -1) goto err; if (j == 0) goto loop; j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0); if (j == -1) goto err; if (j == 0) goto loop; if (callback != NULL) callback(2,c1-1,cb_arg); /* We have a safe prime test pass */ } } /* we have a prime :-) */ found = 1; err: if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd); BN_free(&t); if (ctx != NULL) BN_CTX_free(ctx); return(found ? rnd : NULL); } int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *), BN_CTX *ctx_passed, void *cb_arg) { return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0); } int BN_is_prime_fasttest(const BIGNUM *a, int checks, void (*callback)(int,int,void *), BN_CTX *ctx_passed, void *cb_arg, int do_trial_division) { int i, j, ret = -1; int k; BN_CTX *ctx = NULL; BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ BN_MONT_CTX *mont = NULL; const BIGNUM *A = NULL; if (checks == BN_prime_checks) checks = BN_prime_checks_for_size(BN_num_bits(a)); /* first look for small factors */ if (!BN_is_odd(a)) return(0); if (do_trial_division) { for (i = 1; i < NUMPRIMES; i++) if (BN_mod_word(a, primes[i]) == 0) return 0; if (callback != NULL) callback(1, -1, cb_arg); } if (ctx_passed != NULL) ctx = ctx_passed; else if ((ctx=BN_CTX_new()) == NULL) goto err; BN_CTX_start(ctx); /* A := abs(a) */ if (a->neg) { BIGNUM *t; if ((t = BN_CTX_get(ctx)) == NULL) goto err; BN_copy(t, a); t->neg = 0; A = t; } else A = a; A1 = BN_CTX_get(ctx); A1_odd = BN_CTX_get(ctx); check = BN_CTX_get(ctx); if (check == NULL) goto err; /* compute A1 := A - 1 */ if (!BN_copy(A1, A)) goto err; if (!BN_sub_word(A1, 1)) goto err; if (BN_is_zero(A1)) { ret = 0; goto err; } /* write A1 as A1_odd * 2^k */ k = 1; while (!BN_is_bit_set(A1, k)) k++; if (!BN_rshift(A1_odd, A1, k)) goto err; /* Montgomery setup for computations mod A */ mont = BN_MONT_CTX_new(); if (mont == NULL) goto err; if (!BN_MONT_CTX_set(mont, A, ctx)) goto err; for (i = 0; i < checks; i++) { if (!BN_pseudo_rand(check, BN_num_bits(A1), 0, 0)) goto err; if (BN_cmp(check, A1) >= 0) if (!BN_sub(check, check, A1)) goto err; if (!BN_add_word(check, 1)) goto err; /* now 1 <= check < A */ j = witness(check, A, A1, A1_odd, k, ctx, mont); if (j == -1) goto err; if (j) { ret=0; goto err; } if (callback != NULL) callback(1,i,cb_arg); } ret=1; err: if (ctx != NULL) { BN_CTX_end(ctx); if (ctx_passed == NULL) BN_CTX_free(ctx); } if (mont != NULL) BN_MONT_CTX_free(mont); return(ret); } static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont) { if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ return -1; if (BN_is_one(w)) return 0; /* probably prime */ if (BN_cmp(w, a1) == 0) return 0; /* w == -1 (mod a), 'a' is probably prime */ while (--k) { if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ return -1; if (BN_is_one(w)) return 1; /* 'a' is composite, otherwise a previous 'w' would * have been == -1 (mod 'a') */ if (BN_cmp(w, a1) == 0) return 0; /* w == -1 (mod a), 'a' is probably prime */ } /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', * and it is neither -1 nor +1 -- so 'a' cannot be prime */ return 1; } static int probable_prime(BIGNUM *rnd, int bits) { int i; BN_ULONG mods[NUMPRIMES]; BN_ULONG delta,d; again: if (!BN_rand(rnd,bits,1,1)) return(0); /* we now have a random number 'rand' to test. */ for (i=1; i<NUMPRIMES; i++) mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]); delta=0; loop: for (i=1; i<NUMPRIMES; i++) { /* check that rnd is not a prime and also * that gcd(rnd-1,primes) == 1 (except for 2) */ if (((mods[i]+delta)%primes[i]) <= 1) { d=delta; delta+=2; /* perhaps need to check for overflow of * delta (but delta can be up to 2^32) * 21-May-98 eay - added overflow check */ if (delta < d) goto again; goto loop; } } if (!BN_add_word(rnd,delta)) return(0); return(1); } static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem, BN_CTX *ctx) { int i,ret=0; BIGNUM *t1; BN_CTX_start(ctx); if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_rand(rnd,bits,0,1)) goto err; /* we need ((rnd-rem) % add) == 0 */ if (!BN_mod(t1,rnd,add,ctx)) goto err; if (!BN_sub(rnd,rnd,t1)) goto err; if (rem == NULL) { if (!BN_add_word(rnd,1)) goto err; } else { if (!BN_add(rnd,rnd,rem)) goto err; } /* we now have a random number 'rand' to test. */ loop: for (i=1; i<NUMPRIMES; i++) { /* check that rnd is a prime */ if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1) { if (!BN_add(rnd,rnd,add)) goto err; goto loop; } } ret=1; err: BN_CTX_end(ctx); return(ret); } static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd, BIGNUM *rem, BN_CTX *ctx) { int i,ret=0; BIGNUM *t1,*qadd,*q; bits--; BN_CTX_start(ctx); t1 = BN_CTX_get(ctx); q = BN_CTX_get(ctx); qadd = BN_CTX_get(ctx); if (qadd == NULL) goto err; if (!BN_rshift1(qadd,padd)) goto err; if (!BN_rand(q,bits,0,1)) goto err; /* we need ((rnd-rem) % add) == 0 */ if (!BN_mod(t1,q,qadd,ctx)) goto err; if (!BN_sub(q,q,t1)) goto err; if (rem == NULL) { if (!BN_add_word(q,1)) goto err; } else { if (!BN_rshift1(t1,rem)) goto err; if (!BN_add(q,q,t1)) goto err; } /* we now have a random number 'rand' to test. */ if (!BN_lshift1(p,q)) goto err; if (!BN_add_word(p,1)) goto err; loop: for (i=1; i<NUMPRIMES; i++) { /* check that p and q are prime */ /* check that for p and q * gcd(p-1,primes) == 1 (except for 2) */ if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) || (BN_mod_word(q,(BN_ULONG)primes[i]) == 0)) { if (!BN_add(p,p,padd)) goto err; if (!BN_add(q,q,qadd)) goto err; goto loop; } } ret=1; err: BN_CTX_end(ctx); return(ret); }