/* 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 #include #include "cryptlib.h" #include "bn_lcl.h" #include /* 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; ineg) { BIGNUM *t = &(ctx->bn[ctx->tos++]); BN_copy(t, a); t->neg = 0; A = t; } else A = a; A1 = &(ctx->bn[ctx->tos++]); A1_odd = &(ctx->bn[ctx->tos++]); check = &(ctx->bn[ctx->tos++]);; /* 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_passed != NULL) { ctx_passed->tos -= 3; /* A1, A1_odd, check */ if (a != A) --ctx_passed->tos; /* A */ } else if (ctx != 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; ibn[ctx->tos++]); 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; itos--; 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=NULL,*q=NULL; bits--; t1= &(ctx->bn[ctx->tos++]); q= &(ctx->bn[ctx->tos++]); qadd= &(ctx->bn[ctx->tos++]); 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; itos-=3; return(ret); }