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Diffstat (limited to 'crypto/bn/bn_prime.c')
| -rw-r--r-- | crypto/bn/bn_prime.c | 494 |
1 files changed, 494 insertions, 0 deletions
diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c new file mode 100644 index 0000000..5bab019 --- /dev/null +++ b/crypto/bn/bn_prime.c @@ -0,0 +1,494 @@ +/* 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) 1998-2001 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> + +/* NB: these functions have been "upgraded", the deprecated versions (which are + * compatibility wrappers using these functions) are in bn_depr.c. + * - Geoff + */ + +/* 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, + const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); +static int probable_prime_dh_safe(BIGNUM *rnd, int bits, + const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); + +int BN_GENCB_call(BN_GENCB *cb, int a, int b) + { + /* No callback means continue */ + if(!cb) return 1; + switch(cb->ver) + { + case 1: + /* Deprecated-style callbacks */ + if(!cb->cb.cb_1) + return 1; + cb->cb.cb_1(a, b, cb->arg); + return 1; + case 2: + /* New-style callbacks */ + return cb->cb.cb_2(a, b, cb); + default: + break; + } + /* Unrecognised callback type */ + return 0; + } + +int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, + const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) + { + 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; + BN_CTX_start(ctx); + t = BN_CTX_get(ctx); + if(!t) goto err; +loop: + /* make a random number and set the top and bottom bits */ + if (add == NULL) + { + if (!probable_prime(ret,bits)) goto err; + } + else + { + if (safe) + { + if (!probable_prime_dh_safe(ret,bits,add,rem,ctx)) + goto err; + } + else + { + if (!probable_prime_dh(ret,bits,add,rem,ctx)) + goto err; + } + } + /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ + if(!BN_GENCB_call(cb, 0, c1++)) + /* aborted */ + goto err; + + if (!safe) + { + i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb); + 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,ret)) goto err; + + for (i=0; i<checks; i++) + { + j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb); + if (j == -1) goto err; + if (j == 0) goto loop; + + j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb); + if (j == -1) goto err; + if (j == 0) goto loop; + + if(!BN_GENCB_call(cb, 2, c1-1)) + goto err; + /* We have a safe prime test pass */ + } + } + /* we have a prime :-) */ + found = 1; +err: + if (ctx != NULL) + { + BN_CTX_end(ctx); + BN_CTX_free(ctx); + } + bn_check_top(ret); + return found; + } + +int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) + { + return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); + } + +int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, + int do_trial_division, BN_GENCB *cb) + { + 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 (BN_cmp(a, BN_value_one()) <= 0) + return 0; + + 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)) + /* a is even => a is prime if and only if a == 2 */ + return BN_is_word(a, 2); + if (do_trial_division) + { + for (i = 1; i < NUMPRIMES; i++) + if (BN_mod_word(a, primes[i]) == 0) + return 0; + if(!BN_GENCB_call(cb, 1, -1)) + goto err; + } + + 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_range(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(!BN_GENCB_call(cb, 1, i)) + goto err; + } + 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 */ + bn_check_top(w); + return 1; + } + +static int probable_prime(BIGNUM *rnd, int bits) + { + int i; + BN_ULONG mods[NUMPRIMES]; + BN_ULONG delta,maxdelta; + +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]); + maxdelta=BN_MASK2 - primes[NUMPRIMES-1]; + 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) + { + delta+=2; + if (delta > maxdelta) goto again; + goto loop; + } + } + if (!BN_add_word(rnd,delta)) return(0); + bn_check_top(rnd); + return(1); + } + +static int probable_prime_dh(BIGNUM *rnd, int bits, + const BIGNUM *add, const 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); + bn_check_top(rnd); + return(ret); + } + +static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, + const 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); + bn_check_top(p); + return(ret); + } |
