| /* 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; |
| prime_t 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] = (prime_t) 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); |
| } |
