/* 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);
}