* 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 "bn_prime.h"
-/* number of Miller-Rabin iterations for an error rate of less than 2^-80
- * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
- * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
- * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
- * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
-#define BN_prime_checks_size(b) ((b) >= 1300 ? 2 : \
- (b) >= 850 ? 3 : \
- (b) >= 650 ? 4 : \
- (b) >= 550 ? 5 : \
- (b) >= 450 ? 6 : \
- (b) >= 400 ? 7 : \
- (b) >= 350 ? 8 : \
- (b) >= 300 ? 9 : \
- (b) >= 250 ? 12 : \
- (b) >= 200 ? 15 : \
- (b) >= 150 ? 18 : \
- /* b >= 100 */ 27)
-
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
- BN_MONT_CTX *mont);
+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);
int found=0;
int i,j,c1=0;
BN_CTX *ctx;
- int checks = BN_prime_checks_size(bits);
+ int checks = BN_prime_checks_for_size(bits);
ctx=BN_CTX_new();
if (ctx == NULL) goto err;
if (!safe)
{
- i=BN_is_prime(rnd,checks,callback,ctx,cb_arg);
+ i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
if (i == -1) goto err;
if (i == 0) goto loop;
}
for (i=0; i<checks; i++)
{
- j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
+ 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(&t,1,callback,ctx,cb_arg);
+ j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
if (j == -1) goto err;
if (j == 0) goto loop;
return(found ? rnd : NULL);
}
-int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int,int,void *),
- BN_CTX *ctx_passed, void *cb_arg)
+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,c2=0,ret= -1;
- BIGNUM *check;
- BN_CTX *ctx=NULL,*ctx2=NULL;
- BN_MONT_CTX *mont=NULL;
+ 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;
if (checks == BN_prime_checks)
- {
- int bits = BN_num_bits(a);
- checks = BN_prime_checks_size(bits);
- }
+ 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;
+ ctx = ctx_passed;
else
- if ((ctx=BN_CTX_new()) == NULL) goto err;
-
- if ((ctx2=BN_CTX_new()) == NULL) goto err;
- if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
-
- check= &(ctx->bn[ctx->tos++]);
-
- /* Setup the montgomery structure */
- if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
+ if ((ctx=BN_CTX_new()) == NULL)
+ goto err;
+ /* A := abs(a) */
+ if (a->neg)
+ {
+ 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;
+ }
- for (i=0; i<checks; i++)
+ /* 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_rand(check,BN_num_bits(a)-1,0,0)) goto err;
- j=witness(check,a,ctx,ctx2,mont);
+ 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,c2++,cb_arg);
+ if (callback != NULL) callback(1,i,cb_arg);
}
ret=1;
err:
- ctx->tos--;
- if ((ctx_passed == NULL) && (ctx != NULL))
+ 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 (ctx2 != NULL)
- BN_CTX_free(ctx2);
- if (mont != NULL) BN_MONT_CTX_free(mont);
-
+ if (mont != NULL)
+ BN_MONT_CTX_free(mont);
+
return(ret);
}
-#define RECP_MUL_MOD
-
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
- BN_MONT_CTX *mont)
+static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
+ const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
{
- int k,i,ret= -1,good;
- BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
- BIGNUM *mont_one,*mont_n1,*mont_a;
-
- d1= &(ctx->bn[ctx->tos]);
- d2= &(ctx->bn[ctx->tos+1]);
- n1= &(ctx->bn[ctx->tos+2]);
- ctx->tos+=3;
-
- mont_one= &(ctx2->bn[ctx2->tos]);
- mont_n1= &(ctx2->bn[ctx2->tos+1]);
- mont_a= &(ctx2->bn[ctx2->tos+2]);
- ctx2->tos+=3;
-
- d=d1;
- dd=d2;
- if (!BN_one(d)) goto err;
- if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
- k=BN_num_bits(n1);
-
- if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
- if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
- if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
-
- BN_copy(d,mont_one);
- for (i=k-1; i>=0; i--)
+ 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_cmp(d,mont_one) != 0) &&
- (BN_cmp(d,mont_n1) != 0))
- good=1;
- else
- good=0;
-
- BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
-
- if (good && (BN_cmp(dd,mont_one) == 0))
- {
- ret=1;
- goto err;
- }
- if (BN_is_bit_set(n1,i))
- {
- BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
- }
- else
- {
- tmp=d;
- d=dd;
- dd=tmp;
- }
+ 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 (BN_cmp(d,mont_one) == 0)
- i=0;
- else i=1;
- ret=i;
-err:
- ctx->tos-=3;
- ctx2->tos-=3;
- return(ret);
+ /* 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;
- MS_STATIC BN_ULONG mods[NUMPRIMES];
+ BN_ULONG mods[NUMPRIMES];
BN_ULONG delta,d;
again:
ctx->tos-=3;
return(ret);
}
-
-#if 0
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx)
- {
- int k,i,nb,ret= -1;
- BIGNUM *d,*dd,*tmp;
- BIGNUM *d1,*d2,*x,*n1,*inv;
-
- d1= &(ctx->bn[ctx->tos]);
- d2= &(ctx->bn[ctx->tos+1]);
- x= &(ctx->bn[ctx->tos+2]);
- n1= &(ctx->bn[ctx->tos+3]);
- inv=&(ctx->bn[ctx->tos+4]);
- ctx->tos+=5;
-
- d=d1;
- dd=d2;
- if (!BN_one(d)) goto err;
- if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
- k=BN_num_bits(n1);
-
- /* i=BN_num_bits(n); */
-#ifdef RECP_MUL_MOD
- nb=BN_reciprocal(inv,n,ctx); /**/
- if (nb == -1) goto err;
-#endif
-
- for (i=k-1; i>=0; i--)
- {
- if (BN_copy(x,d) == NULL) goto err;
-#ifndef RECP_MUL_MOD
- if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
-#else
- if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
-#endif
- if ( BN_is_one(dd) &&
- !BN_is_one(x) &&
- (BN_cmp(x,n1) != 0))
- {
- ret=1;
- goto err;
- }
- if (BN_is_bit_set(n1,i))
- {
-#ifndef RECP_MUL_MOD
- if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
-#else
- if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
-#endif
- }
- else
- {
- tmp=d;
- d=dd;
- dd=tmp;
- }
- }
- if (BN_is_one(d))
- i=0;
- else i=1;
- ret=i;
-err:
- ctx->tos-=5;
- return(ret);
- }
-#endif
projects / openssl.git / blobdiff