From e74231ed9e5b7a95fd7af625a09628d69eac76c3 Mon Sep 17 00:00:00 2001
From: =?utf8?q?Bodo=20M=C3=B6ller?= <bodo@openssl.org>
Date: Wed, 2 Feb 2000 21:20:44 +0000
Subject: [PATCH] rndsort{Miller, Rabin} primality test.
---
CHANGES | 5 +
crypto/bn/bn.h | 3 +-
crypto/bn/bn_prime.c | 273 +++++++++++--------------------
crypto/dsa/dsa_gen.c | 8 +-
doc/crypto/BN_generate_prime.pod | 8 +-
5 files changed, 102 insertions(+), 195 deletions(-)
diff --git a/CHANGES b/CHANGES
index fbcf4220c1..4e672597ab 100644
--- a/CHANGES
+++ b/CHANGES
@@ -4,6 +4,11 @@
Changes between 0.9.4 and 0.9.5 [xx XXX 2000]
+ *) Use a less unusual form of the Miller-Rabin primality test (it used
+ a binary algorithm for exponentiation integrated into the Miller-Rabin
+ loop, our standard modexp algorithms are faster).
+ [Bodo Moeller]
+
*) Support for the EBCDIC character set completed.
[Martin Kraemer <Martin.Kraemer@Mch.SNI.De>]
diff --git a/crypto/bn/bn.h b/crypto/bn/bn.h
index e88291d62c..2998738193 100644
--- a/crypto/bn/bn.h
+++ b/crypto/bn/bn.h
@@ -407,8 +407,7 @@ BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,BIGNUM *add,
int BN_is_prime(BIGNUM *p,int nchecks,void (*callback)(int,int,void *),
BN_CTX *ctx,void *cb_arg);
int BN_is_prime_fasttest(BIGNUM *p,int nchecks,
- void (*callback)(int,int,void *),
- BN_CTX *ctx,BN_CTX *ctx2,void *cb_arg,
+ void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
int do_trial_division);
void ERR_load_BN_strings(void );
diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c
index f6de801263..21d49affda 100644
--- a/crypto/bn/bn_prime.c
+++ b/crypto/bn/bn_prime.c
@@ -68,8 +68,8 @@
*/
#include "bn_prime.h"
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
- BN_MONT_CTX *mont);
+static int witness(BIGNUM *w, BIGNUM *a, BIGNUM *a1, 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);
@@ -83,13 +83,11 @@ BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
BIGNUM t;
int found=0;
int i,j,c1=0;
- BN_CTX *ctx,*ctx2=NULL;
+ BN_CTX *ctx;
int checks = BN_prime_checks_for_size(bits);
ctx=BN_CTX_new();
if (ctx == NULL) goto err;
- ctx2=BN_CTX_new();
- if (ctx2 == NULL) goto err;
if (ret == NULL)
{
if ((rnd=BN_new()) == NULL) goto err;
@@ -121,7 +119,7 @@ loop:
if (!safe)
{
- i=BN_is_prime_fasttest(rnd,checks,callback,ctx,ctx2,cb_arg,0);
+ i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
if (i == -1) goto err;
if (i == 0) goto loop;
}
@@ -135,11 +133,11 @@ loop:
for (i=0; i<checks; i++)
{
- j=BN_is_prime_fasttest(rnd,1,callback,ctx,ctx2,cb_arg,0);
+ 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_fasttest(&t,1,callback,ctx,ctx2,cb_arg,0);
+ j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
if (j == -1) goto err;
if (j == 0) goto loop;
@@ -153,26 +151,33 @@ err:
if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
BN_free(&t);
if (ctx != NULL) BN_CTX_free(ctx);
- if (ctx2 != NULL) BN_CTX_free(ctx2);
return(found ? rnd : NULL);
}
+int BN_is_prime(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(BIGNUM *a, int checks,
void (*callback)(int,int,void *),
- BN_CTX *ctx_passed, BN_CTX *ctx2_passed, void *cb_arg,
+ BN_CTX *ctx_passed, void *cb_arg,
int do_trial_division)
{
- int i,j,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;
if (checks == BN_prime_checks)
- {
- int bits = BN_num_bits(a);
- checks = BN_prime_checks_for_size(bits);
- }
+ checks = BN_prime_checks_for_size(BN_num_bits(a));
+
+ if (a->neg) /* for now, refuse to handle negative numbers */
+ return -1;
+ /* first look for small factors */
if (!BN_is_odd(a))
return(0);
if (do_trial_division)
@@ -180,32 +185,55 @@ int BN_is_prime_fasttest(BIGNUM *a, int checks,
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 (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_passed != NULL)
- ctx2=ctx2_passed;
- else
- 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;
+ 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_pseudo_rand(check,BN_num_bits(a),0,0)) goto err;
- if (BN_cmp(check, a) >= 0)
- BN_sub(check, check, a);
- if (BN_is_zero(check)) BN_one(check);
- 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)
{
@@ -216,84 +244,38 @@ int BN_is_prime_fasttest(BIGNUM *a, int checks,
}
ret=1;
err:
- ctx->tos--;
- if ((ctx_passed == NULL) && (ctx != NULL))
+ if (ctx_passed != NULL)
+ ctx_passed->tos -= 3; /* a1, a1_odd, check */
+ else if (ctx != NULL)
BN_CTX_free(ctx);
- if ((ctx2_passed == NULL) && (ctx2 != NULL))
- BN_CTX_free(ctx2);
- if (mont != NULL) BN_MONT_CTX_free(mont);
-
- return(ret);
- }
+ if (mont != NULL)
+ BN_MONT_CTX_free(mont);
-int BN_is_prime(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, NULL, cb_arg, 0);
+ return(ret);
}
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
- BN_MONT_CTX *mont)
+static int witness(BIGNUM *w, BIGNUM *a, BIGNUM *a1, 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)
@@ -411,76 +393,3 @@ err:
ctx->tos-=3;
return(ret);
}
-
-#if 0
-
-#define RECP_MUL_MOD
-
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,
- BN_CTX *unused, BN_MONT_CTX *unused2)
- {
- int k,i,ret= -1;
- BIGNUM *d,*dd,*tmp;
- BIGNUM *d1,*d2,*x,*n1;
- BN_RECP_CTX recp;
-
- d1= &(ctx->bn[ctx->tos]);
- d2= &(ctx->bn[ctx->tos+1]);
- x= &(ctx->bn[ctx->tos+2]);
- n1= &(ctx->bn[ctx->tos+3]);
- ctx->tos+=4;
-
- 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
- BN_RECP_CTX_init(&recp);
- if (BN_RECP_CTX_set(&recp,n,ctx) <= 0) 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,&recp,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,&recp,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-=4;
-#ifdef RECP_MUL_MOD
- BN_RECP_CTX_free(&recp);
-#endif
- return(ret);
- }
-#endif
diff --git a/crypto/dsa/dsa_gen.c b/crypto/dsa/dsa_gen.c
index 710a4faa66..b324840180 100644
--- a/crypto/dsa/dsa_gen.c
+++ b/crypto/dsa/dsa_gen.c
@@ -93,7 +93,7 @@ DSA *DSA_generate_parameters(int bits, unsigned char *seed_in, int seed_len,
int k,n=0,i,b,m=0;
int counter=0;
int r=0;
- BN_CTX *ctx=NULL,*ctx2=NULL,*ctx3=NULL,*ctx4=NULL;
+ BN_CTX *ctx=NULL,*ctx2=NULL,*ctx3=NULL;
unsigned int h=2;
DSA *ret=NULL;
@@ -111,7 +111,6 @@ DSA *DSA_generate_parameters(int bits, unsigned char *seed_in, int seed_len,
if ((ctx=BN_CTX_new()) == NULL) goto err;
if ((ctx2=BN_CTX_new()) == NULL) goto err;
if ((ctx3=BN_CTX_new()) == NULL) goto err;
- if ((ctx4=BN_CTX_new()) == NULL) goto err;
if ((ret=DSA_new()) == NULL) goto err;
if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
@@ -167,7 +166,7 @@ DSA *DSA_generate_parameters(int bits, unsigned char *seed_in, int seed_len,
if (!BN_bin2bn(md,SHA_DIGEST_LENGTH,q)) goto err;
/* step 4 */
- r = BN_is_prime_fasttest(q, DSS_prime_checks, callback, ctx3, ctx4, cb_arg, seed_is_random);
+ r = BN_is_prime_fasttest(q, DSS_prime_checks, callback, ctx3, cb_arg, seed_is_random);
if (r > 0)
break;
if (r != 0)
@@ -228,7 +227,7 @@ DSA *DSA_generate_parameters(int bits, unsigned char *seed_in, int seed_len,
if (BN_cmp(p,test) >= 0)
{
/* step 11 */
- r = BN_is_prime_fasttest(p, DSS_prime_checks, callback, ctx3, ctx4, cb_arg, 1);
+ r = BN_is_prime_fasttest(p, DSS_prime_checks, callback, ctx3, cb_arg, 1);
if (r > 0)
goto end; /* found it */
if (r != 0)
@@ -283,7 +282,6 @@ err:
if (ctx != NULL) BN_CTX_free(ctx);
if (ctx2 != NULL) BN_CTX_free(ctx2);
if (ctx3 != NULL) BN_CTX_free(ctx3);
- if (ctx4 != NULL) BN_CTX_free(ctx4);
if (mont != NULL) BN_MONT_CTX_free(mont);
return(ok?ret:NULL);
}
diff --git a/doc/crypto/BN_generate_prime.pod b/doc/crypto/BN_generate_prime.pod
index c2cc151cf6..ab84d3fcfc 100644
--- a/doc/crypto/BN_generate_prime.pod
+++ b/doc/crypto/BN_generate_prime.pod
@@ -15,8 +15,7 @@ BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - Generate primes and test
void *), BN_CTX *ctx, void *cb_arg);
int BN_is_prime_fasttest(BIGNUM *a, int checks, void (*callback)(int,
- int, void *), BN_CTX *ctx, BN_CTX *ctx2, void *cb_arg,
- int do_trial_division);
+ int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division);
=head1 DESCRIPTION
@@ -76,10 +75,7 @@ yields a false positive rate of at most 2^-80 for random input.
If B<callback> is not B<NULL>, B<callback(1, j, cb_arg)> is called
after the j-th iteration (j = 0, 1, ...). B<ctx> is a
pre-allocated B<BN_CTX> (to save the overhead of allocating and
-freeing the structure in a loop), or B<NULL>. For
-BN_is_prime_fasttest(), B<ctx2> is a second pre-allocated B<BN_CTX> or
-B<NULL> (lacking this parameter, BN_is_prime() always has to allocate
-an additional B<CN_CTX>).
+freeing the structure in a loop), or B<NULL>.
=head1 RETURN VALUES
--
2.25.1