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rndsort{Miller, Rabin} primality test.

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This commit is contained in:
Bodo Möller 2000-02-02 21:20:44 +00:00
parent fb81ac5e6b
commit e74231ed9e
5 changed files with 102 additions and 195 deletions
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5
CHANGES
View File

@ -4,6 +4,11 @@
Changes between 0.9.4 and 0.9.5 [xx XXX 2000] 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. *) Support for the EBCDIC character set completed.
[Martin Kraemer <Martin.Kraemer@Mch.SNI.De>] [Martin Kraemer <Martin.Kraemer@Mch.SNI.De>]

3
crypto/bn/bn.h
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@ -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 *), int BN_is_prime(BIGNUM *p,int nchecks,void (*callback)(int,int,void *),
BN_CTX *ctx,void *cb_arg); BN_CTX *ctx,void *cb_arg);
int BN_is_prime_fasttest(BIGNUM *p,int nchecks, int BN_is_prime_fasttest(BIGNUM *p,int nchecks,
void (*callback)(int,int,void *), void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
BN_CTX *ctx,BN_CTX *ctx2,void *cb_arg,
int do_trial_division); int do_trial_division);
void ERR_load_BN_strings(void ); void ERR_load_BN_strings(void );

257
crypto/bn/bn_prime.c
View File

@ -68,8 +68,8 @@
*/ */
#include "bn_prime.h" #include "bn_prime.h"
static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2, static int witness(BIGNUM *w, BIGNUM *a, BIGNUM *a1, BIGNUM *a1_odd, int k,
BN_MONT_CTX *mont); BN_CTX *ctx, BN_MONT_CTX *mont);
static int probable_prime(BIGNUM *rnd, int bits); static int probable_prime(BIGNUM *rnd, int bits);
static int probable_prime_dh(BIGNUM *rnd, int bits, static int probable_prime_dh(BIGNUM *rnd, int bits,
BIGNUM *add, BIGNUM *rem, BN_CTX *ctx); 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; BIGNUM t;
int found=0; int found=0;
int i,j,c1=0; int i,j,c1=0;
BN_CTX *ctx,*ctx2=NULL; BN_CTX *ctx;
int checks = BN_prime_checks_for_size(bits); int checks = BN_prime_checks_for_size(bits);
ctx=BN_CTX_new(); ctx=BN_CTX_new();
if (ctx == NULL) goto err; if (ctx == NULL) goto err;
ctx2=BN_CTX_new();
if (ctx2 == NULL) goto err;
if (ret == NULL) if (ret == NULL)
{ {
if ((rnd=BN_new()) == NULL) goto err; if ((rnd=BN_new()) == NULL) goto err;
@ -121,7 +119,7 @@ loop:
if (!safe) 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 == -1) goto err;
if (i == 0) goto loop; if (i == 0) goto loop;
} }
@ -135,11 +133,11 @@ loop:
for (i=0; i<checks; i++) 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 == -1) goto err;
if (j == 0) goto loop; 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 == -1) goto err;
if (j == 0) goto loop; if (j == 0) goto loop;
@ -153,26 +151,33 @@ err:
if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd); if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
BN_free(&t); BN_free(&t);
if (ctx != NULL) BN_CTX_free(ctx); if (ctx != NULL) BN_CTX_free(ctx);
if (ctx2 != NULL) BN_CTX_free(ctx2);
return(found ? rnd : NULL); 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, int BN_is_prime_fasttest(BIGNUM *a, int checks,
void (*callback)(int,int,void *), 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 do_trial_division)
{ {
int i, j, ret = -1; int i, j, ret = -1;
BIGNUM *check; int k;
BN_CTX *ctx=NULL,*ctx2=NULL; BN_CTX *ctx = NULL;
BIGNUM *a1, *a1_odd, *check; /* taken from ctx */
BN_MONT_CTX *mont = NULL; BN_MONT_CTX *mont = NULL;
if (checks == BN_prime_checks) if (checks == BN_prime_checks)
{ checks = BN_prime_checks_for_size(BN_num_bits(a));
int bits = BN_num_bits(a);
checks = BN_prime_checks_for_size(bits);
}
if (a->neg) /* for now, refuse to handle negative numbers */
return -1;
/* first look for small factors */
if (!BN_is_odd(a)) if (!BN_is_odd(a))
return(0); return(0);
if (do_trial_division) if (do_trial_division)
@ -186,26 +191,49 @@ int BN_is_prime_fasttest(BIGNUM *a, int checks,
if (ctx_passed != NULL) if (ctx_passed != NULL)
ctx = ctx_passed; ctx = ctx_passed;
else else
if ((ctx=BN_CTX_new()) == NULL) goto err; if ((ctx=BN_CTX_new()) == NULL)
if (ctx2_passed != NULL) goto err;
ctx2=ctx2_passed; a1 = &(ctx->bn[ctx->tos++]);
else a1_odd = &(ctx->bn[ctx->tos++]);
if ((ctx2=BN_CTX_new()) == NULL) goto err; check = &(ctx->bn[ctx->tos++]);;
if ((mont=BN_MONT_CTX_new()) == 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;
}
check= &(ctx->bn[ctx->tos++]); /* 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;
/* Setup the montgomery structure */ /* Montgomery setup for computations mod a */
if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err; 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++) for (i = 0; i < checks; i++)
{ {
if (!BN_pseudo_rand(check,BN_num_bits(a),0,0)) goto err; if (!BN_pseudo_rand(check, BN_num_bits(a1), 0, 0))
if (BN_cmp(check, a) >= 0) goto err;
BN_sub(check, check, a); if (BN_cmp(check, a1) >= 0)
if (BN_is_zero(check)) BN_one(check); if (!BN_sub(check, check, a1))
j=witness(check,a,ctx,ctx2,mont); 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 == -1) goto err;
if (j) if (j)
{ {
@ -216,84 +244,38 @@ int BN_is_prime_fasttest(BIGNUM *a, int checks,
} }
ret=1; ret=1;
err: err:
ctx->tos--; if (ctx_passed != NULL)
if ((ctx_passed == NULL) && (ctx != NULL)) ctx_passed->tos -= 3; /* a1, a1_odd, check */
else if (ctx != NULL)
BN_CTX_free(ctx); BN_CTX_free(ctx);
if ((ctx2_passed == NULL) && (ctx2 != NULL)) if (mont != NULL)
BN_CTX_free(ctx2); BN_MONT_CTX_free(mont);
if (mont != NULL) BN_MONT_CTX_free(mont);
return(ret); return(ret);
} }
int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int,int,void *), static int witness(BIGNUM *w, BIGNUM *a, BIGNUM *a1, BIGNUM *a1_odd, int k,
BN_CTX *ctx_passed, void *cb_arg) BN_CTX *ctx, BN_MONT_CTX *mont)
{ {
return BN_is_prime_fasttest(a, checks, callback, ctx_passed, NULL, cb_arg, 0); 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',
static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2, * and it is neither -1 nor +1 -- so 'a' cannot be prime */
BN_MONT_CTX *mont) return 1;
{
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_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_cmp(d,mont_one) == 0)
i=0;
else i=1;
ret=i;
err:
ctx->tos-=3;
ctx2->tos-=3;
return(ret);
} }
static int probable_prime(BIGNUM *rnd, int bits) static int probable_prime(BIGNUM *rnd, int bits)
@ -411,76 +393,3 @@ err:
ctx->tos-=3; ctx->tos-=3;
return(ret); 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

8
crypto/dsa/dsa_gen.c
View File

@ -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 k,n=0,i,b,m=0;
int counter=0; int counter=0;
int r=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; unsigned int h=2;
DSA *ret=NULL; 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 ((ctx=BN_CTX_new()) == NULL) goto err;
if ((ctx2=BN_CTX_new()) == NULL) goto err; if ((ctx2=BN_CTX_new()) == NULL) goto err;
if ((ctx3=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 ((ret=DSA_new()) == NULL) goto err;
if ((mont=BN_MONT_CTX_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; if (!BN_bin2bn(md,SHA_DIGEST_LENGTH,q)) goto err;
/* step 4 */ /* 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) if (r > 0)
break; break;
if (r != 0) 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) if (BN_cmp(p,test) >= 0)
{ {
/* step 11 */ /* 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) if (r > 0)
goto end; /* found it */ goto end; /* found it */
if (r != 0) if (r != 0)
@ -283,7 +282,6 @@ err:
if (ctx != NULL) BN_CTX_free(ctx); if (ctx != NULL) BN_CTX_free(ctx);
if (ctx2 != NULL) BN_CTX_free(ctx2); if (ctx2 != NULL) BN_CTX_free(ctx2);
if (ctx3 != NULL) BN_CTX_free(ctx3); if (ctx3 != NULL) BN_CTX_free(ctx3);
if (ctx4 != NULL) BN_CTX_free(ctx4);
if (mont != NULL) BN_MONT_CTX_free(mont); if (mont != NULL) BN_MONT_CTX_free(mont);
return(ok?ret:NULL); return(ok?ret:NULL);
} }

8
doc/crypto/BN_generate_prime.pod
View File

@ -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); void *), BN_CTX *ctx, void *cb_arg);
int BN_is_prime_fasttest(BIGNUM *a, int checks, void (*callback)(int, int BN_is_prime_fasttest(BIGNUM *a, int checks, void (*callback)(int,
int, void *), BN_CTX *ctx, BN_CTX *ctx2, void *cb_arg, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division);
int do_trial_division);
=head1 DESCRIPTION =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 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 after the j-th iteration (j = 0, 1, ...). B<ctx> is a
pre-allocated B<BN_CTX> (to save the overhead of allocating and pre-allocated B<BN_CTX> (to save the overhead of allocating and
freeing the structure in a loop), or B<NULL>. For freeing the structure in a loop), or B<NULL>.
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>).
=head1 RETURN VALUES =head1 RETURN VALUES