Commit e74231ed authored by Bodo Möller's avatar Bodo Möller
Browse files

rndsort{Miller, Rabin} primality test.

parent fb81ac5e

CHANGES

+5 −0
Original line number Diff line number Diff line
@@ -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>]

crypto/bn/bn.h

+1 −2
Original line number Diff line number Diff line
@@ -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 );

crypto/bn/bn_prime.c

+91 −182
Original line number Diff line number Diff line
@@ -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;

	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)
@@ -186,26 +191,49 @@ int BN_is_prime_fasttest(BIGNUM *a, int checks, 
	if (ctx_passed != NULL)

		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 ((ctx=BN_CTX_new()) == NULL)

			goto err;

	a1 = &(ctx->bn[ctx->tos++]);

	a1_odd = &(ctx->bn[ctx->tos++]);

	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 */

	if (!BN_MONT_CTX_set(mont,a,ctx2)) 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);

	if (mont != NULL)

		BN_MONT_CTX_free(mont);



	return(ret);

	}



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);

	}



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

crypto/dsa/dsa_gen.c

+3 −5
Original line number Diff line number Diff line
@@ -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);

	}

doc/crypto/BN_generate_prime.pod

+2 −6
Original line number Diff line number Diff line
@@ -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