rndsort{Miller, Rabin} primality test.

diff --git a/CHANGES b/CHANGES
index fbcf4220c16eb73dea3a809e91dc59f0d89af71b..4e672597abd960320ebecb7b173b5462b5a6f100 100644 (file)
--- a/CHANGES
+++ b/CHANGES
@@ -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.
      [Martin Kraemer <Martin.Kraemer@Mch.SNI.De>]
 
   *) 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 e88291d62cb867eb43f751e141a330eeb680e6d9..299873819347713e401e1c50aa1f95e7a60c777e 100644 (file)
--- 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,
 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 );
 
                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 f6de801263cc410974cffcc7ba313945aaef6a5c..21d49affda6435a3b5110c0d2d8973a53821a499 100644 (file)
--- a/crypto/bn/bn_prime.c
+++ b/crypto/bn/bn_prime.c
@@ -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,
-       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);
 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;
        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;
        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;
        if (ret == NULL)
                {
                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 == 0) goto loop;
                }
                if (i == -1) goto err;
                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 == 0) goto loop;
 
                        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;
 
                        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 (!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);
        }
 
        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 *),
 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 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)
 
        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)
        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;
                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)
                }
 
        if (ctx_passed != NULL)

-               ctx=ctx_passed;
+               ctx = ctx_passed;

        else
        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)
                        {
                if (j == -1) goto err;
                if (j)
                        {


@@ -216,84 +244,38 @@ int BN_is_prime_fasttest(BIGNUM *a, int checks,
                }
        ret=1;
 err:
                }
        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);
                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)
        }
 
 static int probable_prime(BIGNUM *rnd, int bits)


@@ -411,76 +393,3 @@ err:
        ctx->tos-=3;
        return(ret);
        }
        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 710a4faa66bd996d0d559d48246607b5337644dd..b3248401804c2cd07e25317146c990441400f658 100644 (file)
--- 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;
        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;
 
        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 ((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;
        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 */
                        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)
                        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 */
                        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)
                                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 (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);
        }
        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 c2cc151cf6f8cc4aea5327af76fd879942c80371..ab84d3fcfccddea754174db77a2e87d0d379a4e8 100644 (file)
--- 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,
      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
 
 
 =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
 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
 
 
 =head1 RETURN VALUES