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Improved prime number test

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This commit is contained in:
Werner Koch 1997-11-27 11:44:13 +00:00
parent 9479cf7e24
commit 649eae8f1b
10 changed files with 392 additions and 267 deletions
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71
cipher/primegen.c
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@ -28,7 +28,7 @@
#include "cipher.h"
static int no_of_small_prime_numbers;
static int rabin_miller( MPI n );
static int is_not_prime( MPI n, unsigned nbits, int steps, int *count );
static MPI gen_prime( unsigned nbits, int mode );
@ -50,7 +50,6 @@ generate_public_prime( unsigned nbits )
static MPI
gen_prime( unsigned nbits, int secret )
{
unsigned nlimbs;
MPI prime, val_2, val_3, result;
int i;
@ -111,22 +110,9 @@ gen_prime( unsigned nbits, int secret )
continue; /* stepping (fermat test failed) */
if( DBG_CIPHER )
fputc('+', stderr);
/* and a second one */
count2++;
mpi_powm( result, val_3, prime, prime );
if( mpi_cmp_ui(result, 3) )
continue; /* stepping (fermat test failed) */
if( DBG_CIPHER )
fputc('+', stderr);
/* perform Rabin-Miller tests */
for(i=5; i > 0; i-- ) {
if( DBG_CIPHER )
fputc('+', stderr);
if( rabin_miller(prime) )
break;
}
if( !i ) {
/* perform stronger tests */
if( !is_not_prime(prime, nbits, 5, &count2 ) ) {
if( !mpi_test_bit( prime, nbits-1 ) ) {
if( DBG_CIPHER ) {
fputc('\n', stderr);
@ -136,7 +122,7 @@ gen_prime( unsigned nbits, int secret )
}
if( DBG_CIPHER ) {
fputc('\n', stderr);
log_debug("performed %u simple and %u Fermat/Rabin-Miller tests\n",
log_debug("performed %u simple and %u stronger tests\n",
count1, count2 );
log_mpidump("found prime: ", prime );
}
@ -158,8 +144,53 @@ gen_prime( unsigned nbits, int secret )
* Return 1 if n is not a prime
*/
static int
rabin_miller( MPI n )
is_not_prime( MPI n, unsigned nbits, int steps, int *count )
{
return 0;
MPI x = mpi_alloc( mpi_get_nlimbs( n ) );
MPI y = mpi_alloc( mpi_get_nlimbs( n ) );
MPI z = mpi_alloc( mpi_get_nlimbs( n ) );
MPI nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
MPI a2 = mpi_alloc_set_ui( 2 );
MPI q;
unsigned i, j, k;
int rc = 1;
mpi_sub_ui( nminus1, n, 1 );
/* find q and k, so that n = 1 + 2^k * q */
q = mpi_copy( nminus1 );
k = mpi_trailing_zeros( q );
mpi_tdiv_q_2exp(q, q, k);
for(i=0 ; i < steps; i++ ) {
++*count;
do {
mpi_set_bytes( x, nbits, get_random_byte, 0 );
} while( mpi_cmp( x, n ) < 0 && mpi_cmp_ui( x, 1 ) > 0 );
mpi_powm( y, x, q, n);
if( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) {
for( j=1; j < k; j++ ) {
mpi_powm(y, y, a2, n);
if( !mpi_cmp_ui( y, 1 ) )
goto leave; /* not a prime */
if( !mpi_cmp( y, nminus1 ) )
break; /* may be a prime */
}
if( j == k )
goto leave;
}
if( DBG_CIPHER )
fputc('+', stderr);
}
rc = 0; /* may be a prime */
leave:
mpi_free( x );
mpi_free( y );
mpi_free( z );
mpi_free( nminus1 );
mpi_free( q );
return rc;
}