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Merged Prime generation improvements

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This commit is contained in:
Paul Bakker
2013-11-25 14:27:28 +01:00
parent 7d2c0c4eda 45f457d872
commit e4c71f0e11
4 changed files with 101 additions and 41 deletions
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126
library/bignum.c
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@ -1797,40 +1797,27 @@ static const int small_prime[] =
};
/*
* Miller-Rabin primality test (HAC 4.24)
* Small divisors test (X must be positive)
*
* Return values:
* 0: no small factor (possible prime, more tests needed)
* 1: certain prime
* POLARSSL_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
* other negative: error
*/
int mpi_is_prime( mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
static int mpi_check_small_factors( const mpi *X )
{
int ret, xs;
size_t i, j, n, s;
mpi W, R, T, A, RR;
int ret = 0;
size_t i;
t_uint r;
if( mpi_cmp_int( X, 0 ) == 0 ||
mpi_cmp_int( X, 1 ) == 0 )
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
if( mpi_cmp_int( X, 2 ) == 0 )
return( 0 );
mpi_init( &W ); mpi_init( &R ); mpi_init( &T ); mpi_init( &A );
mpi_init( &RR );
xs = X->s; X->s = 1;
/*
* test trivial factors first
*/
if( ( X->p[0] & 1 ) == 0 )
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
for( i = 0; small_prime[i] > 0; i++ )
{
t_uint r;
if( mpi_cmp_int( X, small_prime[i] ) <= 0 )
return( 0 );
return( 1 );
MPI_CHK( mpi_mod_int( &r, X, small_prime[i] ) );
@ -1838,6 +1825,24 @@ int mpi_is_prime( mpi *X,
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
}
cleanup:
return( ret );
}
/*
* Miller-Rabin pseudo-primality test (HAC 4.24)
*/
static int mpi_miller_rabin( const mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
size_t i, j, n, s;
mpi W, R, T, A, RR;
mpi_init( &W ); mpi_init( &R ); mpi_init( &T ); mpi_init( &A );
mpi_init( &RR );
/*
* W = |X| - 1
* R = W >> lsb( W )
@ -1905,15 +1910,40 @@ int mpi_is_prime( mpi *X,
}
cleanup:
X->s = xs;
mpi_free( &W ); mpi_free( &R ); mpi_free( &T ); mpi_free( &A );
mpi_free( &RR );
return( ret );
}
/*
* Pseudo-primality test: small factors, then Miller-Rabin
*/
int mpi_is_prime( mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret;
const mpi XX = { 1, X->n, X->p }; /* Abs(X) */
if( mpi_cmp_int( &XX, 0 ) == 0 ||
mpi_cmp_int( &XX, 1 ) == 0 )
return( POLARSSL_ERR_MPI_NOT_ACCEPTABLE );
if( mpi_cmp_int( &XX, 2 ) == 0 )
return( 0 );
if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
{
if( ret == 1 )
return( 0 );
return( ret );
}
return( mpi_miller_rabin( &XX, f_rng, p_rng ) );
}
/*
* Prime number generation
*/
@ -1923,6 +1953,7 @@ int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
{
int ret;
size_t k, n;
t_uint r;
mpi Y;
if( nbits < 3 || nbits > POLARSSL_MPI_MAX_BITS )
@ -1952,26 +1983,45 @@ int mpi_gen_prime( mpi *X, size_t nbits, int dh_flag,
}
else
{
MPI_CHK( mpi_sub_int( &Y, X, 1 ) );
/*
* An necessary condition for Y and X = 2Y + 1 to be prime
* is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
* Make sure it is satisfied, while keeping X = 3 mod 4
*/
MPI_CHK( mpi_mod_int( &r, X, 3 ) );
if( r == 0 )
MPI_CHK( mpi_add_int( X, X, 8 ) );
else if( r == 1 )
MPI_CHK( mpi_add_int( X, X, 4 ) );
/* Set Y = (X-1) / 2, which is X / 2 because X is odd */
MPI_CHK( mpi_copy( &Y, X ) );
MPI_CHK( mpi_shift_r( &Y, 1 ) );
while( 1 )
{
if( ( ret = mpi_is_prime( X, f_rng, p_rng ) ) == 0 )
/*
* First, check small factors for X and Y
* before doing Miller-Rabin on any of them
*/
if( ( ret = mpi_check_small_factors( X ) ) == 0 &&
( ret = mpi_check_small_factors( &Y ) ) == 0 &&
( ret = mpi_miller_rabin( X, f_rng, p_rng ) ) == 0 &&
( ret = mpi_miller_rabin( &Y, f_rng, p_rng ) ) == 0 )
{
if( ( ret = mpi_is_prime( &Y, f_rng, p_rng ) ) == 0 )
break;
if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
goto cleanup;
break;
}
if( ret != POLARSSL_ERR_MPI_NOT_ACCEPTABLE )
goto cleanup;
MPI_CHK( mpi_add_int( &Y, X, 1 ) );
MPI_CHK( mpi_add_int( X, X, 2 ) );
MPI_CHK( mpi_shift_r( &Y, 1 ) );
/*
* Next candidates. We want to preserve Y = (X-1) / 2 and
* Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
* so up Y by 6 and X by 12.
*/
MPI_CHK( mpi_add_int( X, X, 12 ) );
MPI_CHK( mpi_add_int( &Y, &Y, 6 ) );
}
}