Primality tests have to deal with different distribution when generating
primes and when validating primes.
These new tests are testing if mbedtls_mpi_is_prime() is working
properly in the latter setting.
The new tests involve pseudoprimes with maximum number of
non-witnesses. The non-witnesses were generated by printing them
from mpi_miller_rabin(). The pseudoprimes were generated by the
following function:
void gen_monier( mbedtls_mpi* res, int nbits )
{
mbedtls_mpi p_2x_plus_1, p_4x_plus_1, x, tmp;
mbedtls_mpi_init( &p_2x_plus_1 );
mbedtls_mpi_init( &p_4x_plus_1 );
mbedtls_mpi_init( &x ); mbedtls_mpi_init( &tmp );
do
{
mbedtls_mpi_gen_prime( &p_2x_plus_1, nbits >> 1, 0,
rnd_std_rand, NULL );
mbedtls_mpi_sub_int( &x, &p_2x_plus_1, 1 );
mbedtls_mpi_div_int( &x, &tmp, &x, 2 );
if( mbedtls_mpi_get_bit( &x, 0 ) == 0 )
continue;
mbedtls_mpi_mul_int( &p_4x_plus_1, &x, 4 );
mbedtls_mpi_add_int( &p_4x_plus_1, &p_4x_plus_1, 1 );
if( mbedtls_mpi_is_prime( &p_4x_plus_1, rnd_std_rand,
NULL ) == 0 )
break;
} while( 1 );
mbedtls_mpi_mul_mpi( res, &p_2x_plus_1, &p_4x_plus_1 );
}
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