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 );
}
The input distribution to primality testing functions is completely
different when used for generating primes and when for validating
primes. The constants used in the library are geared towards the prime
generation use case and are weak when used for validation. (Maliciously
constructed composite numbers can pass the test with high probability)
The mbedtls_mpi_is_prime() function is in the public API and although it
is not documented, it is reasonable to assume that the primary use case
is validating primes. The RSA module too uses it for validating key
material.
`mbedtls_ssl_get_record_expansion()` is supposed to return the maximum
difference between the size of a protected record and the size of the
encapsulated plaintext.
Previously, it did not correctly estimate the maximum record expansion
in case of CBC ciphersuites in (D)TLS versions 1.1 and higher, in which
case the ciphertext is prefixed by an explicit IV.
This commit fixes this bug. Fixes#1914.
