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Bignum: Add tests for primality testing

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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 );
}
This commit is contained in:
Janos Follath 2018-09-05 17:04:49 +01:00 committed by Darryl Green
parent b728c29114
commit 64eca05ec2
2 changed files with 74 additions and 0 deletions
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8
tests/suites/test_suite_mpi.data
View file

@ -680,6 +680,14 @@ Test mbedtls_mpi_is_prime #20
depends_on:MBEDTLS_GENPRIME
mbedtls_mpi_is_prime:10:"49979687":0
Test mbedtls_mpi_is_prime_det (4 non-witnesses)
depends_on:MBEDTLS_GENPRIME
mbedtls_mpi_is_prime_det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
Test mbedtls_mpi_is_prime_det (39 non-witnesses)
depends_on:MBEDTLS_GENPRIME
mbedtls_mpi_is_prime_det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
Test mbedtls_mpi_gen_prime (Too small)
depends_on:MBEDTLS_GENPRIME
mbedtls_mpi_gen_prime:2:0:MBEDTLS_ERR_MPI_BAD_INPUT_DATA

66
tests/suites/test_suite_mpi.function
View file

@ -1,5 +1,48 @@
/* BEGIN_HEADER */
#include "mbedtls/bignum.h"
typedef struct mbedtls_test_mpi_random
{
data_t *data;
size_t pos;
size_t chunk_len;
} mbedtls_test_mpi_random;
/*
* This function is called by the Miller-Rabin primality test each time it
* chooses a random witness. The witnesses (or non-witnesses as provided by the
* test) are stored in the data member of the state structure. Each number is in
* the format that mbedtls_mpi_read_string understands and is chunk_len long.
*/
int mbedtls_test_mpi_miller_rabin_determinizer( void* state,
unsigned char* buf,
size_t len )
{
mbedtls_test_mpi_random *random = (mbedtls_test_mpi_random*) state;
if( random == NULL || random->data->x == NULL || buf == NULL )
return( -1 );
if( random->pos + random->chunk_len > random->data->len
|| random->chunk_len > len )
{
return( -1 );
}
memset( buf, 0, len );
/* The witness is written to the end of the buffer, since the buffer is
* used as big endian, unsigned binary data in mbedtls_mpi_read_binary.
* Writing the witness to the start of the buffer would result in the
* buffer being 'witness 000...000', which would be treated as
* witness * 2^n for some n. */
memcpy( buf + len - random->chunk_len, &random->data->x[random->pos],
random->chunk_len );
random->pos += random->chunk_len;
return( 0 );
}
/* END_HEADER */
/* BEGIN_DEPENDENCIES
@ -808,6 +851,29 @@ exit:
}
/* END_CASE */
/* BEGIN_CASE depends_on:MBEDTLS_GENPRIME */
void mbedtls_mpi_is_prime_det( data_t * input_X, data_t * witnesses,
int chunk_len, int div_result )
{
mbedtls_mpi X;
int res;
mbedtls_test_mpi_random rand;
mbedtls_mpi_init( &X );
rand.data = witnesses;
rand.pos = 0;
rand.chunk_len = chunk_len;
TEST_ASSERT( mbedtls_mpi_read_binary( &X, input_X->x, input_X->len ) == 0 );
res = mbedtls_mpi_is_prime( &X, mbedtls_test_mpi_miller_rabin_determinizer,
&rand );
TEST_ASSERT( res == div_result );
exit:
mbedtls_mpi_free( &X );
}
/* END_CASE */
/* BEGIN_CASE depends_on:MBEDTLS_GENPRIME */
void mbedtls_mpi_gen_prime( int bits, int flags, int ref_ret )
{