Bignum: Add tests for primality testing

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 );
}

tests/suites/test_suite_mpi.function

@@ -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 )
 {