mbedtls/tests/suites/test_suite_bignum_random.function

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/* BEGIN_HEADER */
/* Dedicated test suite for mbedtls_mpi_core_random() and the upper-layer
* functions. Due to the complexity of how these functions are tested,
* we test all the layers in a single test suite, unlike the way other
* functions are tested with each layer in its own test suite.
*/
#include "mbedtls/bignum.h"
#include "mbedtls/entropy.h"
#include "bignum_core.h"
#include "constant_time_internal.h"
/* This test suite only manipulates non-negative bignums. */
static int sign_is_valid( const mbedtls_mpi *X )
{
return( X->s == 1 );
}
/* A common initializer for test functions that should generate the same
* sequences for reproducibility and good coverage. */
const mbedtls_test_rnd_pseudo_info rnd_pseudo_seed = {
/* 16-word key */
{'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
'a', ' ', 's', 'e', 'e', 'd', '!', 0},
/* 2-word initial state, should be zero */
0, 0};
/* Test whether bytes represents (in big-endian base 256) a number b that
* is significantly above a power of 2. That is, b must not have a long run
* of unset bits after the most significant bit.
*
* Let n be the bit-size of b, i.e. the integer such that 2^n <= b < 2^{n+1}.
* This function returns 1 if, when drawing a number between 0 and b,
* the probability that this number is at least 2^n is not negligible.
* This probability is (b - 2^n) / b and this function checks that this
* number is above some threshold A. The threshold value is heuristic and
* based on the needs of mpi_random_many().
*/
static int is_significantly_above_a_power_of_2( data_t *bytes )
{
const uint8_t *p = bytes->x;
size_t len = bytes->len;
unsigned x;
/* Skip leading null bytes */
while( len > 0 && p[0] == 0 )
{
++p;
--len;
}
/* 0 is not significantly above a power of 2 */
if( len == 0 )
return( 0 );
/* Extract the (up to) 2 most significant bytes */
if( len == 1 )
x = p[0];
else
x = ( p[0] << 8 ) | p[1];
/* Shift the most significant bit of x to position 8 and mask it out */
while( ( x & 0xfe00 ) != 0 )
x >>= 1;
x &= 0x00ff;
/* At this point, x = floor((b - 2^n) / 2^(n-8)). b is significantly above
* a power of 2 iff x is significantly above 0 compared to 2^8.
* Testing x >= 2^4 amounts to picking A = 1/16 in the function
* description above. */
return( x >= 0x10 );
}
/* END_HEADER */
/* BEGIN_DEPENDENCIES
* depends_on:MBEDTLS_BIGNUM_C
* END_DEPENDENCIES
*/
/* BEGIN_CASE */
void mpi_core_random_basic( int min, char *bound_bytes, int expected_ret )
{
/* Same RNG as in mpi_random_values */
mbedtls_test_rnd_pseudo_info rnd = rnd_pseudo_seed;
size_t limbs;
mbedtls_mpi_uint *lower_bound = NULL;
mbedtls_mpi_uint *upper_bound = NULL;
mbedtls_mpi_uint *result = NULL;
TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &upper_bound, &limbs,
bound_bytes ) );
ASSERT_ALLOC( lower_bound, limbs );
lower_bound[0] = min;
ASSERT_ALLOC( result, limbs );
TEST_EQUAL( expected_ret,
mbedtls_mpi_core_random( result, min, upper_bound, limbs,
mbedtls_test_rnd_pseudo_rand, &rnd ) );
if( expected_ret == 0 )
{
TEST_EQUAL( 0, mbedtls_mpi_core_lt_ct( result, lower_bound, limbs ) );
TEST_EQUAL( 1, mbedtls_mpi_core_lt_ct( result, upper_bound, limbs ) );
}
exit:
mbedtls_free( lower_bound );
mbedtls_free( upper_bound );
mbedtls_free( result );
}
/* END_CASE */
/* BEGIN_CASE */
void mpi_legacy_random_values( int min, char *max_hex )
{
/* Same RNG as in mpi_core_random_basic */
mbedtls_test_rnd_pseudo_info rnd_core = rnd_pseudo_seed;
mbedtls_test_rnd_pseudo_info rnd_legacy;
memcpy( &rnd_legacy, &rnd_core, sizeof( rnd_core ) );
mbedtls_mpi max_legacy;
mbedtls_mpi_init( &max_legacy );
mbedtls_mpi_uint *R_core = NULL;
mbedtls_mpi R_legacy;
mbedtls_mpi_init( &R_legacy );
TEST_EQUAL( 0, mbedtls_test_read_mpi( &max_legacy, max_hex ) );
size_t limbs = max_legacy.n;
ASSERT_ALLOC( R_core, limbs );
/* Call the legacy function and the core function with the same random
* stream. */
int core_ret = mbedtls_mpi_core_random( R_core, min, max_legacy.p, limbs,
mbedtls_test_rnd_pseudo_rand,
&rnd_core );
int legacy_ret = mbedtls_mpi_random( &R_legacy, min, &max_legacy,
mbedtls_test_rnd_pseudo_rand,
&rnd_legacy );
/* They must return the same status, and, on success, output the
* same number, with the same limb count. */
TEST_EQUAL( core_ret, legacy_ret );
if( core_ret == 0 )
{
ASSERT_COMPARE( R_core, limbs * ciL,
R_legacy.p, R_legacy.n * ciL );
}
/* Also check that they have consumed the RNG in the same way. */
/* This may theoretically fail on rare platforms with padding in
* the structure! If this is a problem in practice, change to a
* field-by-field comparison. */
ASSERT_COMPARE( &rnd_core, sizeof( rnd_core ),
&rnd_legacy, sizeof( rnd_legacy ) );
exit:
mbedtls_mpi_free( &max_legacy );
mbedtls_free( R_core );
mbedtls_mpi_free( &R_legacy );
}
/* END_CASE */
/* BEGIN_CASE */
void mpi_random_many( int min, char *bound_hex, int iterations )
{
/* Generate numbers in the range 1..bound-1. Do it iterations times.
* This function assumes that the value of bound is at least 2 and
* that iterations is large enough that a one-in-2^iterations chance
* effectively never occurs.
*/
data_t bound_bytes = {NULL, 0};
mbedtls_mpi_uint *upper_bound = NULL;
size_t limbs;
size_t n_bits;
mbedtls_mpi_uint *result = NULL;
size_t b;
/* If upper_bound is small, stats[b] is the number of times the value b
* has been generated. Otherwise stats[b] is the number of times a
* value with bit b set has been generated. */
size_t *stats = NULL;
size_t stats_len;
int full_stats;
size_t i;
TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &upper_bound, &limbs,
bound_hex ) );
ASSERT_ALLOC( result, limbs );
n_bits = mbedtls_mpi_core_bitlen( upper_bound, limbs );
/* Consider a bound "small" if it's less than 2^5. This value is chosen
* to be small enough that the probability of missing one value is
* negligible given the number of iterations. It must be less than
* 256 because some of the code below assumes that "small" values
* fit in a byte. */
if( n_bits <= 5 )
{
full_stats = 1;
stats_len = (uint8_t) upper_bound[0];
}
else
{
full_stats = 0;
stats_len = n_bits;
}
ASSERT_ALLOC( stats, stats_len );
for( i = 0; i < (size_t) iterations; i++ )
{
mbedtls_test_set_step( i );
TEST_EQUAL( 0, mbedtls_mpi_core_random( result,
min, upper_bound, limbs,
mbedtls_test_rnd_std_rand, NULL ) );
/* Temporarily use a legacy MPI for analysis, because the
* necessary auxiliary functions don't exist yet in core. */
mbedtls_mpi B = {1, limbs, upper_bound};
mbedtls_mpi R = {1, limbs, result};
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R, &B ) < 0 );
TEST_ASSERT( mbedtls_mpi_cmp_int( &R, min ) >= 0 );
if( full_stats )
{
uint8_t value;
TEST_EQUAL( 0, mbedtls_mpi_write_binary( &R, &value, 1 ) );
TEST_ASSERT( value < stats_len );
++stats[value];
}
else
{
for( b = 0; b < n_bits; b++ )
stats[b] += mbedtls_mpi_get_bit( &R, b );
}
}
if( full_stats )
{
for( b = min; b < stats_len; b++ )
{
mbedtls_test_set_step( 1000000 + b );
/* Assert that each value has been reached at least once.
* This is almost guaranteed if the iteration count is large
* enough. This is a very crude way of checking the distribution.
*/
TEST_ASSERT( stats[b] > 0 );
}
}
else
{
bound_bytes.len = limbs * sizeof( mbedtls_mpi_uint );
ASSERT_ALLOC( bound_bytes.x, bound_bytes.len );
mbedtls_mpi_core_write_be( upper_bound, limbs,
bound_bytes.x, bound_bytes.len );
int statistically_safe_all_the_way =
is_significantly_above_a_power_of_2( &bound_bytes );
for( b = 0; b < n_bits; b++ )
{
mbedtls_test_set_step( 1000000 + b );
/* Assert that each bit has been set in at least one result and
* clear in at least one result. Provided that iterations is not
* too small, it would be extremely unlikely for this not to be
* the case if the results are uniformly distributed.
*
* As an exception, the top bit may legitimately never be set
* if bound is a power of 2 or only slightly above.
*/
if( statistically_safe_all_the_way || b != n_bits - 1 )
{
TEST_ASSERT( stats[b] > 0 );
}
TEST_ASSERT( stats[b] < (size_t) iterations );
}
}
exit:
mbedtls_free( bound_bytes.x );
mbedtls_free( upper_bound );
mbedtls_free( result );
mbedtls_free( stats );
}
/* END_CASE */
/* BEGIN_CASE */
void mpi_random_sizes( int min, data_t *bound_bytes, int nlimbs, int before )
{
mbedtls_mpi upper_bound;
mbedtls_mpi result;
mbedtls_mpi_init( &upper_bound );
mbedtls_mpi_init( &result );
if( before != 0 )
{
/* Set result to sign(before) * 2^(|before|-1) */
TEST_ASSERT( mbedtls_mpi_lset( &result, before > 0 ? 1 : -1 ) == 0 );
if( before < 0 )
before = - before;
TEST_ASSERT( mbedtls_mpi_shift_l( &result, before - 1 ) == 0 );
}
TEST_EQUAL( 0, mbedtls_mpi_grow( &result, nlimbs ) );
TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
bound_bytes->x, bound_bytes->len ) );
TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
mbedtls_test_rnd_std_rand, NULL ) );
TEST_ASSERT( sign_is_valid( &result ) );
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );
exit:
mbedtls_mpi_free( &upper_bound );
mbedtls_mpi_free( &result );
}
/* END_CASE */
/* BEGIN_CASE */
void mpi_random_fail( int min, data_t *bound_bytes, int expected_ret )
{
mbedtls_mpi upper_bound;
mbedtls_mpi result;
int actual_ret;
mbedtls_mpi_init( &upper_bound );
mbedtls_mpi_init( &result );
TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
bound_bytes->x, bound_bytes->len ) );
actual_ret = mbedtls_mpi_random( &result, min, &upper_bound,
mbedtls_test_rnd_std_rand, NULL );
TEST_EQUAL( expected_ret, actual_ret );
exit:
mbedtls_mpi_free( &upper_bound );
mbedtls_mpi_free( &result );
}
/* END_CASE */