/* 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.
*
* Test strategy
* =============
*
* There are three main goals for testing random() functions:
* - Parameter validation.
* - Correctness of outputs (well-formed, in range).
* - Distribution of outputs.
*
* We test parameter validation in a standard way, with unit tests with
* positive and negative cases:
* - mbedtls_mpi_core_random(): negative cases for mpi_core_random_basic.
* - mbedtls_mpi_mod_raw_random(), mbedtls_mpi_mod_random(): negative
* cases for mpi_mod_random_validation.
* - mbedtls_mpi_random(): mpi_random_fail.
*
* We test the correctness of outputs in positive tests:
* - mbedtls_mpi_core_random(): positive cases for mpi_core_random_basic,
* and mpi_random_many.
* - mbedtls_mpi_mod_raw_random(), mbedtls_mpi_mod_random(): tested indirectly
* via mpi_mod_random_values.
* - mbedtls_mpi_random(): mpi_random_sizes, plus indirectly via
* mpi_random_values.
*
* We test the distribution of outputs only for mbedtls_mpi_core_random(),
* in mpi_random_many, which runs the function multiple times. This also
* helps in validating the output range, through test cases with a small
* range where any output out of range would be very likely to lead to a
* test failure. For the other functions, we validate the distribution
* indirectly by testing that these functions consume the random generator
* in the same way as mbedtls_mpi_core_random(). This is done in
* mpi_mod_random_values and mpi_legacy_random_values.
*/
#include "mbedtls/bignum.h"
#include "mbedtls/entropy.h"
#include "bignum_core.h"
#include "bignum_mod_raw.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));
TEST_CALLOC(lower_bound, limbs);
lower_bound[0] = min;
TEST_CALLOC(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_ASSERT(0 != 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;
TEST_CALLOC(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) {
TEST_MEMORY_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. */
TEST_MEMORY_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 depends_on:MBEDTLS_ECP_WITH_MPI_UINT */
void mpi_mod_random_values(int min, char *max_hex, int rep)
{
/* Same RNG as in mpi_core_random_basic */
mbedtls_test_rnd_pseudo_info rnd_core = rnd_pseudo_seed;
mbedtls_test_rnd_pseudo_info rnd_mod_raw;
memcpy(&rnd_mod_raw, &rnd_core, sizeof(rnd_core));
mbedtls_test_rnd_pseudo_info rnd_mod;
memcpy(&rnd_mod, &rnd_core, sizeof(rnd_core));
mbedtls_mpi_uint *R_core = NULL;
mbedtls_mpi_uint *R_mod_raw = NULL;
mbedtls_mpi_uint *R_mod_digits = NULL;
mbedtls_mpi_mod_residue R_mod;
mbedtls_mpi_mod_modulus N;
mbedtls_mpi_mod_modulus_init(&N);
TEST_EQUAL(mbedtls_test_read_mpi_modulus(&N, max_hex, rep), 0);
TEST_CALLOC(R_core, N.limbs);
TEST_CALLOC(R_mod_raw, N.limbs);
TEST_CALLOC(R_mod_digits, N.limbs);
TEST_EQUAL(mbedtls_mpi_mod_residue_setup(&R_mod, &N,
R_mod_digits, N.limbs),
0);
/* Call the core and mod random() functions with the same random stream. */
int core_ret = mbedtls_mpi_core_random(R_core,
min, N.p, N.limbs,
mbedtls_test_rnd_pseudo_rand,
&rnd_core);
int mod_raw_ret = mbedtls_mpi_mod_raw_random(R_mod_raw,
min, &N,
mbedtls_test_rnd_pseudo_rand,
&rnd_mod_raw);
int mod_ret = mbedtls_mpi_mod_random(&R_mod,
min, &N,
mbedtls_test_rnd_pseudo_rand,
&rnd_mod);
/* They must return the same status, and, on success, output the
* same number, with the same limb count. */
TEST_EQUAL(core_ret, mod_raw_ret);
TEST_EQUAL(core_ret, mod_ret);
if (core_ret == 0) {
TEST_EQUAL(mbedtls_mpi_mod_raw_modulus_to_canonical_rep(R_mod_raw, &N),
0);
TEST_MEMORY_COMPARE(R_core, N.limbs * ciL,
R_mod_raw, N.limbs * ciL);
TEST_EQUAL(mbedtls_mpi_mod_raw_modulus_to_canonical_rep(R_mod_digits, &N),
0);
TEST_MEMORY_COMPARE(R_core, N.limbs * ciL,
R_mod_digits, N.limbs * 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. */
TEST_MEMORY_COMPARE(&rnd_core, sizeof(rnd_core),
&rnd_mod_raw, sizeof(rnd_mod_raw));
TEST_MEMORY_COMPARE(&rnd_core, sizeof(rnd_core),
&rnd_mod, sizeof(rnd_mod));
exit:
mbedtls_test_mpi_mod_modulus_free_with_limbs(&N);
mbedtls_free(R_core);
mbedtls_free(R_mod_raw);
mbedtls_free(R_mod_digits);
}
/* 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));
TEST_CALLOC(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;
}
TEST_CALLOC(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 = { .s = 1, .n = limbs, .p = upper_bound };
mbedtls_mpi R = { .s = 1, .n = limbs, .p = 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);
TEST_CALLOC(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 depends_on:MBEDTLS_ECP_WITH_MPI_UINT */
void mpi_mod_random_validation(int min, char *bound_hex,
int result_limbs_delta,
int expected_ret)
{
mbedtls_mpi_uint *result_digits = NULL;
mbedtls_mpi_mod_modulus N;
mbedtls_mpi_mod_modulus_init(&N);
TEST_EQUAL(mbedtls_test_read_mpi_modulus(&N, bound_hex,
MBEDTLS_MPI_MOD_REP_OPT_RED),
0);
size_t result_limbs = N.limbs + result_limbs_delta;
TEST_CALLOC(result_digits, result_limbs);
/* Build a reside that might not match the modulus, to test that
* the library function rejects that as expected. */
mbedtls_mpi_mod_residue result = { result_digits, result_limbs };
TEST_EQUAL(mbedtls_mpi_mod_random(&result, min, &N,
mbedtls_test_rnd_std_rand, NULL),
expected_ret);
if (expected_ret == 0) {
/* Success should only be expected when the result has the same
* size as the modulus, otherwise it's a mistake in the test data. */
TEST_EQUAL(result_limbs, N.limbs);
/* Sanity check: check that the result is in range */
TEST_ASSERT(0 != mbedtls_mpi_core_lt_ct(result_digits, N.p, N.limbs));
/* Check result >= min (changes result) */
TEST_EQUAL(mbedtls_mpi_core_sub_int(result_digits, result_digits, min,
result_limbs),
0);
}
/* When the result has the right number of limbs, also test mod_raw
* (for which this is an unchecked precondition). */
if (result_limbs_delta == 0) {
TEST_EQUAL(mbedtls_mpi_mod_raw_random(result_digits, min, &N,
mbedtls_test_rnd_std_rand, NULL),
expected_ret);
if (expected_ret == 0) {
TEST_ASSERT(0 != mbedtls_mpi_core_lt_ct(result_digits, N.p, N.limbs));
TEST_EQUAL(mbedtls_mpi_core_sub_int(result_digits, result.p, min,
result_limbs),
0);
}
}
exit:
mbedtls_test_mpi_mod_modulus_free_with_limbs(&N);
mbedtls_free(result_digits);
}
/* 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 */