481 lines
18 KiB
C
481 lines
18 KiB
C
/* BEGIN_HEADER */
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/* Dedicated test suite for mbedtls_mpi_core_random() and the upper-layer
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* functions. Due to the complexity of how these functions are tested,
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* we test all the layers in a single test suite, unlike the way other
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* functions are tested with each layer in its own test suite.
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*
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* Test strategy
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* =============
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*
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* There are three main goals for testing random() functions:
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* - Parameter validation.
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* - Correctness of outputs (well-formed, in range).
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* - Distribution of outputs.
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*
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* We test parameter validation in a standard way, with unit tests with
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* positive and negative cases:
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* - mbedtls_mpi_core_random(): negative cases for mpi_core_random_basic.
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* - mbedtls_mpi_mod_raw_random(), mbedtls_mpi_mod_random(): negative
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* cases for mpi_mod_random_validation.
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* - mbedtls_mpi_random(): mpi_random_fail.
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*
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* We test the correctness of outputs in positive tests:
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* - mbedtls_mpi_core_random(): positive cases for mpi_core_random_basic,
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* and mpi_random_many.
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* - mbedtls_mpi_mod_raw_random(), mbedtls_mpi_mod_random(): tested indirectly
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* via mpi_mod_random_values.
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* - mbedtls_mpi_random(): mpi_random_sizes, plus indirectly via
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* mpi_random_values.
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*
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* We test the distribution of outputs only for mbedtls_mpi_core_random(),
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* in mpi_random_many, which runs the function multiple times. This also
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* helps in validating the output range, through test cases with a small
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* range where any output out of range would be very likely to lead to a
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* test failure. For the other functions, we validate the distribution
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* indirectly by testing that these functions consume the random generator
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* in the same way as mbedtls_mpi_core_random(). This is done in
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* mpi_mod_random_values and mpi_legacy_random_values.
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*/
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#include "mbedtls/bignum.h"
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#include "mbedtls/entropy.h"
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#include "bignum_core.h"
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#include "bignum_mod_raw.h"
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#include "constant_time_internal.h"
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/* This test suite only manipulates non-negative bignums. */
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static int sign_is_valid(const mbedtls_mpi *X)
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{
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return X->s == 1;
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}
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/* A common initializer for test functions that should generate the same
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* sequences for reproducibility and good coverage. */
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const mbedtls_test_rnd_pseudo_info rnd_pseudo_seed = {
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/* 16-word key */
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{ 'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
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'a', ' ', 's', 'e', 'e', 'd', '!', 0 },
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/* 2-word initial state, should be zero */
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0, 0
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};
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/* Test whether bytes represents (in big-endian base 256) a number b that
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* is significantly above a power of 2. That is, b must not have a long run
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* of unset bits after the most significant bit.
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*
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* Let n be the bit-size of b, i.e. the integer such that 2^n <= b < 2^{n+1}.
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* This function returns 1 if, when drawing a number between 0 and b,
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* the probability that this number is at least 2^n is not negligible.
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* This probability is (b - 2^n) / b and this function checks that this
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* number is above some threshold A. The threshold value is heuristic and
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* based on the needs of mpi_random_many().
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*/
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static int is_significantly_above_a_power_of_2(data_t *bytes)
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{
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const uint8_t *p = bytes->x;
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size_t len = bytes->len;
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unsigned x;
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/* Skip leading null bytes */
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while (len > 0 && p[0] == 0) {
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++p;
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--len;
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}
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/* 0 is not significantly above a power of 2 */
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if (len == 0) {
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return 0;
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}
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/* Extract the (up to) 2 most significant bytes */
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if (len == 1) {
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x = p[0];
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} else {
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x = (p[0] << 8) | p[1];
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}
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/* Shift the most significant bit of x to position 8 and mask it out */
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while ((x & 0xfe00) != 0) {
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x >>= 1;
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}
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x &= 0x00ff;
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/* At this point, x = floor((b - 2^n) / 2^(n-8)). b is significantly above
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* a power of 2 iff x is significantly above 0 compared to 2^8.
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* Testing x >= 2^4 amounts to picking A = 1/16 in the function
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* description above. */
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return x >= 0x10;
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}
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/* END_HEADER */
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/* BEGIN_DEPENDENCIES
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* depends_on:MBEDTLS_BIGNUM_C
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* END_DEPENDENCIES
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*/
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/* BEGIN_CASE */
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void mpi_core_random_basic(int min, char *bound_bytes, int expected_ret)
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{
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/* Same RNG as in mpi_random_values */
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mbedtls_test_rnd_pseudo_info rnd = rnd_pseudo_seed;
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size_t limbs;
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mbedtls_mpi_uint *lower_bound = NULL;
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mbedtls_mpi_uint *upper_bound = NULL;
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mbedtls_mpi_uint *result = NULL;
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TEST_EQUAL(0, mbedtls_test_read_mpi_core(&upper_bound, &limbs,
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bound_bytes));
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ASSERT_ALLOC(lower_bound, limbs);
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lower_bound[0] = min;
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ASSERT_ALLOC(result, limbs);
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TEST_EQUAL(expected_ret,
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mbedtls_mpi_core_random(result, min, upper_bound, limbs,
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mbedtls_test_rnd_pseudo_rand, &rnd));
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if (expected_ret == 0) {
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TEST_EQUAL(0, mbedtls_mpi_core_lt_ct(result, lower_bound, limbs));
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TEST_EQUAL(1, mbedtls_mpi_core_lt_ct(result, upper_bound, limbs));
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}
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exit:
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mbedtls_free(lower_bound);
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mbedtls_free(upper_bound);
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mbedtls_free(result);
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}
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/* END_CASE */
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/* BEGIN_CASE */
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void mpi_legacy_random_values(int min, char *max_hex)
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{
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/* Same RNG as in mpi_core_random_basic */
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mbedtls_test_rnd_pseudo_info rnd_core = rnd_pseudo_seed;
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mbedtls_test_rnd_pseudo_info rnd_legacy;
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memcpy(&rnd_legacy, &rnd_core, sizeof(rnd_core));
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mbedtls_mpi max_legacy;
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mbedtls_mpi_init(&max_legacy);
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mbedtls_mpi_uint *R_core = NULL;
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mbedtls_mpi R_legacy;
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mbedtls_mpi_init(&R_legacy);
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TEST_EQUAL(0, mbedtls_test_read_mpi(&max_legacy, max_hex));
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size_t limbs = max_legacy.n;
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ASSERT_ALLOC(R_core, limbs);
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/* Call the legacy function and the core function with the same random
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* stream. */
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int core_ret = mbedtls_mpi_core_random(R_core, min, max_legacy.p, limbs,
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mbedtls_test_rnd_pseudo_rand,
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&rnd_core);
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int legacy_ret = mbedtls_mpi_random(&R_legacy, min, &max_legacy,
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mbedtls_test_rnd_pseudo_rand,
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&rnd_legacy);
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/* They must return the same status, and, on success, output the
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* same number, with the same limb count. */
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TEST_EQUAL(core_ret, legacy_ret);
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if (core_ret == 0) {
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ASSERT_COMPARE(R_core, limbs * ciL,
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R_legacy.p, R_legacy.n * ciL);
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}
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/* Also check that they have consumed the RNG in the same way. */
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/* This may theoretically fail on rare platforms with padding in
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* the structure! If this is a problem in practice, change to a
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* field-by-field comparison. */
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ASSERT_COMPARE(&rnd_core, sizeof(rnd_core),
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&rnd_legacy, sizeof(rnd_legacy));
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exit:
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mbedtls_mpi_free(&max_legacy);
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mbedtls_free(R_core);
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mbedtls_mpi_free(&R_legacy);
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}
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/* END_CASE */
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/* BEGIN_CASE */
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void mpi_mod_random_values(int min, char *max_hex, int rep)
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{
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/* Same RNG as in mpi_core_random_basic */
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mbedtls_test_rnd_pseudo_info rnd_core = rnd_pseudo_seed;
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mbedtls_test_rnd_pseudo_info rnd_mod_raw;
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memcpy(&rnd_mod_raw, &rnd_core, sizeof(rnd_core));
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mbedtls_test_rnd_pseudo_info rnd_mod;
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memcpy(&rnd_mod, &rnd_core, sizeof(rnd_core));
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mbedtls_mpi_uint *R_core = NULL;
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mbedtls_mpi_uint *R_mod_raw = NULL;
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mbedtls_mpi_uint *R_mod_digits = NULL;
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mbedtls_mpi_mod_residue R_mod;
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mbedtls_mpi_mod_modulus N;
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mbedtls_mpi_mod_modulus_init(&N);
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TEST_EQUAL(mbedtls_test_read_mpi_modulus(&N, max_hex, rep), 0);
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ASSERT_ALLOC(R_core, N.limbs);
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ASSERT_ALLOC(R_mod_raw, N.limbs);
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ASSERT_ALLOC(R_mod_digits, N.limbs);
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TEST_EQUAL(mbedtls_mpi_mod_residue_setup(&R_mod, &N,
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R_mod_digits, N.limbs),
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0);
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/* Call the core and mod random() functions with the same random stream. */
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int core_ret = mbedtls_mpi_core_random(R_core,
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min, N.p, N.limbs,
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mbedtls_test_rnd_pseudo_rand,
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&rnd_core);
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int mod_raw_ret = mbedtls_mpi_mod_raw_random(R_mod_raw,
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min, &N,
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mbedtls_test_rnd_pseudo_rand,
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&rnd_mod_raw);
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int mod_ret = mbedtls_mpi_mod_random(&R_mod,
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min, &N,
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mbedtls_test_rnd_pseudo_rand,
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&rnd_mod);
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/* They must return the same status, and, on success, output the
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* same number, with the same limb count. */
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TEST_EQUAL(core_ret, mod_raw_ret);
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TEST_EQUAL(core_ret, mod_ret);
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if (core_ret == 0) {
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TEST_EQUAL(mbedtls_mpi_mod_raw_modulus_to_canonical_rep(R_mod_raw, &N),
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0);
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ASSERT_COMPARE(R_core, N.limbs * ciL,
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R_mod_raw, N.limbs * ciL);
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TEST_EQUAL(mbedtls_mpi_mod_raw_modulus_to_canonical_rep(R_mod_digits, &N),
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0);
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ASSERT_COMPARE(R_core, N.limbs * ciL,
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R_mod_digits, N.limbs * ciL);
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}
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/* Also check that they have consumed the RNG in the same way. */
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/* This may theoretically fail on rare platforms with padding in
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* the structure! If this is a problem in practice, change to a
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* field-by-field comparison. */
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ASSERT_COMPARE(&rnd_core, sizeof(rnd_core),
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&rnd_mod_raw, sizeof(rnd_mod_raw));
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ASSERT_COMPARE(&rnd_core, sizeof(rnd_core),
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&rnd_mod, sizeof(rnd_mod));
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exit:
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mbedtls_test_mpi_mod_modulus_free_with_limbs(&N);
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mbedtls_free(R_core);
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mbedtls_free(R_mod_raw);
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mbedtls_free(R_mod_digits);
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}
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/* END_CASE */
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/* BEGIN_CASE */
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void mpi_random_many(int min, char *bound_hex, int iterations)
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{
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/* Generate numbers in the range 1..bound-1. Do it iterations times.
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* This function assumes that the value of bound is at least 2 and
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* that iterations is large enough that a one-in-2^iterations chance
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* effectively never occurs.
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*/
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data_t bound_bytes = { NULL, 0 };
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mbedtls_mpi_uint *upper_bound = NULL;
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size_t limbs;
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size_t n_bits;
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mbedtls_mpi_uint *result = NULL;
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size_t b;
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/* If upper_bound is small, stats[b] is the number of times the value b
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* has been generated. Otherwise stats[b] is the number of times a
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* value with bit b set has been generated. */
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size_t *stats = NULL;
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size_t stats_len;
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int full_stats;
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size_t i;
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TEST_EQUAL(0, mbedtls_test_read_mpi_core(&upper_bound, &limbs,
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bound_hex));
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ASSERT_ALLOC(result, limbs);
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n_bits = mbedtls_mpi_core_bitlen(upper_bound, limbs);
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/* Consider a bound "small" if it's less than 2^5. This value is chosen
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* to be small enough that the probability of missing one value is
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* negligible given the number of iterations. It must be less than
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* 256 because some of the code below assumes that "small" values
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* fit in a byte. */
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if (n_bits <= 5) {
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full_stats = 1;
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stats_len = (uint8_t) upper_bound[0];
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} else {
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full_stats = 0;
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stats_len = n_bits;
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}
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ASSERT_ALLOC(stats, stats_len);
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for (i = 0; i < (size_t) iterations; i++) {
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mbedtls_test_set_step(i);
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TEST_EQUAL(0, mbedtls_mpi_core_random(result,
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min, upper_bound, limbs,
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mbedtls_test_rnd_std_rand, NULL));
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/* Temporarily use a legacy MPI for analysis, because the
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* necessary auxiliary functions don't exist yet in core. */
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mbedtls_mpi B = { .s = 1, .n = limbs, .p = upper_bound };
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mbedtls_mpi R = { .s = 1, .n = limbs, .p = result };
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TEST_ASSERT(mbedtls_mpi_cmp_mpi(&R, &B) < 0);
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TEST_ASSERT(mbedtls_mpi_cmp_int(&R, min) >= 0);
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if (full_stats) {
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uint8_t value;
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TEST_EQUAL(0, mbedtls_mpi_write_binary(&R, &value, 1));
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TEST_ASSERT(value < stats_len);
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++stats[value];
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} else {
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for (b = 0; b < n_bits; b++) {
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stats[b] += mbedtls_mpi_get_bit(&R, b);
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}
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}
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}
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if (full_stats) {
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for (b = min; b < stats_len; b++) {
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mbedtls_test_set_step(1000000 + b);
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/* Assert that each value has been reached at least once.
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* This is almost guaranteed if the iteration count is large
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* enough. This is a very crude way of checking the distribution.
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*/
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TEST_ASSERT(stats[b] > 0);
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}
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} else {
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bound_bytes.len = limbs * sizeof(mbedtls_mpi_uint);
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ASSERT_ALLOC(bound_bytes.x, bound_bytes.len);
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mbedtls_mpi_core_write_be(upper_bound, limbs,
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bound_bytes.x, bound_bytes.len);
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int statistically_safe_all_the_way =
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is_significantly_above_a_power_of_2(&bound_bytes);
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for (b = 0; b < n_bits; b++) {
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mbedtls_test_set_step(1000000 + b);
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/* Assert that each bit has been set in at least one result and
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* clear in at least one result. Provided that iterations is not
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* too small, it would be extremely unlikely for this not to be
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* the case if the results are uniformly distributed.
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*
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* As an exception, the top bit may legitimately never be set
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* if bound is a power of 2 or only slightly above.
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*/
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if (statistically_safe_all_the_way || b != n_bits - 1) {
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TEST_ASSERT(stats[b] > 0);
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}
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TEST_ASSERT(stats[b] < (size_t) iterations);
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}
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}
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exit:
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mbedtls_free(bound_bytes.x);
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mbedtls_free(upper_bound);
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mbedtls_free(result);
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mbedtls_free(stats);
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}
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/* END_CASE */
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/* BEGIN_CASE */
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void mpi_random_sizes(int min, data_t *bound_bytes, int nlimbs, int before)
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{
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mbedtls_mpi upper_bound;
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mbedtls_mpi result;
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mbedtls_mpi_init(&upper_bound);
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mbedtls_mpi_init(&result);
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if (before != 0) {
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/* Set result to sign(before) * 2^(|before|-1) */
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TEST_ASSERT(mbedtls_mpi_lset(&result, before > 0 ? 1 : -1) == 0);
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if (before < 0) {
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before = -before;
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}
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TEST_ASSERT(mbedtls_mpi_shift_l(&result, before - 1) == 0);
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}
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TEST_EQUAL(0, mbedtls_mpi_grow(&result, nlimbs));
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TEST_EQUAL(0, mbedtls_mpi_read_binary(&upper_bound,
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bound_bytes->x, bound_bytes->len));
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TEST_EQUAL(0, mbedtls_mpi_random(&result, min, &upper_bound,
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mbedtls_test_rnd_std_rand, NULL));
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TEST_ASSERT(sign_is_valid(&result));
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TEST_ASSERT(mbedtls_mpi_cmp_mpi(&result, &upper_bound) < 0);
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TEST_ASSERT(mbedtls_mpi_cmp_int(&result, min) >= 0);
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exit:
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mbedtls_mpi_free(&upper_bound);
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mbedtls_mpi_free(&result);
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}
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/* END_CASE */
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/* BEGIN_CASE */
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void mpi_mod_random_validation(int min, char *bound_hex,
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int result_limbs_delta,
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int expected_ret)
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{
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mbedtls_mpi_uint *result_digits = NULL;
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mbedtls_mpi_mod_modulus N;
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mbedtls_mpi_mod_modulus_init(&N);
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TEST_EQUAL(mbedtls_test_read_mpi_modulus(&N, bound_hex,
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MBEDTLS_MPI_MOD_REP_OPT_RED),
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0);
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size_t result_limbs = N.limbs + result_limbs_delta;
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ASSERT_ALLOC(result_digits, result_limbs);
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/* Build a reside that might not match the modulus, to test that
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* the library function rejects that as expected. */
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mbedtls_mpi_mod_residue result = { result_digits, result_limbs };
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TEST_EQUAL(mbedtls_mpi_mod_random(&result, min, &N,
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mbedtls_test_rnd_std_rand, NULL),
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expected_ret);
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if (expected_ret == 0) {
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/* Success should only be expected when the result has the same
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* size as the modulus, otherwise it's a mistake in the test data. */
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TEST_EQUAL(result_limbs, N.limbs);
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/* Sanity check: check that the result is in range */
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TEST_EQUAL(mbedtls_mpi_core_lt_ct(result_digits, N.p, N.limbs),
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1);
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/* Check result >= min (changes result) */
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TEST_EQUAL(mbedtls_mpi_core_sub_int(result_digits, result_digits, min,
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result_limbs),
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0);
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}
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/* When the result has the right number of limbs, also test mod_raw
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* (for which this is an unchecked precondition). */
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if (result_limbs_delta == 0) {
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TEST_EQUAL(mbedtls_mpi_mod_raw_random(result_digits, min, &N,
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|
mbedtls_test_rnd_std_rand, NULL),
|
|
expected_ret);
|
|
if (expected_ret == 0) {
|
|
TEST_EQUAL(mbedtls_mpi_core_lt_ct(result_digits, N.p, N.limbs),
|
|
1);
|
|
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 */
|