/* 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)); 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_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; 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_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); ASSERT_ALLOC(R_core, N.limbs); ASSERT_ALLOC(R_mod_raw, N.limbs); ASSERT_ALLOC(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); ASSERT_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); ASSERT_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. */ ASSERT_COMPARE(&rnd_core, sizeof(rnd_core), &rnd_mod_raw, sizeof(rnd_mod_raw)); ASSERT_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)); 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_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; ASSERT_ALLOC(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 */