// SPDX-License-Identifier: BSD-2-Clause /* * Copyright (c) 2014, STMicroelectronics International N.V. */ #include "mpa.h" #define USE_PRIME_TABLE #if defined(USE_PRIME_TABLE) #include "mpa_primetable.h" #endif #define DEF_COMPOSITE 0 #define DEF_PRIME 1 #define PROB_PRIME -1 /* Product of all primes < 1000 */ static const mpa_num_base const_small_prime_factors = { 44, 44, {0x2ED42696, 0x2BBFA177, 0x4820594F, 0xF73F4841, 0xBFAC313A, 0xCAC3EB81, 0xF6F26BF8, 0x7FAB5061, 0x59746FB7, 0xF71377F6, 0x3B19855B, 0xCBD03132, 0xBB92EF1B, 0x3AC3152C, 0xE87C8273, 0xC0AE0E69, 0x74A9E295, 0x448CCE86, 0x63CA1907, 0x8A0BF944, 0xF8CC3BE0, 0xC26F0AF5, 0xC501C02F, 0x6579441A, 0xD1099CDA, 0x6BC76A00, 0xC81A3228, 0xBFB1AB25, 0x70FA3841, 0x51B3D076, 0xCC2359ED, 0xD9EE0769, 0x75E47AF0, 0xD45FF31E, 0x52CCE4F6, 0x04DBC891, 0x96658ED2, 0x1753EFE5, 0x3AE4A5A6, 0x8FD4A97F, 0x8B15E7EB, 0x0243C3E1, 0xE0F0C31D, 0x0000000B} }; /* * If n is less than this number (341550071728321 decimal) the Miller-Rabin * test (using specific bases) constitutes a primality proof. */ static const mpa_num_base const_miller_rabin_proof_limit = { 2, 2, {0x52B2C8C1, 0x000136A3} }; static const mpa_num_base const_two = { 1, 1, {0x00000002} }; /* foward declarations */ static int is_small_prime(mpanum n); static int has_small_factors(mpanum n, mpa_scratch_mem pool); static int primality_test_miller_rabin(mpanum n, int conf_level, mpa_scratch_mem pool); /*------------------------------------------------------------ * * mpa_is_prob_prime * * Returns: * 0 if n is definitely composite * 1 if n is definitely prime * -1 if n is composite with a probability less than 2^(-conf_level) * */ int mpa_is_prob_prime(mpanum n, int conf_level, mpa_scratch_mem pool) { int result = 0; /* Check if it's a small prime */ result = is_small_prime(n); if (result != PROB_PRIME) goto cleanup; /* Test if n is divisible by any prime < 1000 */ if (has_small_factors(n, pool)) { result = DEF_COMPOSITE; goto cleanup; } /* Check with Miller Rabin */ result = primality_test_miller_rabin(n, conf_level, pool); cleanup: return result; } #if defined(USE_PRIME_TABLE) /*------------------------------------------------------------ * * check_table * */ static uint32_t check_table(uint32_t v) { return (PRIME_TABLE[v >> 5] >> (v & 0x1f)) & 1; } #endif /*------------------------------------------------------------ * * is_small_prime * * Returns 1 if n is prime, Returns 0 if n is composite * Returns -1 if we cannot decide * */ static int is_small_prime(mpanum n) { mpa_word_t v; /* If n is larger than a mpa_word_t, we can only decide if */ /* n is even. If it's odd we cannot tell. */ if (__mpanum_size(n) > 1) return ((mpa_parity(n) == MPA_EVEN_PARITY) ? 0 : -1); v = mpa_get_word(n); /* will convert negative n:s to positive v:s. */ if ((v | 1) == 1) /* 0 and 1 are not prime */ return DEF_COMPOSITE; if (v == 2) /* 2 is prime */ return DEF_PRIME; if ((v & 1) == 0) return DEF_COMPOSITE; /* but no other even number */ #if defined(USE_PRIME_TABLE) if (mpa_cmp_short(n, MAX_TABULATED_PRIME) > 0) return -1; v = (v - 3) >> 1; return check_table(v); #else return -1; #endif } /*------------------------------------------------------------ * * has_small_factors * * returns 1 if n has small factors * returns 0 if not. */ static int has_small_factors(mpanum n, mpa_scratch_mem pool) { const mpa_num_base *factors = &const_small_prime_factors; int result; mpanum res; mpa_alloc_static_temp_var(&res, pool); mpa_gcd(res, n, (const mpanum)factors, pool); result = (mpa_cmp_short(res, 1) == 0) ? 0 : 1; mpa_free_static_temp_var(&res, pool); return result; } /*------------------------------------------------------------ * * primality_test_miller_rabin * */ static int primality_test_miller_rabin(mpanum n, int conf_level, mpa_scratch_mem pool) { int result; bool proof_version; static const int32_t proof_a[7] = { 2, 3, 5, 7, 11, 13, 17 }; int cnt; int idx; int t; int e = 0; int cmp_one; mpanum a; mpanum q; mpanum n_minus_1; mpanum b; mpanum r_modn; mpanum r2_modn; mpa_word_t n_inv; mpa_alloc_static_temp_var(&r_modn, pool); mpa_alloc_static_temp_var(&r2_modn, pool); if (mpa_compute_fmm_context(n, r_modn, r2_modn, &n_inv, pool) == -1) { result = DEF_COMPOSITE; goto cleanup_short; } mpa_alloc_static_temp_var(&a, pool); mpa_alloc_static_temp_var(&q, pool); mpa_alloc_static_temp_var(&n_minus_1, pool); mpa_alloc_static_temp_var(&b, pool); proof_version = (mpa_cmp(n, (mpanum) &const_miller_rabin_proof_limit) < 0); if (proof_version) cnt = 7; else /* MR has 1/4 chance in failing a composite */ cnt = (conf_level + 1) / 2; mpa_sub_word(n_minus_1, n, 1, pool); mpa_set(q, n_minus_1); t = 0; /* calculate q such that n - 1 = 2^t * q where q is odd */ while (mpa_is_even(q)) { mpa_shift_right(q, q, 1); t++; } result = PROB_PRIME; for (idx = 0; idx < cnt && result == PROB_PRIME; idx++) { if (proof_version) { mpa_set_S32(a, proof_a[idx]); if (mpa_cmp(n, a) == 0) { result = DEF_PRIME; continue; } } else { /* * Get random a, 1 < a < N by * asking for a random in range 0 <= x < N - 2 * and then add 2 to it. */ mpa_sub_word(n_minus_1, n_minus_1, 1, pool); /* n_minus_1 is now N - 2 ! */ mpa_get_random(a, n_minus_1); mpa_add_word(n_minus_1, n_minus_1, 1, pool); /* and a is now 2 <= a < N */ mpa_add_word(a, a, 2, pool); } mpa_exp_mod(b, a, q, n, r_modn, r2_modn, n_inv, pool); e = 0; inner_loop: cmp_one = mpa_cmp_short(b, 1); if ((cmp_one == 0) && (e > 0)) { result = DEF_COMPOSITE; continue; } if ((mpa_cmp(b, n_minus_1) == 0) || ((cmp_one == 0) && (e == 0))) { /* probably prime, try another a */ continue; } e++; if (e < t) { mpa_exp_mod(b, b, (mpanum) &const_two, n, r_modn, r2_modn, n_inv, pool); goto inner_loop; } result = DEF_COMPOSITE; } if (result == PROB_PRIME && proof_version) result = DEF_PRIME; mpa_free_static_temp_var(&a, pool); mpa_free_static_temp_var(&q, pool); mpa_free_static_temp_var(&n_minus_1, pool); mpa_free_static_temp_var(&b, pool); cleanup_short: mpa_free_static_temp_var(&r_modn, pool); mpa_free_static_temp_var(&r2_modn, pool); return result; }