/*------------------------------------------------------------ * * mpa_exp_mod * * Calculates dest = op1 ^ op2 mod n * */ void mpa_exp_mod(mpanum dest, const mpanum op1, const mpanum op2, const mpanum n, const mpanum r_modn, const mpanum r2_modn, const mpa_word_t n_inv, mpa_scratch_mem pool) { mpanum A; mpanum B; mpanum xtilde; mpanum *ptr_a; mpanum *ptr_b; mpanum *swapper; int idx; mpa_alloc_static_temp_var(&A, pool); mpa_alloc_static_temp_var(&B, pool); mpa_alloc_static_temp_var(&xtilde, pool); /* transform to Montgomery space */ /* use internal version since xtidle is big enough */ __mpa_montgomery_mul(xtilde, op1, r2_modn, n, n_inv); mpa_copy(A, r_modn); ptr_a = &A; ptr_b = &B; __mpa_set_unused_digits_to_zero(A); __mpa_set_unused_digits_to_zero(B); for (idx = mpa_highest_bit_index(op2); idx >= 0; idx--) { __mpa_montgomery_mul(*ptr_b, *ptr_a, *ptr_a, n, n_inv); if (mpa_get_bit(op2, idx) == 1) { __mpa_montgomery_mul(*ptr_a, *ptr_b, xtilde, n, n_inv); } else { swapper = ptr_a; ptr_a = ptr_b; ptr_b = swapper; } } /* transform back form Montgomery space */ __mpa_montgomery_mul(*ptr_b, (const mpanum)&const_one, *ptr_a, n, n_inv); mpa_copy(dest, *ptr_b); mpa_free_static_temp_var(&A, pool); mpa_free_static_temp_var(&B, pool); mpa_free_static_temp_var(&xtilde, pool); }
/* * TEE_BigIntConvertFromFMM */ void TEE_BigIntConvertFromFMM(TEE_BigInt *dest, const TEE_BigIntFMM *src, const TEE_BigInt *n, const TEE_BigIntFMMContext *context) { mpanum mpa_dest = (mpa_num_base *)dest; mpanum mpa_op2 = (mpa_num_base *)src; mpanum mpa_n = (mpa_num_base *)n; mpa_fmm_context mpa_context = (mpa_fmm_context_base *)context; mpanum temp_dest; /* * Since dest in BigIntFFMCompute (i.e. dest in mpa_montgomery_mul) * must have alloc one word more than the size of n, we must * use a temp variable during the conversion. */ mpa_alloc_static_temp_var(&temp_dest, mempool); /* calculate dest = Mont(1,src) */ mpa_montgomery_mul(temp_dest, mpa_constant_one(), mpa_op2, mpa_n, mpa_context->n_inv, mempool); mpa_copy(mpa_dest, temp_dest); mpa_free_static_temp_var(&temp_dest, mempool); }
/* * TEE_BigIntMulMod */ void TEE_BigIntMulMod(TEE_BigInt *dest, const TEE_BigInt *op1, const TEE_BigInt *op2, const TEE_BigInt *n) { mpanum mpa_dest = (mpa_num_base *)dest; mpanum mpa_op1 = (mpa_num_base *)op1; mpanum mpa_op2 = (mpa_num_base *)op2; mpanum mpa_n = (mpa_num_base *)n; mpanum tmp_dest; if (TEE_BigIntCmpS32(n, 2) < 0) TEE_BigInt_Panic("Modulus is too short"); /* * From the spec, mpa_dest must be of magnitude "mpa_n" * But internal computations in mpa do not have such assumptions * (as __mpa_div_q_r, where "r" must be of magnitude "op1", * whereas GP provides a magnitude of "op2") * This is a tempory variable is used, before storing the * final result. */ mpa_alloc_static_temp_var(&tmp_dest, mempool); mpa_mul_mod(tmp_dest, mpa_op1, mpa_op2, mpa_n, mempool); if (mpa_cmp_short(tmp_dest, 0) < 0) mpa_add(tmp_dest, tmp_dest, mpa_n, mempool); mpa_copy(mpa_dest, tmp_dest); mpa_free_static_temp_var(&tmp_dest, mempool); }
/*------------------------------------------------------------ * * mpa_mul_mod * */ void mpa_mul_mod(mpanum dest, const mpanum op1, const mpanum op2, const mpanum n, mpa_scratch_mem pool) { mpanum tmp_dest; mpa_alloc_static_temp_var(&tmp_dest, pool); mpa_mul(tmp_dest, op1, op2, pool); mpa_div(NULL, dest, tmp_dest, n, pool); mpa_free_static_temp_var(&tmp_dest, pool); }
/*------------------------------------------------------------ * * 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; }
/*------------------------------------------------------------ * * mpa_inv_mod * */ int mpa_inv_mod(mpanum dest, const mpanum op, const mpanum n, mpa_scratch_mem pool) { mpanum gcd; mpanum tmp_dest; int mem_marker; int res; if (mpa_cmp_short(op, 1) == 0) { mpa_set_S32(dest, 1); return 0; } mem_marker = (dest == op); if (mem_marker) mpa_alloc_static_temp_var(&tmp_dest, pool); else tmp_dest = dest; mpa_alloc_static_temp_var(&gcd, pool); /* The function mpa_extended_gcd behaves badly if tmp_dest = op */ mpa_extended_gcd(gcd, tmp_dest, NULL, op, n, pool); res = mpa_cmp_short(gcd, 1); if (mem_marker) { mpa_copy(dest, tmp_dest); mpa_free_static_temp_var(&tmp_dest, pool); } mpa_free_static_temp_var(&gcd, pool); if (res == 0) { while (mpa_cmp_short(dest, 0) < 0) mpa_add(dest, dest, n, pool); return 0; } else { return -1; } }
/* * TEE_BigIntRelativePrime */ bool TEE_BigIntRelativePrime(const TEE_BigInt *op1, const TEE_BigInt *op2) { mpanum mpa_op1 = (mpa_num_base *)op1; mpanum mpa_op2 = (mpa_num_base *)op2; mpanum gcd; uint32_t cmp; mpa_alloc_static_temp_var(&gcd, mempool); mpa_gcd(gcd, mpa_op1, mpa_op2, mempool); cmp = mpa_cmp_short(gcd, 1); mpa_free_static_temp_var(&gcd, mempool); return cmp == 0 ? true : false; }
static void deinit(void *a) { LTC_ARGCHKVD(a != NULL); mpa_free_static_temp_var((mpanum *) &a, external_mem_pool); }
/*------------------------------------------------------------ * * 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; }
static void deinit(void *a) { LTC_ARGCHKVD(a != NULL); mpa_free_static_temp_var((mpanum *) &a, NULL); }