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391 lines
11 KiB
C
391 lines
11 KiB
C
/*
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* Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include <stdio.h>
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#include <time.h>
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#include "internal/cryptlib.h"
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#include "bn_local.h"
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/*
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* The quick sieve algorithm approach to weeding out primes is Philip
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* Zimmermann's, as implemented in PGP. I have had a read of his comments
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* and implemented my own version.
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*/
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#include "bn_prime.h"
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static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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const BIGNUM *a1_odd, int k, BN_CTX *ctx,
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BN_MONT_CTX *mont);
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static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods);
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static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
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const BIGNUM *add, const BIGNUM *rem,
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BN_CTX *ctx);
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#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
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int BN_GENCB_call(BN_GENCB *cb, int a, int b)
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{
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/* No callback means continue */
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if (!cb)
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return 1;
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switch (cb->ver) {
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case 1:
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/* Deprecated-style callbacks */
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if (!cb->cb.cb_1)
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return 1;
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cb->cb.cb_1(a, b, cb->arg);
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return 1;
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case 2:
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/* New-style callbacks */
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return cb->cb.cb_2(a, b, cb);
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default:
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break;
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}
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/* Unrecognised callback type */
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return 0;
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}
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int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
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const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
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{
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BIGNUM *t;
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int found = 0;
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int i, j, c1 = 0;
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BN_CTX *ctx = NULL;
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prime_t *mods = NULL;
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int checks = BN_prime_checks_for_size(bits);
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if (bits < 2) {
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/* There are no prime numbers this small. */
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BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
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return 0;
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} else if (add == NULL && safe && bits < 6 && bits != 3) {
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/*
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* The smallest safe prime (7) is three bits.
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* But the following two safe primes with less than 6 bits (11, 23)
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* are unreachable for BN_rand with BN_RAND_TOP_TWO.
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*/
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BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
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return 0;
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}
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mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
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if (mods == NULL)
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goto err;
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ctx = BN_CTX_new();
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if (ctx == NULL)
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goto err;
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BN_CTX_start(ctx);
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t = BN_CTX_get(ctx);
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if (t == NULL)
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goto err;
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loop:
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/* make a random number and set the top and bottom bits */
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if (add == NULL) {
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if (!probable_prime(ret, bits, safe, mods))
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goto err;
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} else {
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if (!probable_prime_dh(ret, bits, safe, mods, add, rem, ctx))
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goto err;
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}
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if (!BN_GENCB_call(cb, 0, c1++))
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/* aborted */
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goto err;
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if (!safe) {
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i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
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if (i == -1)
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goto err;
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if (i == 0)
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goto loop;
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} else {
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/*
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* for "safe prime" generation, check that (p-1)/2 is prime. Since a
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* prime is odd, We just need to divide by 2
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*/
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if (!BN_rshift1(t, ret))
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goto err;
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for (i = 0; i < checks; i++) {
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j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
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if (j == -1)
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goto err;
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if (j == 0)
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goto loop;
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j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
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if (j == -1)
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goto err;
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if (j == 0)
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goto loop;
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if (!BN_GENCB_call(cb, 2, c1 - 1))
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goto err;
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/* We have a safe prime test pass */
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}
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}
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/* we have a prime :-) */
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found = 1;
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err:
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OPENSSL_free(mods);
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BN_CTX_end(ctx);
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BN_CTX_free(ctx);
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bn_check_top(ret);
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return found;
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}
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int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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BN_GENCB *cb)
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{
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return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
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}
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int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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int do_trial_division, BN_GENCB *cb)
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{
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int i, j, ret = -1;
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int k;
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BN_CTX *ctx = NULL;
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BIGNUM *A1, *A1_odd, *A3, *check; /* taken from ctx */
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BN_MONT_CTX *mont = NULL;
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/* Take care of the really small primes 2 & 3 */
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if (BN_is_word(a, 2) || BN_is_word(a, 3))
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return 1;
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/* Check odd and bigger than 1 */
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if (!BN_is_odd(a) || BN_cmp(a, BN_value_one()) <= 0)
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return 0;
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if (checks == BN_prime_checks)
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checks = BN_prime_checks_for_size(BN_num_bits(a));
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/* first look for small factors */
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if (do_trial_division) {
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for (i = 1; i < NUMPRIMES; i++) {
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BN_ULONG mod = BN_mod_word(a, primes[i]);
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if (mod == (BN_ULONG)-1)
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goto err;
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if (mod == 0)
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return BN_is_word(a, primes[i]);
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}
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if (!BN_GENCB_call(cb, 1, -1))
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goto err;
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}
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if (ctx_passed != NULL)
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ctx = ctx_passed;
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else if ((ctx = BN_CTX_new()) == NULL)
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goto err;
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BN_CTX_start(ctx);
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A1 = BN_CTX_get(ctx);
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A3 = BN_CTX_get(ctx);
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A1_odd = BN_CTX_get(ctx);
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check = BN_CTX_get(ctx);
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if (check == NULL)
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goto err;
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/* compute A1 := a - 1 */
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if (!BN_copy(A1, a) || !BN_sub_word(A1, 1))
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goto err;
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/* compute A3 := a - 3 */
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if (!BN_copy(A3, a) || !BN_sub_word(A3, 3))
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goto err;
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/* write A1 as A1_odd * 2^k */
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k = 1;
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while (!BN_is_bit_set(A1, k))
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k++;
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if (!BN_rshift(A1_odd, A1, k))
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goto err;
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/* Montgomery setup for computations mod a */
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mont = BN_MONT_CTX_new();
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if (mont == NULL)
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goto err;
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if (!BN_MONT_CTX_set(mont, a, ctx))
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goto err;
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for (i = 0; i < checks; i++) {
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/* 1 < check < a-1 */
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if (!BN_priv_rand_range(check, A3) || !BN_add_word(check, 2))
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goto err;
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j = witness(check, a, A1, A1_odd, k, ctx, mont);
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if (j == -1)
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goto err;
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if (j) {
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ret = 0;
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goto err;
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}
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if (!BN_GENCB_call(cb, 1, i))
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goto err;
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}
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ret = 1;
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err:
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if (ctx != NULL) {
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BN_CTX_end(ctx);
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if (ctx_passed == NULL)
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BN_CTX_free(ctx);
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}
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BN_MONT_CTX_free(mont);
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return ret;
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}
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static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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const BIGNUM *a1_odd, int k, BN_CTX *ctx,
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BN_MONT_CTX *mont)
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{
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if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
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return -1;
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if (BN_is_one(w))
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return 0; /* probably prime */
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if (BN_cmp(w, a1) == 0)
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return 0; /* w == -1 (mod a), 'a' is probably prime */
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while (--k) {
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if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
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return -1;
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if (BN_is_one(w))
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return 1; /* 'a' is composite, otherwise a previous 'w'
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* would have been == -1 (mod 'a') */
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if (BN_cmp(w, a1) == 0)
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return 0; /* w == -1 (mod a), 'a' is probably prime */
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}
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/*
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* If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
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* it is neither -1 nor +1 -- so 'a' cannot be prime
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*/
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bn_check_top(w);
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return 1;
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}
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static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods)
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{
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int i;
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BN_ULONG delta;
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BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
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again:
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/* TODO: Not all primes are private */
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if (!BN_priv_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
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return 0;
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if (safe && !BN_set_bit(rnd, 1))
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return 0;
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/* we now have a random number 'rnd' to test. */
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for (i = 1; i < NUMPRIMES; i++) {
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BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
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if (mod == (BN_ULONG)-1)
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return 0;
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mods[i] = (prime_t) mod;
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}
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delta = 0;
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loop:
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for (i = 1; i < NUMPRIMES; i++) {
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/*
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* check that rnd is a prime and also that
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* gcd(rnd-1,primes) == 1 (except for 2)
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* do the second check only if we are interested in safe primes
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* in the case that the candidate prime is a single word then
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* we check only the primes up to sqrt(rnd)
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*/
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if (bits <= 31 && delta <= 0x7fffffff
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&& square(primes[i]) > BN_get_word(rnd) + delta)
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break;
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if (safe ? (mods[i] + delta) % primes[i] <= 1
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: (mods[i] + delta) % primes[i] == 0) {
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delta += safe ? 4 : 2;
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if (delta > maxdelta)
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goto again;
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goto loop;
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}
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}
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if (!BN_add_word(rnd, delta))
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return 0;
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if (BN_num_bits(rnd) != bits)
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goto again;
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bn_check_top(rnd);
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return 1;
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}
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static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
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const BIGNUM *add, const BIGNUM *rem,
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BN_CTX *ctx)
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{
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int i, ret = 0;
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BIGNUM *t1;
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BN_ULONG delta;
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BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
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BN_CTX_start(ctx);
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if ((t1 = BN_CTX_get(ctx)) == NULL)
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goto err;
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if (maxdelta > BN_MASK2 - BN_get_word(add))
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maxdelta = BN_MASK2 - BN_get_word(add);
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again:
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if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
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goto err;
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/* we need ((rnd-rem) % add) == 0 */
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if (!BN_mod(t1, rnd, add, ctx))
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goto err;
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if (!BN_sub(rnd, rnd, t1))
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goto err;
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if (rem == NULL) {
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if (!BN_add_word(rnd, safe ? 3u : 1u))
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goto err;
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} else {
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if (!BN_add(rnd, rnd, rem))
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goto err;
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}
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if (BN_num_bits(rnd) < bits
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|| BN_get_word(rnd) < (safe ? 5u : 3u)) {
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if (!BN_add(rnd, rnd, add))
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goto err;
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}
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/* we now have a random number 'rnd' to test. */
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for (i = 1; i < NUMPRIMES; i++) {
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BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
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if (mod == (BN_ULONG)-1)
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goto err;
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mods[i] = (prime_t) mod;
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}
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delta = 0;
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loop:
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for (i = 1; i < NUMPRIMES; i++) {
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/* check that rnd is a prime */
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if (bits <= 31 && delta <= 0x7fffffff
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&& square(primes[i]) > BN_get_word(rnd) + delta)
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break;
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/* rnd mod p == 1 implies q = (rnd-1)/2 is divisible by p */
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if (safe ? (mods[i] + delta) % primes[i] <= 1
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: (mods[i] + delta) % primes[i] == 0) {
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delta += BN_get_word(add);
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if (delta > maxdelta)
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goto again;
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goto loop;
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}
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}
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if (!BN_add_word(rnd, delta))
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goto err;
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ret = 1;
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err:
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BN_CTX_end(ctx);
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bn_check_top(rnd);
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return ret;
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}
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