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936c2b9e93
Previous macros suggested that from 3.0, we're only allowed to deprecate things at a major version. However, there's no policy stating this, but there is for removal, saying that to remove something, it must have been deprecated for 5 years, and that removal can only happen at a major version. Meanwhile, the semantic versioning rule is that deprecation should trigger a MINOR version update, which is reflected in the macro names as of this change. Reviewed-by: Tim Hudson <tjh@openssl.org> (Merged from https://github.com/openssl/openssl/pull/10364)
606 lines
17 KiB
C
606 lines
17 KiB
C
/*
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* Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the Apache License 2.0 (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 probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
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BN_CTX *ctx);
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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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static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
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int do_trial_division, BN_GENCB *cb);
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#define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
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#if BN_BITS2 == 64
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# define BN_DEF(lo, hi) (BN_ULONG)hi<<32|lo
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#else
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# define BN_DEF(lo, hi) lo, hi
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#endif
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/*
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* See SP800 89 5.3.3 (Step f)
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* The product of the set of primes ranging from 3 to 751
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* Generated using process in test/bn_internal_test.c test_bn_small_factors().
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* This includes 751 (which is not currently included in SP 800-89).
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*/
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static const BN_ULONG small_prime_factors[] = {
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BN_DEF(0x3ef4e3e1, 0xc4309333), BN_DEF(0xcd2d655f, 0x71161eb6),
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BN_DEF(0x0bf94862, 0x95e2238c), BN_DEF(0x24f7912b, 0x3eb233d3),
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BN_DEF(0xbf26c483, 0x6b55514b), BN_DEF(0x5a144871, 0x0a84d817),
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BN_DEF(0x9b82210a, 0x77d12fee), BN_DEF(0x97f050b3, 0xdb5b93c2),
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BN_DEF(0x4d6c026b, 0x4acad6b9), BN_DEF(0x54aec893, 0xeb7751f3),
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BN_DEF(0x36bc85c4, 0xdba53368), BN_DEF(0x7f5ec78e, 0xd85a1b28),
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BN_DEF(0x6b322244, 0x2eb072d8), BN_DEF(0x5e2b3aea, 0xbba51112),
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BN_DEF(0x0e2486bf, 0x36ed1a6c), BN_DEF(0xec0c5727, 0x5f270460),
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(BN_ULONG)0x000017b1
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};
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#define BN_SMALL_PRIME_FACTORS_TOP OSSL_NELEM(small_prime_factors)
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static const BIGNUM _bignum_small_prime_factors = {
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(BN_ULONG *)small_prime_factors,
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BN_SMALL_PRIME_FACTORS_TOP,
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BN_SMALL_PRIME_FACTORS_TOP,
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0,
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BN_FLG_STATIC_DATA
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};
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const BIGNUM *bn_get0_small_factors(void)
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{
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return &_bignum_small_prime_factors;
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}
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/*
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* Calculate the number of trial divisions that gives the best speed in
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* combination with Miller-Rabin prime test, based on the sized of the prime.
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*/
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static int calc_trial_divisions(int bits)
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{
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if (bits <= 512)
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return 64;
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else if (bits <= 1024)
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return 128;
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else if (bits <= 2048)
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return 384;
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else if (bits <= 4096)
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return 1024;
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return NUMPRIMES;
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}
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/*
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* Use a minimum of 64 rounds of Miller-Rabin, which should give a false
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* positive rate of 2^-128. If the size of the prime is larger than 2048
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* the user probably wants a higher security level than 128, so switch
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* to 128 rounds giving a false positive rate of 2^-256.
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* Returns the number of rounds.
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*/
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static int bn_mr_min_checks(int bits)
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{
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if (bits > 2048)
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return 128;
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return 64;
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}
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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_ex2(BIGNUM *ret, int bits, int safe,
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const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
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BN_CTX *ctx)
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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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prime_t *mods = NULL;
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int checks = bn_mr_min_checks(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_EX2, 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_EX2, 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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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, ctx))
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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_int(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_int(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_int(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_check_top(ret);
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return found;
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}
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#ifndef FIPS_MODE
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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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BN_CTX *ctx = BN_CTX_new();
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int retval;
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if (ctx == NULL)
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return 0;
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retval = BN_generate_prime_ex2(ret, bits, safe, add, rem, cb, ctx);
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BN_CTX_free(ctx);
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return retval;
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}
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#endif
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#ifndef OPENSSL_NO_DEPRECATED_3_0
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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_check_prime_int(a, checks, ctx_passed, 0, cb);
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}
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int BN_is_prime_fasttest_ex(const BIGNUM *w, int checks, BN_CTX *ctx,
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int do_trial_division, BN_GENCB *cb)
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{
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return bn_check_prime_int(w, checks, ctx, do_trial_division, cb);
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}
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#endif
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/* Wrapper around bn_is_prime_int that sets the minimum number of checks */
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int bn_check_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
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int do_trial_division, BN_GENCB *cb)
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{
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int min_checks = bn_mr_min_checks(BN_num_bits(w));
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if (checks < min_checks)
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checks = min_checks;
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return bn_is_prime_int(w, checks, ctx, do_trial_division, cb);
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}
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int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb)
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{
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return bn_check_prime_int(p, 0, ctx, 1, cb);
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}
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/*
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* Tests that |w| is probably prime
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* See FIPS 186-4 C.3.1 Miller Rabin Probabilistic Primality Test.
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*
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* Returns 0 when composite, 1 when probable prime, -1 on error.
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*/
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static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
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int do_trial_division, BN_GENCB *cb)
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{
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int i, status, ret = -1;
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#ifndef FIPS_MODE
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BN_CTX *ctxlocal = NULL;
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#else
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if (ctx == NULL)
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return -1;
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#endif
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/* w must be bigger than 1 */
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if (BN_cmp(w, BN_value_one()) <= 0)
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return 0;
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/* w must be odd */
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if (BN_is_odd(w)) {
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/* Take care of the really small prime 3 */
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if (BN_is_word(w, 3))
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return 1;
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} else {
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/* 2 is the only even prime */
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return BN_is_word(w, 2);
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}
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/* first look for small factors */
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if (do_trial_division) {
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int trial_divisions = calc_trial_divisions(BN_num_bits(w));
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for (i = 1; i < trial_divisions; i++) {
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BN_ULONG mod = BN_mod_word(w, primes[i]);
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if (mod == (BN_ULONG)-1)
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return -1;
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if (mod == 0)
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return BN_is_word(w, primes[i]);
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}
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if (!BN_GENCB_call(cb, 1, -1))
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return -1;
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}
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#ifndef FIPS_MODE
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if (ctx == NULL && (ctxlocal = ctx = BN_CTX_new()) == NULL)
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goto err;
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#endif
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ret = bn_miller_rabin_is_prime(w, checks, ctx, cb, 0, &status);
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if (!ret)
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goto err;
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ret = (status == BN_PRIMETEST_PROBABLY_PRIME);
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err:
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#ifndef FIPS_MODE
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BN_CTX_free(ctxlocal);
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#endif
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return ret;
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}
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/*
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* Refer to FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test.
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* OR C.3.1 Miller-Rabin Probabilistic Primality Test (if enhanced is zero).
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* The Step numbers listed in the code refer to the enhanced case.
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*
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* if enhanced is set, then status returns one of the following:
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* BN_PRIMETEST_PROBABLY_PRIME
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* BN_PRIMETEST_COMPOSITE_WITH_FACTOR
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* BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
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* if enhanced is zero, then status returns either
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* BN_PRIMETEST_PROBABLY_PRIME or
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* BN_PRIMETEST_COMPOSITE
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*
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* returns 0 if there was an error, otherwise it returns 1.
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*/
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int bn_miller_rabin_is_prime(const BIGNUM *w, int iterations, BN_CTX *ctx,
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BN_GENCB *cb, int enhanced, int *status)
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{
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int i, j, a, ret = 0;
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BIGNUM *g, *w1, *w3, *x, *m, *z, *b;
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BN_MONT_CTX *mont = NULL;
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/* w must be odd */
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if (!BN_is_odd(w))
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return 0;
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BN_CTX_start(ctx);
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g = BN_CTX_get(ctx);
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w1 = BN_CTX_get(ctx);
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w3 = BN_CTX_get(ctx);
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x = BN_CTX_get(ctx);
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m = BN_CTX_get(ctx);
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z = BN_CTX_get(ctx);
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b = BN_CTX_get(ctx);
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if (!(b != NULL
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/* w1 := w - 1 */
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&& BN_copy(w1, w)
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&& BN_sub_word(w1, 1)
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/* w3 := w - 3 */
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&& BN_copy(w3, w)
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&& BN_sub_word(w3, 3)))
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goto err;
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/* check w is larger than 3, otherwise the random b will be too small */
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if (BN_is_zero(w3) || BN_is_negative(w3))
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goto err;
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/* (Step 1) Calculate largest integer 'a' such that 2^a divides w-1 */
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a = 1;
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while (!BN_is_bit_set(w1, a))
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a++;
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/* (Step 2) m = (w-1) / 2^a */
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if (!BN_rshift(m, w1, a))
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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 || !BN_MONT_CTX_set(mont, w, ctx))
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goto err;
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if (iterations == 0)
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iterations = bn_mr_min_checks(BN_num_bits(w));
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/* (Step 4) */
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for (i = 0; i < iterations; ++i) {
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/* (Step 4.1) obtain a Random string of bits b where 1 < b < w-1 */
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if (!BN_priv_rand_range_ex(b, w3, ctx)
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|| !BN_add_word(b, 2)) /* 1 < b < w-1 */
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goto err;
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if (enhanced) {
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/* (Step 4.3) */
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if (!BN_gcd(g, b, w, ctx))
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goto err;
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/* (Step 4.4) */
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if (!BN_is_one(g)) {
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*status = BN_PRIMETEST_COMPOSITE_WITH_FACTOR;
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ret = 1;
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goto err;
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}
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}
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/* (Step 4.5) z = b^m mod w */
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if (!BN_mod_exp_mont(z, b, m, w, ctx, mont))
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goto err;
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/* (Step 4.6) if (z = 1 or z = w-1) */
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if (BN_is_one(z) || BN_cmp(z, w1) == 0)
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goto outer_loop;
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/* (Step 4.7) for j = 1 to a-1 */
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for (j = 1; j < a ; ++j) {
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/* (Step 4.7.1 - 4.7.2) x = z. z = x^2 mod w */
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if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx))
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goto err;
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/* (Step 4.7.3) */
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if (BN_cmp(z, w1) == 0)
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goto outer_loop;
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/* (Step 4.7.4) */
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if (BN_is_one(z))
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goto composite;
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}
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/* At this point z = b^((w-1)/2) mod w */
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/* (Steps 4.8 - 4.9) x = z, z = x^2 mod w */
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if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx))
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goto err;
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/* (Step 4.10) */
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if (BN_is_one(z))
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goto composite;
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/* (Step 4.11) x = b^(w-1) mod w */
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if (!BN_copy(x, z))
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goto err;
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composite:
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if (enhanced) {
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/* (Step 4.1.2) g = GCD(x-1, w) */
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if (!BN_sub_word(x, 1) || !BN_gcd(g, x, w, ctx))
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goto err;
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/* (Steps 4.1.3 - 4.1.4) */
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if (BN_is_one(g))
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*status = BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME;
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else
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*status = BN_PRIMETEST_COMPOSITE_WITH_FACTOR;
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} else {
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*status = BN_PRIMETEST_COMPOSITE;
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}
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ret = 1;
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goto err;
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outer_loop: ;
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/* (Step 4.1.5) */
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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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/* (Step 5) */
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*status = BN_PRIMETEST_PROBABLY_PRIME;
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ret = 1;
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err:
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BN_clear(g);
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BN_clear(w1);
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BN_clear(w3);
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BN_clear(x);
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BN_clear(m);
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BN_clear(z);
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BN_clear(b);
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BN_CTX_end(ctx);
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BN_MONT_CTX_free(mont);
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return ret;
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}
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/*
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* Generate a random number of |bits| bits that is probably prime by sieving.
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* If |safe| != 0, it generates a safe prime.
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* |mods| is a preallocated array that gets reused when called again.
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*
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* The probably prime is saved in |rnd|.
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*
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* Returns 1 on success and 0 on error.
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*/
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static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
|
|
BN_CTX *ctx)
|
|
{
|
|
int i;
|
|
BN_ULONG delta;
|
|
int trial_divisions = calc_trial_divisions(bits);
|
|
BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
|
|
|
|
again:
|
|
/* TODO: Not all primes are private */
|
|
if (!BN_priv_rand_ex(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD, ctx))
|
|
return 0;
|
|
if (safe && !BN_set_bit(rnd, 1))
|
|
return 0;
|
|
/* we now have a random number 'rnd' to test. */
|
|
for (i = 1; i < trial_divisions; i++) {
|
|
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
|
|
if (mod == (BN_ULONG)-1)
|
|
return 0;
|
|
mods[i] = (prime_t) mod;
|
|
}
|
|
delta = 0;
|
|
loop:
|
|
for (i = 1; i < trial_divisions; i++) {
|
|
/*
|
|
* check that rnd is a prime and also that
|
|
* gcd(rnd-1,primes) == 1 (except for 2)
|
|
* do the second check only if we are interested in safe primes
|
|
* in the case that the candidate prime is a single word then
|
|
* we check only the primes up to sqrt(rnd)
|
|
*/
|
|
if (bits <= 31 && delta <= 0x7fffffff
|
|
&& square(primes[i]) > BN_get_word(rnd) + delta)
|
|
break;
|
|
if (safe ? (mods[i] + delta) % primes[i] <= 1
|
|
: (mods[i] + delta) % primes[i] == 0) {
|
|
delta += safe ? 4 : 2;
|
|
if (delta > maxdelta)
|
|
goto again;
|
|
goto loop;
|
|
}
|
|
}
|
|
if (!BN_add_word(rnd, delta))
|
|
return 0;
|
|
if (BN_num_bits(rnd) != bits)
|
|
goto again;
|
|
bn_check_top(rnd);
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
* Generate a random number |rnd| of |bits| bits that is probably prime
|
|
* and satisfies |rnd| % |add| == |rem| by sieving.
|
|
* If |safe| != 0, it generates a safe prime.
|
|
* |mods| is a preallocated array that gets reused when called again.
|
|
*
|
|
* Returns 1 on success and 0 on error.
|
|
*/
|
|
static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
|
|
const BIGNUM *add, const BIGNUM *rem,
|
|
BN_CTX *ctx)
|
|
{
|
|
int i, ret = 0;
|
|
BIGNUM *t1;
|
|
BN_ULONG delta;
|
|
int trial_divisions = calc_trial_divisions(bits);
|
|
BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((t1 = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
|
|
if (maxdelta > BN_MASK2 - BN_get_word(add))
|
|
maxdelta = BN_MASK2 - BN_get_word(add);
|
|
|
|
again:
|
|
if (!BN_rand_ex(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD, ctx))
|
|
goto err;
|
|
|
|
/* we need ((rnd-rem) % add) == 0 */
|
|
|
|
if (!BN_mod(t1, rnd, add, ctx))
|
|
goto err;
|
|
if (!BN_sub(rnd, rnd, t1))
|
|
goto err;
|
|
if (rem == NULL) {
|
|
if (!BN_add_word(rnd, safe ? 3u : 1u))
|
|
goto err;
|
|
} else {
|
|
if (!BN_add(rnd, rnd, rem))
|
|
goto err;
|
|
}
|
|
|
|
if (BN_num_bits(rnd) < bits
|
|
|| BN_get_word(rnd) < (safe ? 5u : 3u)) {
|
|
if (!BN_add(rnd, rnd, add))
|
|
goto err;
|
|
}
|
|
|
|
/* we now have a random number 'rnd' to test. */
|
|
for (i = 1; i < trial_divisions; i++) {
|
|
BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
|
|
if (mod == (BN_ULONG)-1)
|
|
goto err;
|
|
mods[i] = (prime_t) mod;
|
|
}
|
|
delta = 0;
|
|
loop:
|
|
for (i = 1; i < trial_divisions; i++) {
|
|
/* check that rnd is a prime */
|
|
if (bits <= 31 && delta <= 0x7fffffff
|
|
&& square(primes[i]) > BN_get_word(rnd) + delta)
|
|
break;
|
|
/* rnd mod p == 1 implies q = (rnd-1)/2 is divisible by p */
|
|
if (safe ? (mods[i] + delta) % primes[i] <= 1
|
|
: (mods[i] + delta) % primes[i] == 0) {
|
|
delta += BN_get_word(add);
|
|
if (delta > maxdelta)
|
|
goto again;
|
|
goto loop;
|
|
}
|
|
}
|
|
if (!BN_add_word(rnd, delta))
|
|
goto err;
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(rnd);
|
|
return ret;
|
|
}
|