/* $OpenBSD: bn_prime.c,v 1.22 2022/07/19 16:19:19 tb Exp $ */ /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include <stdio.h> #include <time.h> #include <openssl/err.h> #include "bn_lcl.h" #define LIBRESSL_HAS_BPSW /* NB: these functions have been "upgraded", the deprecated versions (which are * compatibility wrappers using these functions) are in bn_depr.c. * - Geoff */ /* The quick sieve algorithm approach to weeding out primes is * Philip Zimmermann's, as implemented in PGP. I have had a read of * his comments and implemented my own version. */ #include "bn_prime.h" static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); static int probable_prime(BIGNUM *rnd, int bits); static int probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); int BN_GENCB_call(BN_GENCB *cb, int a, int b) { /* No callback means continue */ if (!cb) return 1; switch (cb->ver) { case 1: /* Deprecated-style callbacks */ if (!cb->cb.cb_1) return 1; cb->cb.cb_1(a, b, cb->arg); return 1; case 2: /* New-style callbacks */ return cb->cb.cb_2(a, b, cb); default: break; } /* Unrecognised callback type */ return 0; } int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) { BIGNUM *t; int found = 0; int i, j, c1 = 0; BN_CTX *ctx; int checks = 1; if (bits < 2 || (bits == 2 && safe)) { /* * There are no prime numbers smaller than 2, and the smallest * safe prime (7) spans three bits. */ BNerror(BN_R_BITS_TOO_SMALL); return 0; } ctx = BN_CTX_new(); if (ctx == NULL) goto err; BN_CTX_start(ctx); if ((t = BN_CTX_get(ctx)) == NULL) goto err; #ifndef LIBRESSL_HAS_BPSW checks = BN_prime_checks_for_size(bits); #endif loop: /* make a random number and set the top and bottom bits */ if (add == NULL) { if (!probable_prime(ret, bits)) goto err; } else { if (safe) { if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) goto err; } else { if (!probable_prime_dh(ret, bits, add, rem, ctx)) goto err; } } /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ if (!BN_GENCB_call(cb, 0, c1++)) /* aborted */ goto err; if (!safe) { i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); if (i == -1) goto err; if (i == 0) goto loop; } else { /* for "safe prime" generation, * check that (p-1)/2 is prime. * Since a prime is odd, We just * need to divide by 2 */ if (!BN_rshift1(t, ret)) goto err; for (i = 0; i < checks; i++) { j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); if (j == -1) goto err; if (j == 0) goto loop; j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); if (j == -1) goto err; if (j == 0) goto loop; if (!BN_GENCB_call(cb, 2, c1 - 1)) goto err; /* We have a safe prime test pass */ } } /* we have a prime :-) */ found = 1; err: if (ctx != NULL) { BN_CTX_end(ctx); BN_CTX_free(ctx); } bn_check_top(ret); return found; } int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) { return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); } int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, int do_trial_division, BN_GENCB *cb) { BN_CTX *ctx = NULL; BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ BN_MONT_CTX *mont = NULL; const BIGNUM *A = NULL; int i, j, k; int ret = -1; #ifdef LIBRESSL_HAS_BPSW int is_prime; /* XXX - tickle BN_GENCB in bn_is_prime_bpsw(). */ if (!bn_is_prime_bpsw(&is_prime, a, ctx_passed)) return -1; return is_prime; #endif if (BN_cmp(a, BN_value_one()) <= 0) return 0; if (checks == BN_prime_checks) checks = BN_prime_checks_for_size(BN_num_bits(a)); /* first look for small factors */ if (!BN_is_odd(a)) /* a is even => a is prime if and only if a == 2 */ return BN_is_word(a, 2); if (do_trial_division) { for (i = 1; i < NUMPRIMES; i++) { BN_ULONG mod = BN_mod_word(a, primes[i]); if (mod == (BN_ULONG)-1) goto err; if (mod == 0) return BN_is_word(a, primes[i]); } if (!BN_GENCB_call(cb, 1, -1)) goto err; } if (ctx_passed != NULL) ctx = ctx_passed; else if ((ctx = BN_CTX_new()) == NULL) goto err; BN_CTX_start(ctx); /* A := abs(a) */ if (a->neg) { BIGNUM *t; if ((t = BN_CTX_get(ctx)) == NULL) goto err; BN_copy(t, a); t->neg = 0; A = t; } else A = a; if ((A1 = BN_CTX_get(ctx)) == NULL) goto err; if ((A1_odd = BN_CTX_get(ctx)) == NULL) goto err; if ((check = BN_CTX_get(ctx)) == NULL) goto err; /* compute A1 := A - 1 */ if (!BN_copy(A1, A)) goto err; if (!BN_sub_word(A1, 1)) goto err; if (BN_is_zero(A1)) { ret = 0; goto err; } /* write A1 as A1_odd * 2^k */ k = 1; while (!BN_is_bit_set(A1, k)) k++; if (!BN_rshift(A1_odd, A1, k)) goto err; /* Montgomery setup for computations mod A */ mont = BN_MONT_CTX_new(); if (mont == NULL) goto err; if (!BN_MONT_CTX_set(mont, A, ctx)) goto err; for (i = 0; i < checks; i++) { if (!BN_pseudo_rand_range(check, A1)) goto err; if (!BN_add_word(check, 1)) goto err; /* now 1 <= check < A */ j = witness(check, A, A1, A1_odd, k, ctx, mont); if (j == -1) goto err; if (j) { ret = 0; goto err; } if (!BN_GENCB_call(cb, 1, i)) goto err; } ret = 1; err: if (ctx != NULL) { BN_CTX_end(ctx); if (ctx_passed == NULL) BN_CTX_free(ctx); } BN_MONT_CTX_free(mont); return (ret); } static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont) { if (!BN_mod_exp_mont_ct(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ return -1; if (BN_is_one(w)) return 0; /* probably prime */ if (BN_cmp(w, a1) == 0) return 0; /* w == -1 (mod a), 'a' is probably prime */ while (--k) { if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ return -1; if (BN_is_one(w)) return 1; /* 'a' is composite, otherwise a previous 'w' would * have been == -1 (mod 'a') */ if (BN_cmp(w, a1) == 0) return 0; /* w == -1 (mod a), 'a' is probably prime */ } /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', * and it is neither -1 nor +1 -- so 'a' cannot be prime */ bn_check_top(w); return 1; } static int probable_prime(BIGNUM *rnd, int bits) { int i; prime_t mods[NUMPRIMES]; BN_ULONG delta, maxdelta; again: if (!BN_rand(rnd, bits, 1, 1)) return (0); /* we now have a random number 'rand' to test. */ for (i = 1; i < NUMPRIMES; i++) { BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); if (mod == (BN_ULONG)-1) return (0); mods[i] = (prime_t)mod; } maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; delta = 0; loop: for (i = 1; i < NUMPRIMES; i++) { /* check that rnd is not a prime and also * that gcd(rnd-1,primes) == 1 (except for 2) */ if (((mods[i] + delta) % primes[i]) <= 1) { delta += 2; if (delta > maxdelta) goto again; goto loop; } } if (!BN_add_word(rnd, delta)) return (0); bn_check_top(rnd); return (1); } static int probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) { int i, ret = 0; BIGNUM *t1; BN_CTX_start(ctx); if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_rand(rnd, bits, 0, 1)) goto err; /* we need ((rnd-rem) % add) == 0 */ if (!BN_mod_ct(t1, rnd, add, ctx)) goto err; if (!BN_sub(rnd, rnd, t1)) goto err; if (rem == NULL) { if (!BN_add_word(rnd, 1)) goto err; } else { if (!BN_add(rnd, rnd, rem)) goto err; } /* we now have a random number 'rand' to test. */ loop: for (i = 1; i < NUMPRIMES; i++) { /* check that rnd is a prime */ BN_LONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); if (mod == (BN_ULONG)-1) goto err; if (mod <= 1) { if (!BN_add(rnd, rnd, add)) goto err; goto loop; } } ret = 1; err: BN_CTX_end(ctx); bn_check_top(rnd); return (ret); } static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, const BIGNUM *rem, BN_CTX *ctx) { int i, ret = 0; BIGNUM *t1, *qadd, *q; bits--; BN_CTX_start(ctx); if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; if ((q = BN_CTX_get(ctx)) == NULL) goto err; if ((qadd = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_rshift1(qadd, padd)) goto err; if (!BN_rand(q, bits, 0, 1)) goto err; /* we need ((rnd-rem) % add) == 0 */ if (!BN_mod_ct(t1, q,qadd, ctx)) goto err; if (!BN_sub(q, q, t1)) goto err; if (rem == NULL) { if (!BN_add_word(q, 1)) goto err; } else { if (!BN_rshift1(t1, rem)) goto err; if (!BN_add(q, q, t1)) goto err; } /* we now have a random number 'rand' to test. */ if (!BN_lshift1(p, q)) goto err; if (!BN_add_word(p, 1)) goto err; loop: for (i = 1; i < NUMPRIMES; i++) { /* check that p and q are prime */ /* check that for p and q * gcd(p-1,primes) == 1 (except for 2) */ BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]); BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]); if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1) goto err; if (pmod == 0 || qmod == 0) { if (!BN_add(p, p, padd)) goto err; if (!BN_add(q, q, qadd)) goto err; goto loop; } } ret = 1; err: BN_CTX_end(ctx); bn_check_top(p); return (ret); }
