-/* crypto/dh/dh_gen.c */
-/* 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.
+/*
+ * Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
*
- * 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.]
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
*/
/*
#include <stdio.h>
#include "internal/cryptlib.h"
#include <openssl/bn.h>
-#include <openssl/dh.h>
+#include "dh_locl.h"
static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
BN_GENCB *cb);
/*-
* We generate DH parameters as follows
- * find a prime q which is prime_len/2 bits long.
- * p=(2*q)+1 or (p-1)/2 = q
- * For this case, g is a generator if
- * g^((p-1)/q) mod p != 1 for values of q which are the factors of p-1.
- * Since the factors of p-1 are q and 2, we just need to check
- * g^2 mod p != 1 and g^q mod p != 1.
+ * find a prime p which is prime_len bits long,
+ * where q=(p-1)/2 is also prime.
+ * In the following we assume that g is not 0, 1 or p-1, since it
+ * would generate only trivial subgroups.
+ * For this case, g is a generator of the order-q subgroup if
+ * g^q mod p == 1.
+ * Or in terms of the Legendre symbol: (g/p) == 1.
*
* Having said all that,
* there is another special case method for the generators 2, 3 and 5.
- * for 2, p mod 24 == 11
- * for 3, p mod 12 == 5 <<<<< does not work for safe primes.
- * for 5, p mod 10 == 3 or 7
- *
- * Thanks to Phil Karn <karn@qualcomm.com> for the pointers about the
- * special generators and for answering some of my questions.
+ * Using the quadratic reciprocity law it is possible to solve
+ * (g/p) == 1 for the special values 2, 3, 5:
+ * (2/p) == 1 if p mod 8 == 1 or 7.
+ * (3/p) == 1 if p mod 12 == 1 or 11.
+ * (5/p) == 1 if p mod 5 == 1 or 4.
+ * See for instance: https://en.wikipedia.org/wiki/Legendre_symbol
*
- * I've implemented the second simple method :-).
- * Since DH should be using a safe prime (both p and q are prime),
- * this generator function can take a very very long time to run.
- */
-/*
- * Actually there is no reason to insist that 'generator' be a generator.
- * It's just as OK (and in some sense better) to use a generator of the
- * order-q subgroup.
+ * Since all safe primes > 7 must satisfy p mod 12 == 11
+ * and all safe primes > 11 must satisfy p mod 5 != 1
+ * we can further improve the condition for g = 2, 3 and 5:
+ * for 2, p mod 24 == 23
+ * for 3, p mod 12 == 11
+ * for 5, p mod 60 == 59
*/
static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
BN_GENCB *cb)
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
t2 = BN_CTX_get(ctx);
- if (t1 == NULL || t2 == NULL)
+ if (t2 == NULL)
goto err;
/* Make sure 'ret' has the necessary elements */
if (generator == DH_GENERATOR_2) {
if (!BN_set_word(t1, 24))
goto err;
- if (!BN_set_word(t2, 11))
+ if (!BN_set_word(t2, 23))
goto err;
g = 2;
} else if (generator == DH_GENERATOR_5) {
- if (!BN_set_word(t1, 10))
+ if (!BN_set_word(t1, 60))
goto err;
- if (!BN_set_word(t2, 3))
+ if (!BN_set_word(t2, 59))
goto err;
- /*
- * BN_set_word(t3,7); just have to miss out on these ones :-(
- */
g = 5;
} else {
/*
* not: since we are using safe primes, it will generate either an
* order-q or an order-2q group, which both is OK
*/
- if (!BN_set_word(t1, 2))
+ if (!BN_set_word(t1, 12))
goto err;
- if (!BN_set_word(t2, 1))
+ if (!BN_set_word(t2, 11))
goto err;
g = generator;
}
ok = 0;
}
- if (ctx != NULL) {
- BN_CTX_end(ctx);
- BN_CTX_free(ctx);
- }
+ BN_CTX_end(ctx);
+ BN_CTX_free(ctx);
return ok;
}
projects / openssl.git / blobdiff