dh.c - security/openssh-library - Rivoreo Source Code Repositories

 /* $OpenBSD: dh.c,v 1.46 2008/04/13 00:22:17 djm Exp $ */
 /*
  * Copyright (c) 2000 Niels Provos.  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.
  *
  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``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 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.
  */

 #include "includes.h"

 #include <sys/param.h>

 #include <openssl/bn.h>
 #include <openssl/dh.h>

 #include <stdarg.h>
 #include <stdio.h>
 #include <stdlib.h>
 #include <string.h>

 #include "dh.h"
 #include "pathnames.h"
 #include "log.h"
 #include "misc.h"

 static int
 parse_prime(int linenum, char *line, struct dhgroup *dhg)
 {
 	char *cp, *arg;
 	char *strsize, *gen, *prime;
 	const char *errstr = NULL;

 	cp = line;
 	if ((arg = strdelim(&cp)) == NULL)
 		return 0;
 	/* Ignore leading whitespace */
 	if (*arg == '\0')
 		arg = strdelim(&cp);
 	if (!arg || !*arg || *arg == '#')
 		return 0;

 	/* time */
 	if (cp == NULL || *arg == '\0')
 		goto fail;
 	arg = strsep(&cp, " "); /* type */
 	if (cp == NULL || *arg == '\0')
 		goto fail;
 	arg = strsep(&cp, " "); /* tests */
 	if (cp == NULL || *arg == '\0')
 		goto fail;
 	arg = strsep(&cp, " "); /* tries */
 	if (cp == NULL || *arg == '\0')
 		goto fail;
 	strsize = strsep(&cp, " "); /* size */
 	if (cp == NULL || *strsize == '\0' ||
 	    (dhg->size = (u_int)strtonum(strsize, 0, 64*1024, &errstr)) == 0 ||
 	    errstr)
 		goto fail;
 	/* The whole group is one bit larger */
 	dhg->size++;
 	gen = strsep(&cp, " "); /* gen */
 	if (cp == NULL || *gen == '\0')
 		goto fail;
 	prime = strsep(&cp, " "); /* prime */
 	if (cp != NULL || *prime == '\0')
 		goto fail;

 	if ((dhg->g = BN_new()) == NULL)
 		fatal("parse_prime: BN_new failed");
 	if ((dhg->p = BN_new()) == NULL)
 		fatal("parse_prime: BN_new failed");
 	if (BN_hex2bn(&dhg->g, gen) == 0)
 		goto failclean;

 	if (BN_hex2bn(&dhg->p, prime) == 0)
 		goto failclean;

 	if (BN_num_bits(dhg->p) != dhg->size)
 		goto failclean;

 	if (BN_is_zero(dhg->g) || BN_is_one(dhg->g))
 		goto failclean;

 	return (1);

  failclean:
 	BN_clear_free(dhg->g);
 	BN_clear_free(dhg->p);
  fail:
 	error("Bad prime description in line %d", linenum);
 	return (0);
 }

 DH *
 choose_dh(int min, int wantbits, int max)
 {
 	FILE *f;
 	char line[4096];
 	int best, bestcount, which;
 	int linenum;
 	struct dhgroup dhg;

 	if ((f = fopen(_PATH_DH_MODULI, "r")) == NULL &&
 	    (f = fopen(_PATH_DH_PRIMES, "r")) == NULL) {
 		logit("WARNING: %s does not exist, using fixed modulus",
 		    _PATH_DH_MODULI);
 		return (dh_new_group14());
 	}

 	linenum = 0;
 	best = bestcount = 0;
 	while (fgets(line, sizeof(line), f)) {
 		linenum++;
 		if (!parse_prime(linenum, line, &dhg))
 			continue;
 		BN_clear_free(dhg.g);
 		BN_clear_free(dhg.p);

 		if (dhg.size > max || dhg.size < min)
 			continue;

 		if ((dhg.size > wantbits && dhg.size < best) ||
 		    (dhg.size > best && best < wantbits)) {
 			best = dhg.size;
 			bestcount = 0;
 		}
 		if (dhg.size == best)
 			bestcount++;
 	}
 	rewind(f);

 	if (bestcount == 0) {
 		fclose(f);
 		logit("WARNING: no suitable primes in %s", _PATH_DH_PRIMES);
 		return (dh_new_group14());
 	}

 	linenum = 0;
 	which = arc4random_uniform(bestcount);
 	while (fgets(line, sizeof(line), f)) {
 		if (!parse_prime(linenum, line, &dhg))
 			continue;
 		if ((dhg.size > max || dhg.size < min) ||
 		    dhg.size != best ||
 		    linenum++ != which) {
 			BN_clear_free(dhg.g);
 			BN_clear_free(dhg.p);
 			continue;
 		}
 		break;
 	}
 	fclose(f);
 	if (linenum != which+1)
 		fatal("WARNING: line %d disappeared in %s, giving up",
 		    which, _PATH_DH_PRIMES);

 	return (dh_new_group(dhg.g, dhg.p));
 }

 /* diffie-hellman-groupN-sha1 */

 int
 dh_pub_is_valid(DH *dh, BIGNUM *dh_pub)
 {
 	int i;
 	int n = BN_num_bits(dh_pub);
 	int bits_set = 0;
 	BIGNUM *tmp;

 	if (dh_pub->neg) {
 		logit("invalid public DH value: negative");
 		return 0;
 	}
 	if (BN_cmp(dh_pub, BN_value_one()) != 1) {	/* pub_exp <= 1 */
 		logit("invalid public DH value: <= 1");
 		return 0;
 	}

 	if ((tmp = BN_new()) == NULL) {
 		error("%s: BN_new failed", __func__);
 		return 0;
 	}
 	if (!BN_sub(tmp, dh->p, BN_value_one()) ||
 	    BN_cmp(dh_pub, tmp) != -1) {		/* pub_exp > p-2 */
 		BN_clear_free(tmp);
 		logit("invalid public DH value: >= p-1");
 		return 0;
 	}
 	BN_clear_free(tmp);

 	for (i = 0; i <= n; i++)
 		if (BN_is_bit_set(dh_pub, i))
 			bits_set++;
 	debug2("bits set: %d/%d", bits_set, BN_num_bits(dh->p));

 	/* if g==2 and bits_set==1 then computing log_g(dh_pub) is trivial */
 	if (bits_set > 1)
 		return 1;

 	logit("invalid public DH value (%d/%d)", bits_set, BN_num_bits(dh->p));
 	return 0;
 }

 void
 dh_gen_key(DH *dh, int need)
 {
 	int i, bits_set, tries = 0;

 	if (dh->p == NULL)
 		fatal("dh_gen_key: dh->p == NULL");
 	if (need > INT_MAX / 2 || 2 * need >= BN_num_bits(dh->p))
 		fatal("dh_gen_key: group too small: %d (2*need %d)",
 		    BN_num_bits(dh->p), 2*need);
 	do {
 		if (dh->priv_key != NULL)
 			BN_clear_free(dh->priv_key);
 		if ((dh->priv_key = BN_new()) == NULL)
 			fatal("dh_gen_key: BN_new failed");
 		/* generate a 2*need bits random private exponent */
 		if (!BN_rand(dh->priv_key, 2*need, 0, 0))
 			fatal("dh_gen_key: BN_rand failed");
 		if (DH_generate_key(dh) == 0)
 			fatal("DH_generate_key");
 		for (i = 0, bits_set = 0; i <= BN_num_bits(dh->priv_key); i++)
 			if (BN_is_bit_set(dh->priv_key, i))
 				bits_set++;
 		debug2("dh_gen_key: priv key bits set: %d/%d",
 		    bits_set, BN_num_bits(dh->priv_key));
 		if (tries++ > 10)
 			fatal("dh_gen_key: too many bad keys: giving up");
 	} while (!dh_pub_is_valid(dh, dh->pub_key));
 }

 DH *
 dh_new_group_asc(const char *gen, const char *modulus)
 {
 	DH *dh;

 	if ((dh = DH_new()) == NULL)
 		fatal("dh_new_group_asc: DH_new");

 	if (BN_hex2bn(&dh->p, modulus) == 0)
 		fatal("BN_hex2bn p");
 	if (BN_hex2bn(&dh->g, gen) == 0)
 		fatal("BN_hex2bn g");

 	return (dh);
 }

 /*
  * This just returns the group, we still need to generate the exchange
  * value.
  */

 DH *
 dh_new_group(BIGNUM *gen, BIGNUM *modulus)
 {
 	DH *dh;

 	if ((dh = DH_new()) == NULL)
 		fatal("dh_new_group: DH_new");
 	dh->p = modulus;
 	dh->g = gen;

 	return (dh);
 }

 DH *
 dh_new_group1(void)
 {
 	static char *gen = "2", *group1 =
 	    "FFFFFFFF" "FFFFFFFF" "C90FDAA2" "2168C234" "C4C6628B" "80DC1CD1"
 	    "29024E08" "8A67CC74" "020BBEA6" "3B139B22" "514A0879" "8E3404DD"
 	    "EF9519B3" "CD3A431B" "302B0A6D" "F25F1437" "4FE1356D" "6D51C245"
 	    "E485B576" "625E7EC6" "F44C42E9" "A637ED6B" "0BFF5CB6" "F406B7ED"
 	    "EE386BFB" "5A899FA5" "AE9F2411" "7C4B1FE6" "49286651" "ECE65381"
 	    "FFFFFFFF" "FFFFFFFF";

 	return (dh_new_group_asc(gen, group1));
 }

 DH *
 dh_new_group14(void)
 {
 	static char *gen = "2", *group14 =
 	    "FFFFFFFF" "FFFFFFFF" "C90FDAA2" "2168C234" "C4C6628B" "80DC1CD1"
 	    "29024E08" "8A67CC74" "020BBEA6" "3B139B22" "514A0879" "8E3404DD"
 	    "EF9519B3" "CD3A431B" "302B0A6D" "F25F1437" "4FE1356D" "6D51C245"
 	    "E485B576" "625E7EC6" "F44C42E9" "A637ED6B" "0BFF5CB6" "F406B7ED"
 	    "EE386BFB" "5A899FA5" "AE9F2411" "7C4B1FE6" "49286651" "ECE45B3D"
 	    "C2007CB8" "A163BF05" "98DA4836" "1C55D39A" "69163FA8" "FD24CF5F"
 	    "83655D23" "DCA3AD96" "1C62F356" "208552BB" "9ED52907" "7096966D"
 	    "670C354E" "4ABC9804" "F1746C08" "CA18217C" "32905E46" "2E36CE3B"
 	    "E39E772C" "180E8603" "9B2783A2" "EC07A28F" "B5C55DF0" "6F4C52C9"
 	    "DE2BCBF6" "95581718" "3995497C" "EA956AE5" "15D22618" "98FA0510"
 	    "15728E5A" "8AACAA68" "FFFFFFFF" "FFFFFFFF";

 	return (dh_new_group_asc(gen, group14));
 }

 /*
  * Estimates the group order for a Diffie-Hellman group that has an
  * attack complexity approximately the same as O(2**bits).  Estimate
  * with:  O(exp(1.9223 * (ln q)^(1/3) (ln ln q)^(2/3)))
  */

 int
 dh_estimate(int bits)
 {

 	if (bits <= 128)
 		return (1024);	/* O(2**86) */
 	if (bits <= 192)
 		return (2048);	/* O(2**116) */
 	return (4096);		/* O(2**156) */
 }
	/* $OpenBSD: dh.c,v 1.46 2008/04/13 00:22:17 djm Exp $ */
	/*
	* Copyright (c) 2000 Niels Provos. 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.
	*
	* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``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 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.
	*/

	#include "includes.h"

	#include <sys/param.h>

	#include <openssl/bn.h>
	#include <openssl/dh.h>

	#include <stdarg.h>
	#include <stdio.h>
	#include <stdlib.h>
	#include <string.h>

	#include "dh.h"
	#include "pathnames.h"
	#include "log.h"
	#include "misc.h"

	static int
	parse_prime(int linenum, char line, struct dhgroup dhg)
	{
	char cp, arg;
	char strsize, gen, *prime;
	const char *errstr = NULL;

	cp = line;
	if ((arg = strdelim(&cp)) == NULL)
	return 0;
	/* Ignore leading whitespace */
	if (*arg == '\0')
	arg = strdelim(&cp);
	if (!arg \|\| !arg \|\| arg == '#')
	return 0;

	/* time */
	if (cp == NULL \|\| *arg == '\0')
	goto fail;
	arg = strsep(&cp, " "); /* type */
	if (cp == NULL \|\| *arg == '\0')
	goto fail;
	arg = strsep(&cp, " "); /* tests */
	if (cp == NULL \|\| *arg == '\0')
	goto fail;
	arg = strsep(&cp, " "); /* tries */
	if (cp == NULL \|\| *arg == '\0')
	goto fail;
	strsize = strsep(&cp, " "); /* size */
	if (cp == NULL \|\| *strsize == '\0' \|\|
	(dhg->size = (u_int)strtonum(strsize, 0, 64*1024, &errstr)) == 0 \|\|
	errstr)
	goto fail;
	/* The whole group is one bit larger */
	dhg->size++;
	gen = strsep(&cp, " "); /* gen */
	if (cp == NULL \|\| *gen == '\0')
	goto fail;
	prime = strsep(&cp, " "); /* prime */
	if (cp != NULL \|\| *prime == '\0')
	goto fail;

	if ((dhg->g = BN_new()) == NULL)
	fatal("parse_prime: BN_new failed");
	if ((dhg->p = BN_new()) == NULL)
	fatal("parse_prime: BN_new failed");
	if (BN_hex2bn(&dhg->g, gen) == 0)
	goto failclean;

	if (BN_hex2bn(&dhg->p, prime) == 0)
	goto failclean;

	if (BN_num_bits(dhg->p) != dhg->size)
	goto failclean;

	if (BN_is_zero(dhg->g) \|\| BN_is_one(dhg->g))
	goto failclean;

	return (1);

	failclean:
	BN_clear_free(dhg->g);
	BN_clear_free(dhg->p);
	fail:
	error("Bad prime description in line %d", linenum);
	return (0);
	}

	DH *
	choose_dh(int min, int wantbits, int max)
	{
	FILE *f;
	char line[4096];
	int best, bestcount, which;
	int linenum;
	struct dhgroup dhg;

	if ((f = fopen(_PATH_DH_MODULI, "r")) == NULL &&
	(f = fopen(_PATH_DH_PRIMES, "r")) == NULL) {
	logit("WARNING: %s does not exist, using fixed modulus",
	_PATH_DH_MODULI);
	return (dh_new_group14());
	}

	linenum = 0;
	best = bestcount = 0;
	while (fgets(line, sizeof(line), f)) {
	linenum++;
	if (!parse_prime(linenum, line, &dhg))
	continue;
	BN_clear_free(dhg.g);
	BN_clear_free(dhg.p);

	if (dhg.size > max \|\| dhg.size < min)
	continue;

	if ((dhg.size > wantbits && dhg.size < best) \|\|
	(dhg.size > best && best < wantbits)) {
	best = dhg.size;
	bestcount = 0;
	}
	if (dhg.size == best)
	bestcount++;
	}
	rewind(f);

	if (bestcount == 0) {
	fclose(f);
	logit("WARNING: no suitable primes in %s", _PATH_DH_PRIMES);
	return (dh_new_group14());
	}

	linenum = 0;
	which = arc4random_uniform(bestcount);
	while (fgets(line, sizeof(line), f)) {
	if (!parse_prime(linenum, line, &dhg))
	continue;
	if ((dhg.size > max \|\| dhg.size < min) \|\|
	dhg.size != best \|\|
	linenum++ != which) {
	BN_clear_free(dhg.g);
	BN_clear_free(dhg.p);
	continue;
	}
	break;
	}
	fclose(f);
	if (linenum != which+1)
	fatal("WARNING: line %d disappeared in %s, giving up",
	which, _PATH_DH_PRIMES);

	return (dh_new_group(dhg.g, dhg.p));
	}

	/* diffie-hellman-groupN-sha1 */

	int
	dh_pub_is_valid(DH dh, BIGNUM dh_pub)
	{
	int i;
	int n = BN_num_bits(dh_pub);
	int bits_set = 0;
	BIGNUM *tmp;

	if (dh_pub->neg) {
	logit("invalid public DH value: negative");
	return 0;
	}
	if (BN_cmp(dh_pub, BN_value_one()) != 1) { /* pub_exp <= 1 */
	logit("invalid public DH value: <= 1");
	return 0;
	}

	if ((tmp = BN_new()) == NULL) {
	error("%s: BN_new failed", __func__);
	return 0;
	}
	if (!BN_sub(tmp, dh->p, BN_value_one()) \|\|
	BN_cmp(dh_pub, tmp) != -1) { /* pub_exp > p-2 */
	BN_clear_free(tmp);
	logit("invalid public DH value: >= p-1");
	return 0;
	}
	BN_clear_free(tmp);

	for (i = 0; i <= n; i++)
	if (BN_is_bit_set(dh_pub, i))
	bits_set++;
	debug2("bits set: %d/%d", bits_set, BN_num_bits(dh->p));

	/* if g==2 and bits_set==1 then computing log_g(dh_pub) is trivial */
	if (bits_set > 1)
	return 1;

	logit("invalid public DH value (%d/%d)", bits_set, BN_num_bits(dh->p));
	return 0;
	}

	void
	dh_gen_key(DH *dh, int need)
	{
	int i, bits_set, tries = 0;

	if (dh->p == NULL)
	fatal("dh_gen_key: dh->p == NULL");
	if (need > INT_MAX / 2 \|\| 2 * need >= BN_num_bits(dh->p))
	fatal("dh_gen_key: group too small: %d (2*need %d)",
	BN_num_bits(dh->p), 2*need);
	do {
	if (dh->priv_key != NULL)
	BN_clear_free(dh->priv_key);
	if ((dh->priv_key = BN_new()) == NULL)
	fatal("dh_gen_key: BN_new failed");
	/* generate a 2need bits random private exponent /
	if (!BN_rand(dh->priv_key, 2*need, 0, 0))
	fatal("dh_gen_key: BN_rand failed");
	if (DH_generate_key(dh) == 0)
	fatal("DH_generate_key");
	for (i = 0, bits_set = 0; i <= BN_num_bits(dh->priv_key); i++)
	if (BN_is_bit_set(dh->priv_key, i))
	bits_set++;
	debug2("dh_gen_key: priv key bits set: %d/%d",
	bits_set, BN_num_bits(dh->priv_key));
	if (tries++ > 10)
	fatal("dh_gen_key: too many bad keys: giving up");
	} while (!dh_pub_is_valid(dh, dh->pub_key));
	}

	DH *
	dh_new_group_asc(const char gen, const char modulus)
	{
	DH *dh;

	if ((dh = DH_new()) == NULL)
	fatal("dh_new_group_asc: DH_new");

	if (BN_hex2bn(&dh->p, modulus) == 0)
	fatal("BN_hex2bn p");
	if (BN_hex2bn(&dh->g, gen) == 0)
	fatal("BN_hex2bn g");

	return (dh);
	}

	/*
	* This just returns the group, we still need to generate the exchange
	* value.
	*/

	DH *
	dh_new_group(BIGNUM gen, BIGNUM modulus)
	{
	DH *dh;

	if ((dh = DH_new()) == NULL)
	fatal("dh_new_group: DH_new");
	dh->p = modulus;
	dh->g = gen;

	return (dh);
	}

	DH *
	dh_new_group1(void)
	{
	static char gen = "2", group1 =
	"FFFFFFFF" "FFFFFFFF" "C90FDAA2" "2168C234" "C4C6628B" "80DC1CD1"
	"29024E08" "8A67CC74" "020BBEA6" "3B139B22" "514A0879" "8E3404DD"
	"EF9519B3" "CD3A431B" "302B0A6D" "F25F1437" "4FE1356D" "6D51C245"
	"E485B576" "625E7EC6" "F44C42E9" "A637ED6B" "0BFF5CB6" "F406B7ED"
	"EE386BFB" "5A899FA5" "AE9F2411" "7C4B1FE6" "49286651" "ECE65381"
	"FFFFFFFF" "FFFFFFFF";

	return (dh_new_group_asc(gen, group1));
	}

	DH *
	dh_new_group14(void)
	{
	static char gen = "2", group14 =
	"FFFFFFFF" "FFFFFFFF" "C90FDAA2" "2168C234" "C4C6628B" "80DC1CD1"
	"29024E08" "8A67CC74" "020BBEA6" "3B139B22" "514A0879" "8E3404DD"
	"EF9519B3" "CD3A431B" "302B0A6D" "F25F1437" "4FE1356D" "6D51C245"
	"E485B576" "625E7EC6" "F44C42E9" "A637ED6B" "0BFF5CB6" "F406B7ED"
	"EE386BFB" "5A899FA5" "AE9F2411" "7C4B1FE6" "49286651" "ECE45B3D"
	"C2007CB8" "A163BF05" "98DA4836" "1C55D39A" "69163FA8" "FD24CF5F"
	"83655D23" "DCA3AD96" "1C62F356" "208552BB" "9ED52907" "7096966D"
	"670C354E" "4ABC9804" "F1746C08" "CA18217C" "32905E46" "2E36CE3B"
	"E39E772C" "180E8603" "9B2783A2" "EC07A28F" "B5C55DF0" "6F4C52C9"
	"DE2BCBF6" "95581718" "3995497C" "EA956AE5" "15D22618" "98FA0510"
	"15728E5A" "8AACAA68" "FFFFFFFF" "FFFFFFFF";

	return (dh_new_group_asc(gen, group14));
	}

	/*
	* Estimates the group order for a Diffie-Hellman group that has an
	* attack complexity approximately the same as O(2**bits). Estimate
	* with: O(exp(1.9223 * (ln q)^(1/3) (ln ln q)^(2/3)))
	*/

	int
	dh_estimate(int bits)
	{

	if (bits <= 128)
	return (1024); /* O(2*86) /
	if (bits <= 192)
	return (2048); /* O(2*116) /
	return (4096); /* O(2*156) /
	}