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freebsd/crypto/openssh/moduli.c
Dag-Erling Smørgrav d4af9e693f Upgrade to OpenSSH 5.1p1.
I have worked hard to reduce diffs against the vendor branch.  One
notable change in that respect is that we no longer prefer DSA over
RSA - the reasons for doing so went away years ago.  This may cause
some surprises, as ssh will warn about unknown host keys even for
hosts whose keys haven't changed.

MFC after:	6 weeks
2008-08-01 02:48:36 +00:00

651 lines
16 KiB
C

/* $OpenBSD: moduli.c,v 1.21 2008/06/26 09:19:40 djm Exp $ */
/*
* Copyright 1994 Phil Karn <karn@qualcomm.com>
* Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com>
* Copyright 2000 Niels Provos <provos@citi.umich.edu>
* 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.
*/
/*
* Two-step process to generate safe primes for DHGEX
*
* Sieve candidates for "safe" primes,
* suitable for use as Diffie-Hellman moduli;
* that is, where q = (p-1)/2 is also prime.
*
* First step: generate candidate primes (memory intensive)
* Second step: test primes' safety (processor intensive)
*/
#include "includes.h"
#include <sys/types.h>
#include <openssl/bn.h>
#include <openssl/dh.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdarg.h>
#include <time.h>
#include "xmalloc.h"
#include "dh.h"
#include "log.h"
/*
* File output defines
*/
/* need line long enough for largest moduli plus headers */
#define QLINESIZE (100+8192)
/*
* Size: decimal.
* Specifies the number of the most significant bit (0 to M).
* WARNING: internally, usually 1 to N.
*/
#define QSIZE_MINIMUM (511)
/*
* Prime sieving defines
*/
/* Constant: assuming 8 bit bytes and 32 bit words */
#define SHIFT_BIT (3)
#define SHIFT_BYTE (2)
#define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE)
#define SHIFT_MEGABYTE (20)
#define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE)
/*
* Using virtual memory can cause thrashing. This should be the largest
* number that is supported without a large amount of disk activity --
* that would increase the run time from hours to days or weeks!
*/
#define LARGE_MINIMUM (8UL) /* megabytes */
/*
* Do not increase this number beyond the unsigned integer bit size.
* Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
*/
#define LARGE_MAXIMUM (127UL) /* megabytes */
/*
* Constant: when used with 32-bit integers, the largest sieve prime
* has to be less than 2**32.
*/
#define SMALL_MAXIMUM (0xffffffffUL)
/* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
#define TINY_NUMBER (1UL<<16)
/* Ensure enough bit space for testing 2*q. */
#define TEST_MAXIMUM (1UL<<16)
#define TEST_MINIMUM (QSIZE_MINIMUM + 1)
/* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */
#define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */
/* bit operations on 32-bit words */
#define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
#define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
#define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
/*
* Prime testing defines
*/
/* Minimum number of primality tests to perform */
#define TRIAL_MINIMUM (4)
/*
* Sieving data (XXX - move to struct)
*/
/* sieve 2**16 */
static u_int32_t *TinySieve, tinybits;
/* sieve 2**30 in 2**16 parts */
static u_int32_t *SmallSieve, smallbits, smallbase;
/* sieve relative to the initial value */
static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
static u_int32_t largebits, largememory; /* megabytes */
static BIGNUM *largebase;
int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
int prime_test(FILE *, FILE *, u_int32_t, u_int32_t);
/*
* print moduli out in consistent form,
*/
static int
qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
{
struct tm *gtm;
time_t time_now;
int res;
time(&time_now);
gtm = gmtime(&time_now);
res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
otype, otests, otries, osize, ogenerator);
if (res < 0)
return (-1);
if (BN_print_fp(ofile, omodulus) < 1)
return (-1);
res = fprintf(ofile, "\n");
fflush(ofile);
return (res > 0 ? 0 : -1);
}
/*
** Sieve p's and q's with small factors
*/
static void
sieve_large(u_int32_t s)
{
u_int32_t r, u;
debug3("sieve_large %u", s);
largetries++;
/* r = largebase mod s */
r = BN_mod_word(largebase, s);
if (r == 0)
u = 0; /* s divides into largebase exactly */
else
u = s - r; /* largebase+u is first entry divisible by s */
if (u < largebits * 2) {
/*
* The sieve omits p's and q's divisible by 2, so ensure that
* largebase+u is odd. Then, step through the sieve in
* increments of 2*s
*/
if (u & 0x1)
u += s; /* Make largebase+u odd, and u even */
/* Mark all multiples of 2*s */
for (u /= 2; u < largebits; u += s)
BIT_SET(LargeSieve, u);
}
/* r = p mod s */
r = (2 * r + 1) % s;
if (r == 0)
u = 0; /* s divides p exactly */
else
u = s - r; /* p+u is first entry divisible by s */
if (u < largebits * 4) {
/*
* The sieve omits p's divisible by 4, so ensure that
* largebase+u is not. Then, step through the sieve in
* increments of 4*s
*/
while (u & 0x3) {
if (SMALL_MAXIMUM - u < s)
return;
u += s;
}
/* Mark all multiples of 4*s */
for (u /= 4; u < largebits; u += s)
BIT_SET(LargeSieve, u);
}
}
/*
* list candidates for Sophie-Germain primes (where q = (p-1)/2)
* to standard output.
* The list is checked against small known primes (less than 2**30).
*/
int
gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
{
BIGNUM *q;
u_int32_t j, r, s, t;
u_int32_t smallwords = TINY_NUMBER >> 6;
u_int32_t tinywords = TINY_NUMBER >> 6;
time_t time_start, time_stop;
u_int32_t i;
int ret = 0;
largememory = memory;
if (memory != 0 &&
(memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
error("Invalid memory amount (min %ld, max %ld)",
LARGE_MINIMUM, LARGE_MAXIMUM);
return (-1);
}
/*
* Set power to the length in bits of the prime to be generated.
* This is changed to 1 less than the desired safe prime moduli p.
*/
if (power > TEST_MAXIMUM) {
error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
return (-1);
} else if (power < TEST_MINIMUM) {
error("Too few bits: %u < %u", power, TEST_MINIMUM);
return (-1);
}
power--; /* decrement before squaring */
/*
* The density of ordinary primes is on the order of 1/bits, so the
* density of safe primes should be about (1/bits)**2. Set test range
* to something well above bits**2 to be reasonably sure (but not
* guaranteed) of catching at least one safe prime.
*/
largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
/*
* Need idea of how much memory is available. We don't have to use all
* of it.
*/
if (largememory > LARGE_MAXIMUM) {
logit("Limited memory: %u MB; limit %lu MB",
largememory, LARGE_MAXIMUM);
largememory = LARGE_MAXIMUM;
}
if (largewords <= (largememory << SHIFT_MEGAWORD)) {
logit("Increased memory: %u MB; need %u bytes",
largememory, (largewords << SHIFT_BYTE));
largewords = (largememory << SHIFT_MEGAWORD);
} else if (largememory > 0) {
logit("Decreased memory: %u MB; want %u bytes",
largememory, (largewords << SHIFT_BYTE));
largewords = (largememory << SHIFT_MEGAWORD);
}
TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
tinybits = tinywords << SHIFT_WORD;
SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
smallbits = smallwords << SHIFT_WORD;
/*
* dynamically determine available memory
*/
while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
largebits = largewords << SHIFT_WORD;
largenumbers = largebits * 2; /* even numbers excluded */
/* validation check: count the number of primes tried */
largetries = 0;
if ((q = BN_new()) == NULL)
fatal("BN_new failed");
/*
* Generate random starting point for subprime search, or use
* specified parameter.
*/
if ((largebase = BN_new()) == NULL)
fatal("BN_new failed");
if (start == NULL) {
if (BN_rand(largebase, power, 1, 1) == 0)
fatal("BN_rand failed");
} else {
if (BN_copy(largebase, start) == NULL)
fatal("BN_copy: failed");
}
/* ensure odd */
if (BN_set_bit(largebase, 0) == 0)
fatal("BN_set_bit: failed");
time(&time_start);
logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
largenumbers, power);
debug2("start point: 0x%s", BN_bn2hex(largebase));
/*
* TinySieve
*/
for (i = 0; i < tinybits; i++) {
if (BIT_TEST(TinySieve, i))
continue; /* 2*i+3 is composite */
/* The next tiny prime */
t = 2 * i + 3;
/* Mark all multiples of t */
for (j = i + t; j < tinybits; j += t)
BIT_SET(TinySieve, j);
sieve_large(t);
}
/*
* Start the small block search at the next possible prime. To avoid
* fencepost errors, the last pass is skipped.
*/
for (smallbase = TINY_NUMBER + 3;
smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
smallbase += TINY_NUMBER) {
for (i = 0; i < tinybits; i++) {
if (BIT_TEST(TinySieve, i))
continue; /* 2*i+3 is composite */
/* The next tiny prime */
t = 2 * i + 3;
r = smallbase % t;
if (r == 0) {
s = 0; /* t divides into smallbase exactly */
} else {
/* smallbase+s is first entry divisible by t */
s = t - r;
}
/*
* The sieve omits even numbers, so ensure that
* smallbase+s is odd. Then, step through the sieve
* in increments of 2*t
*/
if (s & 1)
s += t; /* Make smallbase+s odd, and s even */
/* Mark all multiples of 2*t */
for (s /= 2; s < smallbits; s += t)
BIT_SET(SmallSieve, s);
}
/*
* SmallSieve
*/
for (i = 0; i < smallbits; i++) {
if (BIT_TEST(SmallSieve, i))
continue; /* 2*i+smallbase is composite */
/* The next small prime */
sieve_large((2 * i) + smallbase);
}
memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
}
time(&time_stop);
logit("%.24s Sieved with %u small primes in %ld seconds",
ctime(&time_stop), largetries, (long) (time_stop - time_start));
for (j = r = 0; j < largebits; j++) {
if (BIT_TEST(LargeSieve, j))
continue; /* Definitely composite, skip */
debug2("test q = largebase+%u", 2 * j);
if (BN_set_word(q, 2 * j) == 0)
fatal("BN_set_word failed");
if (BN_add(q, q, largebase) == 0)
fatal("BN_add failed");
if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
MODULI_TESTS_SIEVE, largetries,
(power - 1) /* MSB */, (0), q) == -1) {
ret = -1;
break;
}
r++; /* count q */
}
time(&time_stop);
xfree(LargeSieve);
xfree(SmallSieve);
xfree(TinySieve);
logit("%.24s Found %u candidates", ctime(&time_stop), r);
return (ret);
}
/*
* perform a Miller-Rabin primality test
* on the list of candidates
* (checking both q and p)
* The result is a list of so-call "safe" primes
*/
int
prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted)
{
BIGNUM *q, *p, *a;
BN_CTX *ctx;
char *cp, *lp;
u_int32_t count_in = 0, count_out = 0, count_possible = 0;
u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
time_t time_start, time_stop;
int res;
if (trials < TRIAL_MINIMUM) {
error("Minimum primality trials is %d", TRIAL_MINIMUM);
return (-1);
}
time(&time_start);
if ((p = BN_new()) == NULL)
fatal("BN_new failed");
if ((q = BN_new()) == NULL)
fatal("BN_new failed");
if ((ctx = BN_CTX_new()) == NULL)
fatal("BN_CTX_new failed");
debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
ctime(&time_start), trials, generator_wanted);
res = 0;
lp = xmalloc(QLINESIZE + 1);
while (fgets(lp, QLINESIZE + 1, in) != NULL) {
count_in++;
if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
debug2("%10u: comment or short line", count_in);
continue;
}
/* XXX - fragile parser */
/* time */
cp = &lp[14]; /* (skip) */
/* type */
in_type = strtoul(cp, &cp, 10);
/* tests */
in_tests = strtoul(cp, &cp, 10);
if (in_tests & MODULI_TESTS_COMPOSITE) {
debug2("%10u: known composite", count_in);
continue;
}
/* tries */
in_tries = strtoul(cp, &cp, 10);
/* size (most significant bit) */
in_size = strtoul(cp, &cp, 10);
/* generator (hex) */
generator_known = strtoul(cp, &cp, 16);
/* Skip white space */
cp += strspn(cp, " ");
/* modulus (hex) */
switch (in_type) {
case MODULI_TYPE_SOPHIE_GERMAIN:
debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
a = q;
if (BN_hex2bn(&a, cp) == 0)
fatal("BN_hex2bn failed");
/* p = 2*q + 1 */
if (BN_lshift(p, q, 1) == 0)
fatal("BN_lshift failed");
if (BN_add_word(p, 1) == 0)
fatal("BN_add_word failed");
in_size += 1;
generator_known = 0;
break;
case MODULI_TYPE_UNSTRUCTURED:
case MODULI_TYPE_SAFE:
case MODULI_TYPE_SCHNORR:
case MODULI_TYPE_STRONG:
case MODULI_TYPE_UNKNOWN:
debug2("%10u: (%u)", count_in, in_type);
a = p;
if (BN_hex2bn(&a, cp) == 0)
fatal("BN_hex2bn failed");
/* q = (p-1) / 2 */
if (BN_rshift(q, p, 1) == 0)
fatal("BN_rshift failed");
break;
default:
debug2("Unknown prime type");
break;
}
/*
* due to earlier inconsistencies in interpretation, check
* the proposed bit size.
*/
if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
debug2("%10u: bit size %u mismatch", count_in, in_size);
continue;
}
if (in_size < QSIZE_MINIMUM) {
debug2("%10u: bit size %u too short", count_in, in_size);
continue;
}
if (in_tests & MODULI_TESTS_MILLER_RABIN)
in_tries += trials;
else
in_tries = trials;
/*
* guess unknown generator
*/
if (generator_known == 0) {
if (BN_mod_word(p, 24) == 11)
generator_known = 2;
else if (BN_mod_word(p, 12) == 5)
generator_known = 3;
else {
u_int32_t r = BN_mod_word(p, 10);
if (r == 3 || r == 7)
generator_known = 5;
}
}
/*
* skip tests when desired generator doesn't match
*/
if (generator_wanted > 0 &&
generator_wanted != generator_known) {
debug2("%10u: generator %d != %d",
count_in, generator_known, generator_wanted);
continue;
}
/*
* Primes with no known generator are useless for DH, so
* skip those.
*/
if (generator_known == 0) {
debug2("%10u: no known generator", count_in);
continue;
}
count_possible++;
/*
* The (1/4)^N performance bound on Miller-Rabin is
* extremely pessimistic, so don't spend a lot of time
* really verifying that q is prime until after we know
* that p is also prime. A single pass will weed out the
* vast majority of composite q's.
*/
if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) {
debug("%10u: q failed first possible prime test",
count_in);
continue;
}
/*
* q is possibly prime, so go ahead and really make sure
* that p is prime. If it is, then we can go back and do
* the same for q. If p is composite, chances are that
* will show up on the first Rabin-Miller iteration so it
* doesn't hurt to specify a high iteration count.
*/
if (!BN_is_prime(p, trials, NULL, ctx, NULL)) {
debug("%10u: p is not prime", count_in);
continue;
}
debug("%10u: p is almost certainly prime", count_in);
/* recheck q more rigorously */
if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) {
debug("%10u: q is not prime", count_in);
continue;
}
debug("%10u: q is almost certainly prime", count_in);
if (qfileout(out, MODULI_TYPE_SAFE,
in_tests | MODULI_TESTS_MILLER_RABIN,
in_tries, in_size, generator_known, p)) {
res = -1;
break;
}
count_out++;
}
time(&time_stop);
xfree(lp);
BN_free(p);
BN_free(q);
BN_CTX_free(ctx);
logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
ctime(&time_stop), count_out, count_possible,
(long) (time_stop - time_start));
return (res);
}