1 files changed, 669 insertions, 0 deletions

diff --git a/moduli.c b/moduli.c
new file mode 100644
index 000000000000..44e5ddfc0c03
--- /dev/null
+++ b/moduli.c
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+/* $OpenBSD: moduli.c,v 1.19 2006/11/06 21:25:28 markus 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 <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdarg.h>
+#include <time.h>
+
+#include "xmalloc.h"
+#include "log.h"
+
+/*
+ * File output defines
+ */
+
+/* need line long enough for largest moduli plus headers */
+#define QLINESIZE		(100+8192)
+
+/* Type: decimal.
+ * Specifies the internal structure of the prime modulus.
+ */
+#define QTYPE_UNKNOWN		(0)
+#define QTYPE_UNSTRUCTURED	(1)
+#define QTYPE_SAFE		(2)
+#define QTYPE_SCHNORR		(3)
+#define QTYPE_SOPHIE_GERMAIN	(4)
+#define QTYPE_STRONG		(5)
+
+/* Tests: decimal (bit field).
+ * Specifies the methods used in checking for primality.
+ * Usually, more than one test is used.
+ */
+#define QTEST_UNTESTED		(0x00)
+#define QTEST_COMPOSITE		(0x01)
+#define QTEST_SIEVE		(0x02)
+#define QTEST_MILLER_RABIN	(0x04)
+#define QTEST_JACOBI		(0x08)
+#define QTEST_ELLIPTIC		(0x10)
+
+/*
+ * 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, QTYPE_SOPHIE_GERMAIN, QTEST_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, in) != NULL) {
+		int ll = strlen(lp);
+
+		count_in++;
+		if (ll < 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 & QTEST_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 QTYPE_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 QTYPE_UNSTRUCTURED:
+		case QTYPE_SAFE:
+		case QTYPE_SCHNORR:
+		case QTYPE_STRONG:
+		case QTYPE_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 & QTEST_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, QTYPE_SAFE, (in_tests | QTEST_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);
+}