1/* $OpenBSD: moduli.c,v 1.22 2010/11/10 01:33:07 djm Exp $ */
2/*
3 * Copyright 1994 Phil Karn <karn@qualcomm.com>
4 * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com>
5 * Copyright 2000 Niels Provos <provos@citi.umich.edu>
6 * All rights reserved.
7 *
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 * 1. Redistributions of source code must retain the above copyright
12 *    notice, this list of conditions and the following disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 *    notice, this list of conditions and the following disclaimer in the
15 *    documentation and/or other materials provided with the distribution.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27 */
28
29/*
30 * Two-step process to generate safe primes for DHGEX
31 *
32 *  Sieve candidates for "safe" primes,
33 *  suitable for use as Diffie-Hellman moduli;
34 *  that is, where q = (p-1)/2 is also prime.
35 *
36 * First step: generate candidate primes (memory intensive)
37 * Second step: test primes' safety (processor intensive)
38 */
39
40#include "includes.h"
41
42#include <sys/types.h>
43
44#include <openssl/bn.h>
45#include <openssl/dh.h>
46
47#include <stdio.h>
48#include <stdlib.h>
49#include <string.h>
50#include <stdarg.h>
51#include <time.h>
52
53#include "xmalloc.h"
54#include "dh.h"
55#include "log.h"
56
57#include "openbsd-compat/openssl-compat.h"
58
59/*
60 * File output defines
61 */
62
63/* need line long enough for largest moduli plus headers */
64#define QLINESIZE		(100+8192)
65
66/*
67 * Size: decimal.
68 * Specifies the number of the most significant bit (0 to M).
69 * WARNING: internally, usually 1 to N.
70 */
71#define QSIZE_MINIMUM		(511)
72
73/*
74 * Prime sieving defines
75 */
76
77/* Constant: assuming 8 bit bytes and 32 bit words */
78#define SHIFT_BIT	(3)
79#define SHIFT_BYTE	(2)
80#define SHIFT_WORD	(SHIFT_BIT+SHIFT_BYTE)
81#define SHIFT_MEGABYTE	(20)
82#define SHIFT_MEGAWORD	(SHIFT_MEGABYTE-SHIFT_BYTE)
83
84/*
85 * Using virtual memory can cause thrashing.  This should be the largest
86 * number that is supported without a large amount of disk activity --
87 * that would increase the run time from hours to days or weeks!
88 */
89#define LARGE_MINIMUM	(8UL)	/* megabytes */
90
91/*
92 * Do not increase this number beyond the unsigned integer bit size.
93 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
94 */
95#define LARGE_MAXIMUM	(127UL)	/* megabytes */
96
97/*
98 * Constant: when used with 32-bit integers, the largest sieve prime
99 * has to be less than 2**32.
100 */
101#define SMALL_MAXIMUM	(0xffffffffUL)
102
103/* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
104#define TINY_NUMBER	(1UL<<16)
105
106/* Ensure enough bit space for testing 2*q. */
107#define TEST_MAXIMUM	(1UL<<16)
108#define TEST_MINIMUM	(QSIZE_MINIMUM + 1)
109/* real TEST_MINIMUM	(1UL << (SHIFT_WORD - TEST_POWER)) */
110#define TEST_POWER	(3)	/* 2**n, n < SHIFT_WORD */
111
112/* bit operations on 32-bit words */
113#define BIT_CLEAR(a,n)	((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
114#define BIT_SET(a,n)	((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
115#define BIT_TEST(a,n)	((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
116
117/*
118 * Prime testing defines
119 */
120
121/* Minimum number of primality tests to perform */
122#define TRIAL_MINIMUM	(4)
123
124/*
125 * Sieving data (XXX - move to struct)
126 */
127
128/* sieve 2**16 */
129static u_int32_t *TinySieve, tinybits;
130
131/* sieve 2**30 in 2**16 parts */
132static u_int32_t *SmallSieve, smallbits, smallbase;
133
134/* sieve relative to the initial value */
135static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
136static u_int32_t largebits, largememory;	/* megabytes */
137static BIGNUM *largebase;
138
139int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
140int prime_test(FILE *, FILE *, u_int32_t, u_int32_t);
141
142/*
143 * print moduli out in consistent form,
144 */
145static int
146qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
147    u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
148{
149	struct tm *gtm;
150	time_t time_now;
151	int res;
152
153	time(&time_now);
154	gtm = gmtime(&time_now);
155
156	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
157	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
158	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
159	    otype, otests, otries, osize, ogenerator);
160
161	if (res < 0)
162		return (-1);
163
164	if (BN_print_fp(ofile, omodulus) < 1)
165		return (-1);
166
167	res = fprintf(ofile, "\n");
168	fflush(ofile);
169
170	return (res > 0 ? 0 : -1);
171}
172
173
174/*
175 ** Sieve p's and q's with small factors
176 */
177static void
178sieve_large(u_int32_t s)
179{
180	u_int32_t r, u;
181
182	debug3("sieve_large %u", s);
183	largetries++;
184	/* r = largebase mod s */
185	r = BN_mod_word(largebase, s);
186	if (r == 0)
187		u = 0; /* s divides into largebase exactly */
188	else
189		u = s - r; /* largebase+u is first entry divisible by s */
190
191	if (u < largebits * 2) {
192		/*
193		 * The sieve omits p's and q's divisible by 2, so ensure that
194		 * largebase+u is odd. Then, step through the sieve in
195		 * increments of 2*s
196		 */
197		if (u & 0x1)
198			u += s; /* Make largebase+u odd, and u even */
199
200		/* Mark all multiples of 2*s */
201		for (u /= 2; u < largebits; u += s)
202			BIT_SET(LargeSieve, u);
203	}
204
205	/* r = p mod s */
206	r = (2 * r + 1) % s;
207	if (r == 0)
208		u = 0; /* s divides p exactly */
209	else
210		u = s - r; /* p+u is first entry divisible by s */
211
212	if (u < largebits * 4) {
213		/*
214		 * The sieve omits p's divisible by 4, so ensure that
215		 * largebase+u is not. Then, step through the sieve in
216		 * increments of 4*s
217		 */
218		while (u & 0x3) {
219			if (SMALL_MAXIMUM - u < s)
220				return;
221			u += s;
222		}
223
224		/* Mark all multiples of 4*s */
225		for (u /= 4; u < largebits; u += s)
226			BIT_SET(LargeSieve, u);
227	}
228}
229
230/*
231 * list candidates for Sophie-Germain primes (where q = (p-1)/2)
232 * to standard output.
233 * The list is checked against small known primes (less than 2**30).
234 */
235int
236gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
237{
238	BIGNUM *q;
239	u_int32_t j, r, s, t;
240	u_int32_t smallwords = TINY_NUMBER >> 6;
241	u_int32_t tinywords = TINY_NUMBER >> 6;
242	time_t time_start, time_stop;
243	u_int32_t i;
244	int ret = 0;
245
246	largememory = memory;
247
248	if (memory != 0 &&
249	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
250		error("Invalid memory amount (min %ld, max %ld)",
251		    LARGE_MINIMUM, LARGE_MAXIMUM);
252		return (-1);
253	}
254
255	/*
256	 * Set power to the length in bits of the prime to be generated.
257	 * This is changed to 1 less than the desired safe prime moduli p.
258	 */
259	if (power > TEST_MAXIMUM) {
260		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
261		return (-1);
262	} else if (power < TEST_MINIMUM) {
263		error("Too few bits: %u < %u", power, TEST_MINIMUM);
264		return (-1);
265	}
266	power--; /* decrement before squaring */
267
268	/*
269	 * The density of ordinary primes is on the order of 1/bits, so the
270	 * density of safe primes should be about (1/bits)**2. Set test range
271	 * to something well above bits**2 to be reasonably sure (but not
272	 * guaranteed) of catching at least one safe prime.
273	 */
274	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
275
276	/*
277	 * Need idea of how much memory is available. We don't have to use all
278	 * of it.
279	 */
280	if (largememory > LARGE_MAXIMUM) {
281		logit("Limited memory: %u MB; limit %lu MB",
282		    largememory, LARGE_MAXIMUM);
283		largememory = LARGE_MAXIMUM;
284	}
285
286	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
287		logit("Increased memory: %u MB; need %u bytes",
288		    largememory, (largewords << SHIFT_BYTE));
289		largewords = (largememory << SHIFT_MEGAWORD);
290	} else if (largememory > 0) {
291		logit("Decreased memory: %u MB; want %u bytes",
292		    largememory, (largewords << SHIFT_BYTE));
293		largewords = (largememory << SHIFT_MEGAWORD);
294	}
295
296	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
297	tinybits = tinywords << SHIFT_WORD;
298
299	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
300	smallbits = smallwords << SHIFT_WORD;
301
302	/*
303	 * dynamically determine available memory
304	 */
305	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
306		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
307
308	largebits = largewords << SHIFT_WORD;
309	largenumbers = largebits * 2;	/* even numbers excluded */
310
311	/* validation check: count the number of primes tried */
312	largetries = 0;
313	if ((q = BN_new()) == NULL)
314		fatal("BN_new failed");
315
316	/*
317	 * Generate random starting point for subprime search, or use
318	 * specified parameter.
319	 */
320	if ((largebase = BN_new()) == NULL)
321		fatal("BN_new failed");
322	if (start == NULL) {
323		if (BN_rand(largebase, power, 1, 1) == 0)
324			fatal("BN_rand failed");
325	} else {
326		if (BN_copy(largebase, start) == NULL)
327			fatal("BN_copy: failed");
328	}
329
330	/* ensure odd */
331	if (BN_set_bit(largebase, 0) == 0)
332		fatal("BN_set_bit: failed");
333
334	time(&time_start);
335
336	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
337	    largenumbers, power);
338	debug2("start point: 0x%s", BN_bn2hex(largebase));
339
340	/*
341	 * TinySieve
342	 */
343	for (i = 0; i < tinybits; i++) {
344		if (BIT_TEST(TinySieve, i))
345			continue; /* 2*i+3 is composite */
346
347		/* The next tiny prime */
348		t = 2 * i + 3;
349
350		/* Mark all multiples of t */
351		for (j = i + t; j < tinybits; j += t)
352			BIT_SET(TinySieve, j);
353
354		sieve_large(t);
355	}
356
357	/*
358	 * Start the small block search at the next possible prime. To avoid
359	 * fencepost errors, the last pass is skipped.
360	 */
361	for (smallbase = TINY_NUMBER + 3;
362	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
363	    smallbase += TINY_NUMBER) {
364		for (i = 0; i < tinybits; i++) {
365			if (BIT_TEST(TinySieve, i))
366				continue; /* 2*i+3 is composite */
367
368			/* The next tiny prime */
369			t = 2 * i + 3;
370			r = smallbase % t;
371
372			if (r == 0) {
373				s = 0; /* t divides into smallbase exactly */
374			} else {
375				/* smallbase+s is first entry divisible by t */
376				s = t - r;
377			}
378
379			/*
380			 * The sieve omits even numbers, so ensure that
381			 * smallbase+s is odd. Then, step through the sieve
382			 * in increments of 2*t
383			 */
384			if (s & 1)
385				s += t; /* Make smallbase+s odd, and s even */
386
387			/* Mark all multiples of 2*t */
388			for (s /= 2; s < smallbits; s += t)
389				BIT_SET(SmallSieve, s);
390		}
391
392		/*
393		 * SmallSieve
394		 */
395		for (i = 0; i < smallbits; i++) {
396			if (BIT_TEST(SmallSieve, i))
397				continue; /* 2*i+smallbase is composite */
398
399			/* The next small prime */
400			sieve_large((2 * i) + smallbase);
401		}
402
403		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
404	}
405
406	time(&time_stop);
407
408	logit("%.24s Sieved with %u small primes in %ld seconds",
409	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
410
411	for (j = r = 0; j < largebits; j++) {
412		if (BIT_TEST(LargeSieve, j))
413			continue; /* Definitely composite, skip */
414
415		debug2("test q = largebase+%u", 2 * j);
416		if (BN_set_word(q, 2 * j) == 0)
417			fatal("BN_set_word failed");
418		if (BN_add(q, q, largebase) == 0)
419			fatal("BN_add failed");
420		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
421		    MODULI_TESTS_SIEVE, largetries,
422		    (power - 1) /* MSB */, (0), q) == -1) {
423			ret = -1;
424			break;
425		}
426
427		r++; /* count q */
428	}
429
430	time(&time_stop);
431
432	xfree(LargeSieve);
433	xfree(SmallSieve);
434	xfree(TinySieve);
435
436	logit("%.24s Found %u candidates", ctime(&time_stop), r);
437
438	return (ret);
439}
440
441/*
442 * perform a Miller-Rabin primality test
443 * on the list of candidates
444 * (checking both q and p)
445 * The result is a list of so-call "safe" primes
446 */
447int
448prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted)
449{
450	BIGNUM *q, *p, *a;
451	BN_CTX *ctx;
452	char *cp, *lp;
453	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
454	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
455	time_t time_start, time_stop;
456	int res;
457
458	if (trials < TRIAL_MINIMUM) {
459		error("Minimum primality trials is %d", TRIAL_MINIMUM);
460		return (-1);
461	}
462
463	time(&time_start);
464
465	if ((p = BN_new()) == NULL)
466		fatal("BN_new failed");
467	if ((q = BN_new()) == NULL)
468		fatal("BN_new failed");
469	if ((ctx = BN_CTX_new()) == NULL)
470		fatal("BN_CTX_new failed");
471
472	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
473	    ctime(&time_start), trials, generator_wanted);
474
475	res = 0;
476	lp = xmalloc(QLINESIZE + 1);
477	while (fgets(lp, QLINESIZE + 1, in) != NULL) {
478		count_in++;
479		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
480			debug2("%10u: comment or short line", count_in);
481			continue;
482		}
483
484		/* XXX - fragile parser */
485		/* time */
486		cp = &lp[14];	/* (skip) */
487
488		/* type */
489		in_type = strtoul(cp, &cp, 10);
490
491		/* tests */
492		in_tests = strtoul(cp, &cp, 10);
493
494		if (in_tests & MODULI_TESTS_COMPOSITE) {
495			debug2("%10u: known composite", count_in);
496			continue;
497		}
498
499		/* tries */
500		in_tries = strtoul(cp, &cp, 10);
501
502		/* size (most significant bit) */
503		in_size = strtoul(cp, &cp, 10);
504
505		/* generator (hex) */
506		generator_known = strtoul(cp, &cp, 16);
507
508		/* Skip white space */
509		cp += strspn(cp, " ");
510
511		/* modulus (hex) */
512		switch (in_type) {
513		case MODULI_TYPE_SOPHIE_GERMAIN:
514			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
515			a = q;
516			if (BN_hex2bn(&a, cp) == 0)
517				fatal("BN_hex2bn failed");
518			/* p = 2*q + 1 */
519			if (BN_lshift(p, q, 1) == 0)
520				fatal("BN_lshift failed");
521			if (BN_add_word(p, 1) == 0)
522				fatal("BN_add_word failed");
523			in_size += 1;
524			generator_known = 0;
525			break;
526		case MODULI_TYPE_UNSTRUCTURED:
527		case MODULI_TYPE_SAFE:
528		case MODULI_TYPE_SCHNORR:
529		case MODULI_TYPE_STRONG:
530		case MODULI_TYPE_UNKNOWN:
531			debug2("%10u: (%u)", count_in, in_type);
532			a = p;
533			if (BN_hex2bn(&a, cp) == 0)
534				fatal("BN_hex2bn failed");
535			/* q = (p-1) / 2 */
536			if (BN_rshift(q, p, 1) == 0)
537				fatal("BN_rshift failed");
538			break;
539		default:
540			debug2("Unknown prime type");
541			break;
542		}
543
544		/*
545		 * due to earlier inconsistencies in interpretation, check
546		 * the proposed bit size.
547		 */
548		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
549			debug2("%10u: bit size %u mismatch", count_in, in_size);
550			continue;
551		}
552		if (in_size < QSIZE_MINIMUM) {
553			debug2("%10u: bit size %u too short", count_in, in_size);
554			continue;
555		}
556
557		if (in_tests & MODULI_TESTS_MILLER_RABIN)
558			in_tries += trials;
559		else
560			in_tries = trials;
561
562		/*
563		 * guess unknown generator
564		 */
565		if (generator_known == 0) {
566			if (BN_mod_word(p, 24) == 11)
567				generator_known = 2;
568			else if (BN_mod_word(p, 12) == 5)
569				generator_known = 3;
570			else {
571				u_int32_t r = BN_mod_word(p, 10);
572
573				if (r == 3 || r == 7)
574					generator_known = 5;
575			}
576		}
577		/*
578		 * skip tests when desired generator doesn't match
579		 */
580		if (generator_wanted > 0 &&
581		    generator_wanted != generator_known) {
582			debug2("%10u: generator %d != %d",
583			    count_in, generator_known, generator_wanted);
584			continue;
585		}
586
587		/*
588		 * Primes with no known generator are useless for DH, so
589		 * skip those.
590		 */
591		if (generator_known == 0) {
592			debug2("%10u: no known generator", count_in);
593			continue;
594		}
595
596		count_possible++;
597
598		/*
599		 * The (1/4)^N performance bound on Miller-Rabin is
600		 * extremely pessimistic, so don't spend a lot of time
601		 * really verifying that q is prime until after we know
602		 * that p is also prime. A single pass will weed out the
603		 * vast majority of composite q's.
604		 */
605		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
606			debug("%10u: q failed first possible prime test",
607			    count_in);
608			continue;
609		}
610
611		/*
612		 * q is possibly prime, so go ahead and really make sure
613		 * that p is prime. If it is, then we can go back and do
614		 * the same for q. If p is composite, chances are that
615		 * will show up on the first Rabin-Miller iteration so it
616		 * doesn't hurt to specify a high iteration count.
617		 */
618		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
619			debug("%10u: p is not prime", count_in);
620			continue;
621		}
622		debug("%10u: p is almost certainly prime", count_in);
623
624		/* recheck q more rigorously */
625		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
626			debug("%10u: q is not prime", count_in);
627			continue;
628		}
629		debug("%10u: q is almost certainly prime", count_in);
630
631		if (qfileout(out, MODULI_TYPE_SAFE,
632		    in_tests | MODULI_TESTS_MILLER_RABIN,
633		    in_tries, in_size, generator_known, p)) {
634			res = -1;
635			break;
636		}
637
638		count_out++;
639	}
640
641	time(&time_stop);
642	xfree(lp);
643	BN_free(p);
644	BN_free(q);
645	BN_CTX_free(ctx);
646
647	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
648	    ctime(&time_stop), count_out, count_possible,
649	    (long) (time_stop - time_start));
650
651	return (res);
652}
653