xref: /openbsd/usr.bin/ssh/moduli.c (revision 91f110e0)
1 /* $OpenBSD: moduli.c,v 1.28 2013/10/24 00:49:49 dtucker 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 <sys/param.h>
41 #include <sys/types.h>
42 
43 #include <openssl/bn.h>
44 #include <openssl/dh.h>
45 
46 #include <errno.h>
47 #include <stdio.h>
48 #include <stdlib.h>
49 #include <string.h>
50 #include <stdarg.h>
51 #include <time.h>
52 #include <unistd.h>
53 
54 #include "xmalloc.h"
55 #include "dh.h"
56 #include "log.h"
57 #include "misc.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 */
129 static u_int32_t *TinySieve, tinybits;
130 
131 /* sieve 2**30 in 2**16 parts */
132 static u_int32_t *SmallSieve, smallbits, smallbase;
133 
134 /* sieve relative to the initial value */
135 static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
136 static u_int32_t largebits, largememory;	/* megabytes */
137 static BIGNUM *largebase;
138 
139 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
140 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
141     unsigned long);
142 
143 /*
144  * print moduli out in consistent form,
145  */
146 static int
147 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
148     u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
149 {
150 	struct tm *gtm;
151 	time_t time_now;
152 	int res;
153 
154 	time(&time_now);
155 	gtm = gmtime(&time_now);
156 
157 	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
158 	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
159 	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
160 	    otype, otests, otries, osize, ogenerator);
161 
162 	if (res < 0)
163 		return (-1);
164 
165 	if (BN_print_fp(ofile, omodulus) < 1)
166 		return (-1);
167 
168 	res = fprintf(ofile, "\n");
169 	fflush(ofile);
170 
171 	return (res > 0 ? 0 : -1);
172 }
173 
174 
175 /*
176  ** Sieve p's and q's with small factors
177  */
178 static void
179 sieve_large(u_int32_t s)
180 {
181 	u_int32_t r, u;
182 
183 	debug3("sieve_large %u", s);
184 	largetries++;
185 	/* r = largebase mod s */
186 	r = BN_mod_word(largebase, s);
187 	if (r == 0)
188 		u = 0; /* s divides into largebase exactly */
189 	else
190 		u = s - r; /* largebase+u is first entry divisible by s */
191 
192 	if (u < largebits * 2) {
193 		/*
194 		 * The sieve omits p's and q's divisible by 2, so ensure that
195 		 * largebase+u is odd. Then, step through the sieve in
196 		 * increments of 2*s
197 		 */
198 		if (u & 0x1)
199 			u += s; /* Make largebase+u odd, and u even */
200 
201 		/* Mark all multiples of 2*s */
202 		for (u /= 2; u < largebits; u += s)
203 			BIT_SET(LargeSieve, u);
204 	}
205 
206 	/* r = p mod s */
207 	r = (2 * r + 1) % s;
208 	if (r == 0)
209 		u = 0; /* s divides p exactly */
210 	else
211 		u = s - r; /* p+u is first entry divisible by s */
212 
213 	if (u < largebits * 4) {
214 		/*
215 		 * The sieve omits p's divisible by 4, so ensure that
216 		 * largebase+u is not. Then, step through the sieve in
217 		 * increments of 4*s
218 		 */
219 		while (u & 0x3) {
220 			if (SMALL_MAXIMUM - u < s)
221 				return;
222 			u += s;
223 		}
224 
225 		/* Mark all multiples of 4*s */
226 		for (u /= 4; u < largebits; u += s)
227 			BIT_SET(LargeSieve, u);
228 	}
229 }
230 
231 /*
232  * list candidates for Sophie-Germain primes (where q = (p-1)/2)
233  * to standard output.
234  * The list is checked against small known primes (less than 2**30).
235  */
236 int
237 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
238 {
239 	BIGNUM *q;
240 	u_int32_t j, r, s, t;
241 	u_int32_t smallwords = TINY_NUMBER >> 6;
242 	u_int32_t tinywords = TINY_NUMBER >> 6;
243 	time_t time_start, time_stop;
244 	u_int32_t i;
245 	int ret = 0;
246 
247 	largememory = memory;
248 
249 	if (memory != 0 &&
250 	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
251 		error("Invalid memory amount (min %ld, max %ld)",
252 		    LARGE_MINIMUM, LARGE_MAXIMUM);
253 		return (-1);
254 	}
255 
256 	/*
257 	 * Set power to the length in bits of the prime to be generated.
258 	 * This is changed to 1 less than the desired safe prime moduli p.
259 	 */
260 	if (power > TEST_MAXIMUM) {
261 		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
262 		return (-1);
263 	} else if (power < TEST_MINIMUM) {
264 		error("Too few bits: %u < %u", power, TEST_MINIMUM);
265 		return (-1);
266 	}
267 	power--; /* decrement before squaring */
268 
269 	/*
270 	 * The density of ordinary primes is on the order of 1/bits, so the
271 	 * density of safe primes should be about (1/bits)**2. Set test range
272 	 * to something well above bits**2 to be reasonably sure (but not
273 	 * guaranteed) of catching at least one safe prime.
274 	 */
275 	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
276 
277 	/*
278 	 * Need idea of how much memory is available. We don't have to use all
279 	 * of it.
280 	 */
281 	if (largememory > LARGE_MAXIMUM) {
282 		logit("Limited memory: %u MB; limit %lu MB",
283 		    largememory, LARGE_MAXIMUM);
284 		largememory = LARGE_MAXIMUM;
285 	}
286 
287 	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
288 		logit("Increased memory: %u MB; need %u bytes",
289 		    largememory, (largewords << SHIFT_BYTE));
290 		largewords = (largememory << SHIFT_MEGAWORD);
291 	} else if (largememory > 0) {
292 		logit("Decreased memory: %u MB; want %u bytes",
293 		    largememory, (largewords << SHIFT_BYTE));
294 		largewords = (largememory << SHIFT_MEGAWORD);
295 	}
296 
297 	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
298 	tinybits = tinywords << SHIFT_WORD;
299 
300 	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
301 	smallbits = smallwords << SHIFT_WORD;
302 
303 	/*
304 	 * dynamically determine available memory
305 	 */
306 	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
307 		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
308 
309 	largebits = largewords << SHIFT_WORD;
310 	largenumbers = largebits * 2;	/* even numbers excluded */
311 
312 	/* validation check: count the number of primes tried */
313 	largetries = 0;
314 	if ((q = BN_new()) == NULL)
315 		fatal("BN_new failed");
316 
317 	/*
318 	 * Generate random starting point for subprime search, or use
319 	 * specified parameter.
320 	 */
321 	if ((largebase = BN_new()) == NULL)
322 		fatal("BN_new failed");
323 	if (start == NULL) {
324 		if (BN_rand(largebase, power, 1, 1) == 0)
325 			fatal("BN_rand failed");
326 	} else {
327 		if (BN_copy(largebase, start) == NULL)
328 			fatal("BN_copy: failed");
329 	}
330 
331 	/* ensure odd */
332 	if (BN_set_bit(largebase, 0) == 0)
333 		fatal("BN_set_bit: failed");
334 
335 	time(&time_start);
336 
337 	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
338 	    largenumbers, power);
339 	debug2("start point: 0x%s", BN_bn2hex(largebase));
340 
341 	/*
342 	 * TinySieve
343 	 */
344 	for (i = 0; i < tinybits; i++) {
345 		if (BIT_TEST(TinySieve, i))
346 			continue; /* 2*i+3 is composite */
347 
348 		/* The next tiny prime */
349 		t = 2 * i + 3;
350 
351 		/* Mark all multiples of t */
352 		for (j = i + t; j < tinybits; j += t)
353 			BIT_SET(TinySieve, j);
354 
355 		sieve_large(t);
356 	}
357 
358 	/*
359 	 * Start the small block search at the next possible prime. To avoid
360 	 * fencepost errors, the last pass is skipped.
361 	 */
362 	for (smallbase = TINY_NUMBER + 3;
363 	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
364 	    smallbase += TINY_NUMBER) {
365 		for (i = 0; i < tinybits; i++) {
366 			if (BIT_TEST(TinySieve, i))
367 				continue; /* 2*i+3 is composite */
368 
369 			/* The next tiny prime */
370 			t = 2 * i + 3;
371 			r = smallbase % t;
372 
373 			if (r == 0) {
374 				s = 0; /* t divides into smallbase exactly */
375 			} else {
376 				/* smallbase+s is first entry divisible by t */
377 				s = t - r;
378 			}
379 
380 			/*
381 			 * The sieve omits even numbers, so ensure that
382 			 * smallbase+s is odd. Then, step through the sieve
383 			 * in increments of 2*t
384 			 */
385 			if (s & 1)
386 				s += t; /* Make smallbase+s odd, and s even */
387 
388 			/* Mark all multiples of 2*t */
389 			for (s /= 2; s < smallbits; s += t)
390 				BIT_SET(SmallSieve, s);
391 		}
392 
393 		/*
394 		 * SmallSieve
395 		 */
396 		for (i = 0; i < smallbits; i++) {
397 			if (BIT_TEST(SmallSieve, i))
398 				continue; /* 2*i+smallbase is composite */
399 
400 			/* The next small prime */
401 			sieve_large((2 * i) + smallbase);
402 		}
403 
404 		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
405 	}
406 
407 	time(&time_stop);
408 
409 	logit("%.24s Sieved with %u small primes in %ld seconds",
410 	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
411 
412 	for (j = r = 0; j < largebits; j++) {
413 		if (BIT_TEST(LargeSieve, j))
414 			continue; /* Definitely composite, skip */
415 
416 		debug2("test q = largebase+%u", 2 * j);
417 		if (BN_set_word(q, 2 * j) == 0)
418 			fatal("BN_set_word failed");
419 		if (BN_add(q, q, largebase) == 0)
420 			fatal("BN_add failed");
421 		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
422 		    MODULI_TESTS_SIEVE, largetries,
423 		    (power - 1) /* MSB */, (0), q) == -1) {
424 			ret = -1;
425 			break;
426 		}
427 
428 		r++; /* count q */
429 	}
430 
431 	time(&time_stop);
432 
433 	free(LargeSieve);
434 	free(SmallSieve);
435 	free(TinySieve);
436 
437 	logit("%.24s Found %u candidates", ctime(&time_stop), r);
438 
439 	return (ret);
440 }
441 
442 static void
443 write_checkpoint(char *cpfile, u_int32_t lineno)
444 {
445 	FILE *fp;
446 	char tmp[MAXPATHLEN];
447 	int r;
448 
449 	r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
450 	if (r == -1 || r >= MAXPATHLEN) {
451 		logit("write_checkpoint: temp pathname too long");
452 		return;
453 	}
454 	if ((r = mkstemp(tmp)) == -1) {
455 		logit("mkstemp(%s): %s", tmp, strerror(errno));
456 		return;
457 	}
458 	if ((fp = fdopen(r, "w")) == NULL) {
459 		logit("write_checkpoint: fdopen: %s", strerror(errno));
460 		close(r);
461 		return;
462 	}
463 	if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0
464 	    && rename(tmp, cpfile) == 0)
465 		debug3("wrote checkpoint line %lu to '%s'",
466 		    (unsigned long)lineno, cpfile);
467 	else
468 		logit("failed to write to checkpoint file '%s': %s", cpfile,
469 		    strerror(errno));
470 }
471 
472 static unsigned long
473 read_checkpoint(char *cpfile)
474 {
475 	FILE *fp;
476 	unsigned long lineno = 0;
477 
478 	if ((fp = fopen(cpfile, "r")) == NULL)
479 		return 0;
480 	if (fscanf(fp, "%lu\n", &lineno) < 1)
481 		logit("Failed to load checkpoint from '%s'", cpfile);
482 	else
483 		logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
484 	fclose(fp);
485 	return lineno;
486 }
487 
488 static unsigned long
489 count_lines(FILE *f)
490 {
491 	unsigned long count = 0;
492 	char lp[QLINESIZE + 1];
493 
494 	if (fseek(f, 0, SEEK_SET) != 0) {
495 		debug("input file is not seekable");
496 		return ULONG_MAX;
497 	}
498 	while (fgets(lp, QLINESIZE + 1, f) != NULL)
499 		count++;
500 	rewind(f);
501 	debug("input file has %lu lines", count);
502 	return count;
503 }
504 
505 static char *
506 fmt_time(time_t seconds)
507 {
508 	int day, hr, min;
509 	static char buf[128];
510 
511 	min = (seconds / 60) % 60;
512 	hr = (seconds / 60 / 60) % 24;
513 	day = seconds / 60 / 60 / 24;
514 	if (day > 0)
515 		snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min);
516 	else
517 		snprintf(buf, sizeof buf, "%d:%02d", hr, min);
518 	return buf;
519 }
520 
521 static void
522 print_progress(unsigned long start_lineno, unsigned long current_lineno,
523     unsigned long end_lineno)
524 {
525 	static time_t time_start, time_prev;
526 	time_t time_now, elapsed;
527 	unsigned long num_to_process, processed, remaining, percent, eta;
528 	double time_per_line;
529 	char *eta_str;
530 
531 	time_now = monotime();
532 	if (time_start == 0) {
533 		time_start = time_prev = time_now;
534 		return;
535 	}
536 	/* print progress after 1m then once per 5m */
537 	if (time_now - time_prev < 5 * 60)
538 		return;
539 	time_prev = time_now;
540 	elapsed = time_now - time_start;
541 	processed = current_lineno - start_lineno;
542 	remaining = end_lineno - current_lineno;
543 	num_to_process = end_lineno - start_lineno;
544 	time_per_line = (double)elapsed / processed;
545 	/* if we don't know how many we're processing just report count+time */
546 	time(&time_now);
547 	if (end_lineno == ULONG_MAX) {
548 		logit("%.24s processed %lu in %s", ctime(&time_now),
549 		    processed, fmt_time(elapsed));
550 		return;
551 	}
552 	percent = 100 * processed / num_to_process;
553 	eta = time_per_line * remaining;
554 	eta_str = xstrdup(fmt_time(eta));
555 	logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s",
556 	    ctime(&time_now), processed, num_to_process, percent,
557 	    fmt_time(elapsed), eta_str);
558 	free(eta_str);
559 }
560 
561 /*
562  * perform a Miller-Rabin primality test
563  * on the list of candidates
564  * (checking both q and p)
565  * The result is a list of so-call "safe" primes
566  */
567 int
568 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
569     char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
570 {
571 	BIGNUM *q, *p, *a;
572 	BN_CTX *ctx;
573 	char *cp, *lp;
574 	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
575 	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
576 	unsigned long last_processed = 0, end_lineno;
577 	time_t time_start, time_stop;
578 	int res;
579 
580 	if (trials < TRIAL_MINIMUM) {
581 		error("Minimum primality trials is %d", TRIAL_MINIMUM);
582 		return (-1);
583 	}
584 
585 	if (num_lines == 0)
586 		end_lineno = count_lines(in);
587 	else
588 		end_lineno = start_lineno + num_lines;
589 
590 	time(&time_start);
591 
592 	if ((p = BN_new()) == NULL)
593 		fatal("BN_new failed");
594 	if ((q = BN_new()) == NULL)
595 		fatal("BN_new failed");
596 	if ((ctx = BN_CTX_new()) == NULL)
597 		fatal("BN_CTX_new failed");
598 
599 	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
600 	    ctime(&time_start), trials, generator_wanted);
601 
602 	if (checkpoint_file != NULL)
603 		last_processed = read_checkpoint(checkpoint_file);
604 	last_processed = start_lineno = MAX(last_processed, start_lineno);
605 	if (end_lineno == ULONG_MAX)
606 		debug("process from line %lu from pipe", last_processed);
607 	else
608 		debug("process from line %lu to line %lu", last_processed,
609 		    end_lineno);
610 
611 	res = 0;
612 	lp = xmalloc(QLINESIZE + 1);
613 	while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
614 		count_in++;
615 		if (count_in <= last_processed) {
616 			debug3("skipping line %u, before checkpoint or "
617 			    "specified start line", count_in);
618 			continue;
619 		}
620 		if (checkpoint_file != NULL)
621 			write_checkpoint(checkpoint_file, count_in);
622 		print_progress(start_lineno, count_in, end_lineno);
623 		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
624 			debug2("%10u: comment or short line", count_in);
625 			continue;
626 		}
627 
628 		/* XXX - fragile parser */
629 		/* time */
630 		cp = &lp[14];	/* (skip) */
631 
632 		/* type */
633 		in_type = strtoul(cp, &cp, 10);
634 
635 		/* tests */
636 		in_tests = strtoul(cp, &cp, 10);
637 
638 		if (in_tests & MODULI_TESTS_COMPOSITE) {
639 			debug2("%10u: known composite", count_in);
640 			continue;
641 		}
642 
643 		/* tries */
644 		in_tries = strtoul(cp, &cp, 10);
645 
646 		/* size (most significant bit) */
647 		in_size = strtoul(cp, &cp, 10);
648 
649 		/* generator (hex) */
650 		generator_known = strtoul(cp, &cp, 16);
651 
652 		/* Skip white space */
653 		cp += strspn(cp, " ");
654 
655 		/* modulus (hex) */
656 		switch (in_type) {
657 		case MODULI_TYPE_SOPHIE_GERMAIN:
658 			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
659 			a = q;
660 			if (BN_hex2bn(&a, cp) == 0)
661 				fatal("BN_hex2bn failed");
662 			/* p = 2*q + 1 */
663 			if (BN_lshift(p, q, 1) == 0)
664 				fatal("BN_lshift failed");
665 			if (BN_add_word(p, 1) == 0)
666 				fatal("BN_add_word failed");
667 			in_size += 1;
668 			generator_known = 0;
669 			break;
670 		case MODULI_TYPE_UNSTRUCTURED:
671 		case MODULI_TYPE_SAFE:
672 		case MODULI_TYPE_SCHNORR:
673 		case MODULI_TYPE_STRONG:
674 		case MODULI_TYPE_UNKNOWN:
675 			debug2("%10u: (%u)", count_in, in_type);
676 			a = p;
677 			if (BN_hex2bn(&a, cp) == 0)
678 				fatal("BN_hex2bn failed");
679 			/* q = (p-1) / 2 */
680 			if (BN_rshift(q, p, 1) == 0)
681 				fatal("BN_rshift failed");
682 			break;
683 		default:
684 			debug2("Unknown prime type");
685 			break;
686 		}
687 
688 		/*
689 		 * due to earlier inconsistencies in interpretation, check
690 		 * the proposed bit size.
691 		 */
692 		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
693 			debug2("%10u: bit size %u mismatch", count_in, in_size);
694 			continue;
695 		}
696 		if (in_size < QSIZE_MINIMUM) {
697 			debug2("%10u: bit size %u too short", count_in, in_size);
698 			continue;
699 		}
700 
701 		if (in_tests & MODULI_TESTS_MILLER_RABIN)
702 			in_tries += trials;
703 		else
704 			in_tries = trials;
705 
706 		/*
707 		 * guess unknown generator
708 		 */
709 		if (generator_known == 0) {
710 			if (BN_mod_word(p, 24) == 11)
711 				generator_known = 2;
712 			else if (BN_mod_word(p, 12) == 5)
713 				generator_known = 3;
714 			else {
715 				u_int32_t r = BN_mod_word(p, 10);
716 
717 				if (r == 3 || r == 7)
718 					generator_known = 5;
719 			}
720 		}
721 		/*
722 		 * skip tests when desired generator doesn't match
723 		 */
724 		if (generator_wanted > 0 &&
725 		    generator_wanted != generator_known) {
726 			debug2("%10u: generator %d != %d",
727 			    count_in, generator_known, generator_wanted);
728 			continue;
729 		}
730 
731 		/*
732 		 * Primes with no known generator are useless for DH, so
733 		 * skip those.
734 		 */
735 		if (generator_known == 0) {
736 			debug2("%10u: no known generator", count_in);
737 			continue;
738 		}
739 
740 		count_possible++;
741 
742 		/*
743 		 * The (1/4)^N performance bound on Miller-Rabin is
744 		 * extremely pessimistic, so don't spend a lot of time
745 		 * really verifying that q is prime until after we know
746 		 * that p is also prime. A single pass will weed out the
747 		 * vast majority of composite q's.
748 		 */
749 		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
750 			debug("%10u: q failed first possible prime test",
751 			    count_in);
752 			continue;
753 		}
754 
755 		/*
756 		 * q is possibly prime, so go ahead and really make sure
757 		 * that p is prime. If it is, then we can go back and do
758 		 * the same for q. If p is composite, chances are that
759 		 * will show up on the first Rabin-Miller iteration so it
760 		 * doesn't hurt to specify a high iteration count.
761 		 */
762 		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
763 			debug("%10u: p is not prime", count_in);
764 			continue;
765 		}
766 		debug("%10u: p is almost certainly prime", count_in);
767 
768 		/* recheck q more rigorously */
769 		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
770 			debug("%10u: q is not prime", count_in);
771 			continue;
772 		}
773 		debug("%10u: q is almost certainly prime", count_in);
774 
775 		if (qfileout(out, MODULI_TYPE_SAFE,
776 		    in_tests | MODULI_TESTS_MILLER_RABIN,
777 		    in_tries, in_size, generator_known, p)) {
778 			res = -1;
779 			break;
780 		}
781 
782 		count_out++;
783 	}
784 
785 	time(&time_stop);
786 	free(lp);
787 	BN_free(p);
788 	BN_free(q);
789 	BN_CTX_free(ctx);
790 
791 	if (checkpoint_file != NULL)
792 		unlink(checkpoint_file);
793 
794 	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
795 	    ctime(&time_stop), count_out, count_possible,
796 	    (long) (time_stop - time_start));
797 
798 	return (res);
799 }
800