xref: /freebsd/crypto/openssh/moduli.c (revision 27c43fe1f3795622c5bd4bbfc465a29a800c0799)
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 "includes.h"
41 
42 #include <sys/param.h>
43 #include <sys/types.h>
44 
45 #include <openssl/bn.h>
46 #include <openssl/dh.h>
47 
48 #include <errno.h>
49 #include <stdio.h>
50 #include <stdlib.h>
51 #include <string.h>
52 #include <stdarg.h>
53 #include <time.h>
54 #include <unistd.h>
55 
56 #include "xmalloc.h"
57 #include "dh.h"
58 #include "log.h"
59 #include "misc.h"
60 
61 #include "openbsd-compat/openssl-compat.h"
62 
63 /*
64  * File output defines
65  */
66 
67 /* need line long enough for largest moduli plus headers */
68 #define QLINESIZE		(100+8192)
69 
70 /*
71  * Size: decimal.
72  * Specifies the number of the most significant bit (0 to M).
73  * WARNING: internally, usually 1 to N.
74  */
75 #define QSIZE_MINIMUM		(511)
76 
77 /*
78  * Prime sieving defines
79  */
80 
81 /* Constant: assuming 8 bit bytes and 32 bit words */
82 #define SHIFT_BIT	(3)
83 #define SHIFT_BYTE	(2)
84 #define SHIFT_WORD	(SHIFT_BIT+SHIFT_BYTE)
85 #define SHIFT_MEGABYTE	(20)
86 #define SHIFT_MEGAWORD	(SHIFT_MEGABYTE-SHIFT_BYTE)
87 
88 /*
89  * Using virtual memory can cause thrashing.  This should be the largest
90  * number that is supported without a large amount of disk activity --
91  * that would increase the run time from hours to days or weeks!
92  */
93 #define LARGE_MINIMUM	(8UL)	/* megabytes */
94 
95 /*
96  * Do not increase this number beyond the unsigned integer bit size.
97  * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
98  */
99 #define LARGE_MAXIMUM	(127UL)	/* megabytes */
100 
101 /*
102  * Constant: when used with 32-bit integers, the largest sieve prime
103  * has to be less than 2**32.
104  */
105 #define SMALL_MAXIMUM	(0xffffffffUL)
106 
107 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
108 #define TINY_NUMBER	(1UL<<16)
109 
110 /* Ensure enough bit space for testing 2*q. */
111 #define TEST_MAXIMUM	(1UL<<16)
112 #define TEST_MINIMUM	(QSIZE_MINIMUM + 1)
113 /* real TEST_MINIMUM	(1UL << (SHIFT_WORD - TEST_POWER)) */
114 #define TEST_POWER	(3)	/* 2**n, n < SHIFT_WORD */
115 
116 /* bit operations on 32-bit words */
117 #define BIT_CLEAR(a,n)	((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
118 #define BIT_SET(a,n)	((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
119 #define BIT_TEST(a,n)	((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
120 
121 /*
122  * Prime testing defines
123  */
124 
125 /* Minimum number of primality tests to perform */
126 #define TRIAL_MINIMUM	(4)
127 
128 /*
129  * Sieving data (XXX - move to struct)
130  */
131 
132 /* sieve 2**16 */
133 static u_int32_t *TinySieve, tinybits;
134 
135 /* sieve 2**30 in 2**16 parts */
136 static u_int32_t *SmallSieve, smallbits, smallbase;
137 
138 /* sieve relative to the initial value */
139 static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
140 static u_int32_t largebits, largememory;	/* megabytes */
141 static BIGNUM *largebase;
142 
143 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
144 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
145     unsigned long);
146 
147 /*
148  * print moduli out in consistent form,
149  */
150 static int
151 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
152     u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
153 {
154 	struct tm *gtm;
155 	time_t time_now;
156 	int res;
157 
158 	time(&time_now);
159 	gtm = gmtime(&time_now);
160 
161 	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
162 	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
163 	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
164 	    otype, otests, otries, osize, ogenerator);
165 
166 	if (res < 0)
167 		return (-1);
168 
169 	if (BN_print_fp(ofile, omodulus) < 1)
170 		return (-1);
171 
172 	res = fprintf(ofile, "\n");
173 	fflush(ofile);
174 
175 	return (res > 0 ? 0 : -1);
176 }
177 
178 
179 /*
180  ** Sieve p's and q's with small factors
181  */
182 static void
183 sieve_large(u_int32_t s)
184 {
185 	u_int32_t r, u;
186 
187 	debug3("sieve_large %u", s);
188 	largetries++;
189 	/* r = largebase mod s */
190 	r = BN_mod_word(largebase, s);
191 	if (r == 0)
192 		u = 0; /* s divides into largebase exactly */
193 	else
194 		u = s - r; /* largebase+u is first entry divisible by s */
195 
196 	if (u < largebits * 2) {
197 		/*
198 		 * The sieve omits p's and q's divisible by 2, so ensure that
199 		 * largebase+u is odd. Then, step through the sieve in
200 		 * increments of 2*s
201 		 */
202 		if (u & 0x1)
203 			u += s; /* Make largebase+u odd, and u even */
204 
205 		/* Mark all multiples of 2*s */
206 		for (u /= 2; u < largebits; u += s)
207 			BIT_SET(LargeSieve, u);
208 	}
209 
210 	/* r = p mod s */
211 	r = (2 * r + 1) % s;
212 	if (r == 0)
213 		u = 0; /* s divides p exactly */
214 	else
215 		u = s - r; /* p+u is first entry divisible by s */
216 
217 	if (u < largebits * 4) {
218 		/*
219 		 * The sieve omits p's divisible by 4, so ensure that
220 		 * largebase+u is not. Then, step through the sieve in
221 		 * increments of 4*s
222 		 */
223 		while (u & 0x3) {
224 			if (SMALL_MAXIMUM - u < s)
225 				return;
226 			u += s;
227 		}
228 
229 		/* Mark all multiples of 4*s */
230 		for (u /= 4; u < largebits; u += s)
231 			BIT_SET(LargeSieve, u);
232 	}
233 }
234 
235 /*
236  * list candidates for Sophie-Germain primes (where q = (p-1)/2)
237  * to standard output.
238  * The list is checked against small known primes (less than 2**30).
239  */
240 int
241 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
242 {
243 	BIGNUM *q;
244 	u_int32_t j, r, s, t;
245 	u_int32_t smallwords = TINY_NUMBER >> 6;
246 	u_int32_t tinywords = TINY_NUMBER >> 6;
247 	time_t time_start, time_stop;
248 	u_int32_t i;
249 	int ret = 0;
250 
251 	largememory = memory;
252 
253 	if (memory != 0 &&
254 	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
255 		error("Invalid memory amount (min %ld, max %ld)",
256 		    LARGE_MINIMUM, LARGE_MAXIMUM);
257 		return (-1);
258 	}
259 
260 	/*
261 	 * Set power to the length in bits of the prime to be generated.
262 	 * This is changed to 1 less than the desired safe prime moduli p.
263 	 */
264 	if (power > TEST_MAXIMUM) {
265 		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
266 		return (-1);
267 	} else if (power < TEST_MINIMUM) {
268 		error("Too few bits: %u < %u", power, TEST_MINIMUM);
269 		return (-1);
270 	}
271 	power--; /* decrement before squaring */
272 
273 	/*
274 	 * The density of ordinary primes is on the order of 1/bits, so the
275 	 * density of safe primes should be about (1/bits)**2. Set test range
276 	 * to something well above bits**2 to be reasonably sure (but not
277 	 * guaranteed) of catching at least one safe prime.
278 	 */
279 	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
280 
281 	/*
282 	 * Need idea of how much memory is available. We don't have to use all
283 	 * of it.
284 	 */
285 	if (largememory > LARGE_MAXIMUM) {
286 		logit("Limited memory: %u MB; limit %lu MB",
287 		    largememory, LARGE_MAXIMUM);
288 		largememory = LARGE_MAXIMUM;
289 	}
290 
291 	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
292 		logit("Increased memory: %u MB; need %u bytes",
293 		    largememory, (largewords << SHIFT_BYTE));
294 		largewords = (largememory << SHIFT_MEGAWORD);
295 	} else if (largememory > 0) {
296 		logit("Decreased memory: %u MB; want %u bytes",
297 		    largememory, (largewords << SHIFT_BYTE));
298 		largewords = (largememory << SHIFT_MEGAWORD);
299 	}
300 
301 	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
302 	tinybits = tinywords << SHIFT_WORD;
303 
304 	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
305 	smallbits = smallwords << SHIFT_WORD;
306 
307 	/*
308 	 * dynamically determine available memory
309 	 */
310 	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
311 		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
312 
313 	largebits = largewords << SHIFT_WORD;
314 	largenumbers = largebits * 2;	/* even numbers excluded */
315 
316 	/* validation check: count the number of primes tried */
317 	largetries = 0;
318 	if ((q = BN_new()) == NULL)
319 		fatal("BN_new failed");
320 
321 	/*
322 	 * Generate random starting point for subprime search, or use
323 	 * specified parameter.
324 	 */
325 	if ((largebase = BN_new()) == NULL)
326 		fatal("BN_new failed");
327 	if (start == NULL) {
328 		if (BN_rand(largebase, power, 1, 1) == 0)
329 			fatal("BN_rand failed");
330 	} else {
331 		if (BN_copy(largebase, start) == NULL)
332 			fatal("BN_copy: failed");
333 	}
334 
335 	/* ensure odd */
336 	if (BN_set_bit(largebase, 0) == 0)
337 		fatal("BN_set_bit: failed");
338 
339 	time(&time_start);
340 
341 	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
342 	    largenumbers, power);
343 	debug2("start point: 0x%s", BN_bn2hex(largebase));
344 
345 	/*
346 	 * TinySieve
347 	 */
348 	for (i = 0; i < tinybits; i++) {
349 		if (BIT_TEST(TinySieve, i))
350 			continue; /* 2*i+3 is composite */
351 
352 		/* The next tiny prime */
353 		t = 2 * i + 3;
354 
355 		/* Mark all multiples of t */
356 		for (j = i + t; j < tinybits; j += t)
357 			BIT_SET(TinySieve, j);
358 
359 		sieve_large(t);
360 	}
361 
362 	/*
363 	 * Start the small block search at the next possible prime. To avoid
364 	 * fencepost errors, the last pass is skipped.
365 	 */
366 	for (smallbase = TINY_NUMBER + 3;
367 	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
368 	    smallbase += TINY_NUMBER) {
369 		for (i = 0; i < tinybits; i++) {
370 			if (BIT_TEST(TinySieve, i))
371 				continue; /* 2*i+3 is composite */
372 
373 			/* The next tiny prime */
374 			t = 2 * i + 3;
375 			r = smallbase % t;
376 
377 			if (r == 0) {
378 				s = 0; /* t divides into smallbase exactly */
379 			} else {
380 				/* smallbase+s is first entry divisible by t */
381 				s = t - r;
382 			}
383 
384 			/*
385 			 * The sieve omits even numbers, so ensure that
386 			 * smallbase+s is odd. Then, step through the sieve
387 			 * in increments of 2*t
388 			 */
389 			if (s & 1)
390 				s += t; /* Make smallbase+s odd, and s even */
391 
392 			/* Mark all multiples of 2*t */
393 			for (s /= 2; s < smallbits; s += t)
394 				BIT_SET(SmallSieve, s);
395 		}
396 
397 		/*
398 		 * SmallSieve
399 		 */
400 		for (i = 0; i < smallbits; i++) {
401 			if (BIT_TEST(SmallSieve, i))
402 				continue; /* 2*i+smallbase is composite */
403 
404 			/* The next small prime */
405 			sieve_large((2 * i) + smallbase);
406 		}
407 
408 		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
409 	}
410 
411 	time(&time_stop);
412 
413 	logit("%.24s Sieved with %u small primes in %ld seconds",
414 	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
415 
416 	for (j = r = 0; j < largebits; j++) {
417 		if (BIT_TEST(LargeSieve, j))
418 			continue; /* Definitely composite, skip */
419 
420 		debug2("test q = largebase+%u", 2 * j);
421 		if (BN_set_word(q, 2 * j) == 0)
422 			fatal("BN_set_word failed");
423 		if (BN_add(q, q, largebase) == 0)
424 			fatal("BN_add failed");
425 		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
426 		    MODULI_TESTS_SIEVE, largetries,
427 		    (power - 1) /* MSB */, (0), q) == -1) {
428 			ret = -1;
429 			break;
430 		}
431 
432 		r++; /* count q */
433 	}
434 
435 	time(&time_stop);
436 
437 	free(LargeSieve);
438 	free(SmallSieve);
439 	free(TinySieve);
440 
441 	logit("%.24s Found %u candidates", ctime(&time_stop), r);
442 
443 	return (ret);
444 }
445 
446 static void
447 write_checkpoint(char *cpfile, u_int32_t lineno)
448 {
449 	FILE *fp;
450 	char tmp[MAXPATHLEN];
451 	int r;
452 
453 	r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
454 	if (r == -1 || r >= MAXPATHLEN) {
455 		logit("write_checkpoint: temp pathname too long");
456 		return;
457 	}
458 	if ((r = mkstemp(tmp)) == -1) {
459 		logit("mkstemp(%s): %s", tmp, strerror(errno));
460 		return;
461 	}
462 	if ((fp = fdopen(r, "w")) == NULL) {
463 		logit("write_checkpoint: fdopen: %s", strerror(errno));
464 		close(r);
465 		return;
466 	}
467 	if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0
468 	    && rename(tmp, cpfile) == 0)
469 		debug3("wrote checkpoint line %lu to '%s'",
470 		    (unsigned long)lineno, cpfile);
471 	else
472 		logit("failed to write to checkpoint file '%s': %s", cpfile,
473 		    strerror(errno));
474 }
475 
476 static unsigned long
477 read_checkpoint(char *cpfile)
478 {
479 	FILE *fp;
480 	unsigned long lineno = 0;
481 
482 	if ((fp = fopen(cpfile, "r")) == NULL)
483 		return 0;
484 	if (fscanf(fp, "%lu\n", &lineno) < 1)
485 		logit("Failed to load checkpoint from '%s'", cpfile);
486 	else
487 		logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
488 	fclose(fp);
489 	return lineno;
490 }
491 
492 static unsigned long
493 count_lines(FILE *f)
494 {
495 	unsigned long count = 0;
496 	char lp[QLINESIZE + 1];
497 
498 	if (fseek(f, 0, SEEK_SET) != 0) {
499 		debug("input file is not seekable");
500 		return ULONG_MAX;
501 	}
502 	while (fgets(lp, QLINESIZE + 1, f) != NULL)
503 		count++;
504 	rewind(f);
505 	debug("input file has %lu lines", count);
506 	return count;
507 }
508 
509 static char *
510 fmt_time(time_t seconds)
511 {
512 	int day, hr, min;
513 	static char buf[128];
514 
515 	min = (seconds / 60) % 60;
516 	hr = (seconds / 60 / 60) % 24;
517 	day = seconds / 60 / 60 / 24;
518 	if (day > 0)
519 		snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min);
520 	else
521 		snprintf(buf, sizeof buf, "%d:%02d", hr, min);
522 	return buf;
523 }
524 
525 static void
526 print_progress(unsigned long start_lineno, unsigned long current_lineno,
527     unsigned long end_lineno)
528 {
529 	static time_t time_start, time_prev;
530 	time_t time_now, elapsed;
531 	unsigned long num_to_process, processed, remaining, percent, eta;
532 	double time_per_line;
533 	char *eta_str;
534 
535 	time_now = monotime();
536 	if (time_start == 0) {
537 		time_start = time_prev = time_now;
538 		return;
539 	}
540 	/* print progress after 1m then once per 5m */
541 	if (time_now - time_prev < 5 * 60)
542 		return;
543 	time_prev = time_now;
544 	elapsed = time_now - time_start;
545 	processed = current_lineno - start_lineno;
546 	remaining = end_lineno - current_lineno;
547 	num_to_process = end_lineno - start_lineno;
548 	time_per_line = (double)elapsed / processed;
549 	/* if we don't know how many we're processing just report count+time */
550 	time(&time_now);
551 	if (end_lineno == ULONG_MAX) {
552 		logit("%.24s processed %lu in %s", ctime(&time_now),
553 		    processed, fmt_time(elapsed));
554 		return;
555 	}
556 	percent = 100 * processed / num_to_process;
557 	eta = time_per_line * remaining;
558 	eta_str = xstrdup(fmt_time(eta));
559 	logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s",
560 	    ctime(&time_now), processed, num_to_process, percent,
561 	    fmt_time(elapsed), eta_str);
562 	free(eta_str);
563 }
564 
565 /*
566  * perform a Miller-Rabin primality test
567  * on the list of candidates
568  * (checking both q and p)
569  * The result is a list of so-call "safe" primes
570  */
571 int
572 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
573     char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
574 {
575 	BIGNUM *q, *p, *a;
576 	BN_CTX *ctx;
577 	char *cp, *lp;
578 	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
579 	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
580 	unsigned long last_processed = 0, end_lineno;
581 	time_t time_start, time_stop;
582 	int res;
583 
584 	if (trials < TRIAL_MINIMUM) {
585 		error("Minimum primality trials is %d", TRIAL_MINIMUM);
586 		return (-1);
587 	}
588 
589 	if (num_lines == 0)
590 		end_lineno = count_lines(in);
591 	else
592 		end_lineno = start_lineno + num_lines;
593 
594 	time(&time_start);
595 
596 	if ((p = BN_new()) == NULL)
597 		fatal("BN_new failed");
598 	if ((q = BN_new()) == NULL)
599 		fatal("BN_new failed");
600 	if ((ctx = BN_CTX_new()) == NULL)
601 		fatal("BN_CTX_new failed");
602 
603 	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
604 	    ctime(&time_start), trials, generator_wanted);
605 
606 	if (checkpoint_file != NULL)
607 		last_processed = read_checkpoint(checkpoint_file);
608 	last_processed = start_lineno = MAX(last_processed, start_lineno);
609 	if (end_lineno == ULONG_MAX)
610 		debug("process from line %lu from pipe", last_processed);
611 	else
612 		debug("process from line %lu to line %lu", last_processed,
613 		    end_lineno);
614 
615 	res = 0;
616 	lp = xmalloc(QLINESIZE + 1);
617 	while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
618 		count_in++;
619 		if (count_in <= last_processed) {
620 			debug3("skipping line %u, before checkpoint or "
621 			    "specified start line", count_in);
622 			continue;
623 		}
624 		if (checkpoint_file != NULL)
625 			write_checkpoint(checkpoint_file, count_in);
626 		print_progress(start_lineno, count_in, end_lineno);
627 		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
628 			debug2("%10u: comment or short line", count_in);
629 			continue;
630 		}
631 
632 		/* XXX - fragile parser */
633 		/* time */
634 		cp = &lp[14];	/* (skip) */
635 
636 		/* type */
637 		in_type = strtoul(cp, &cp, 10);
638 
639 		/* tests */
640 		in_tests = strtoul(cp, &cp, 10);
641 
642 		if (in_tests & MODULI_TESTS_COMPOSITE) {
643 			debug2("%10u: known composite", count_in);
644 			continue;
645 		}
646 
647 		/* tries */
648 		in_tries = strtoul(cp, &cp, 10);
649 
650 		/* size (most significant bit) */
651 		in_size = strtoul(cp, &cp, 10);
652 
653 		/* generator (hex) */
654 		generator_known = strtoul(cp, &cp, 16);
655 
656 		/* Skip white space */
657 		cp += strspn(cp, " ");
658 
659 		/* modulus (hex) */
660 		switch (in_type) {
661 		case MODULI_TYPE_SOPHIE_GERMAIN:
662 			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
663 			a = q;
664 			if (BN_hex2bn(&a, cp) == 0)
665 				fatal("BN_hex2bn failed");
666 			/* p = 2*q + 1 */
667 			if (BN_lshift(p, q, 1) == 0)
668 				fatal("BN_lshift failed");
669 			if (BN_add_word(p, 1) == 0)
670 				fatal("BN_add_word failed");
671 			in_size += 1;
672 			generator_known = 0;
673 			break;
674 		case MODULI_TYPE_UNSTRUCTURED:
675 		case MODULI_TYPE_SAFE:
676 		case MODULI_TYPE_SCHNORR:
677 		case MODULI_TYPE_STRONG:
678 		case MODULI_TYPE_UNKNOWN:
679 			debug2("%10u: (%u)", count_in, in_type);
680 			a = p;
681 			if (BN_hex2bn(&a, cp) == 0)
682 				fatal("BN_hex2bn failed");
683 			/* q = (p-1) / 2 */
684 			if (BN_rshift(q, p, 1) == 0)
685 				fatal("BN_rshift failed");
686 			break;
687 		default:
688 			debug2("Unknown prime type");
689 			break;
690 		}
691 
692 		/*
693 		 * due to earlier inconsistencies in interpretation, check
694 		 * the proposed bit size.
695 		 */
696 		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
697 			debug2("%10u: bit size %u mismatch", count_in, in_size);
698 			continue;
699 		}
700 		if (in_size < QSIZE_MINIMUM) {
701 			debug2("%10u: bit size %u too short", count_in, in_size);
702 			continue;
703 		}
704 
705 		if (in_tests & MODULI_TESTS_MILLER_RABIN)
706 			in_tries += trials;
707 		else
708 			in_tries = trials;
709 
710 		/*
711 		 * guess unknown generator
712 		 */
713 		if (generator_known == 0) {
714 			if (BN_mod_word(p, 24) == 11)
715 				generator_known = 2;
716 			else if (BN_mod_word(p, 12) == 5)
717 				generator_known = 3;
718 			else {
719 				u_int32_t r = BN_mod_word(p, 10);
720 
721 				if (r == 3 || r == 7)
722 					generator_known = 5;
723 			}
724 		}
725 		/*
726 		 * skip tests when desired generator doesn't match
727 		 */
728 		if (generator_wanted > 0 &&
729 		    generator_wanted != generator_known) {
730 			debug2("%10u: generator %d != %d",
731 			    count_in, generator_known, generator_wanted);
732 			continue;
733 		}
734 
735 		/*
736 		 * Primes with no known generator are useless for DH, so
737 		 * skip those.
738 		 */
739 		if (generator_known == 0) {
740 			debug2("%10u: no known generator", count_in);
741 			continue;
742 		}
743 
744 		count_possible++;
745 
746 		/*
747 		 * The (1/4)^N performance bound on Miller-Rabin is
748 		 * extremely pessimistic, so don't spend a lot of time
749 		 * really verifying that q is prime until after we know
750 		 * that p is also prime. A single pass will weed out the
751 		 * vast majority of composite q's.
752 		 */
753 		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
754 			debug("%10u: q failed first possible prime test",
755 			    count_in);
756 			continue;
757 		}
758 
759 		/*
760 		 * q is possibly prime, so go ahead and really make sure
761 		 * that p is prime. If it is, then we can go back and do
762 		 * the same for q. If p is composite, chances are that
763 		 * will show up on the first Rabin-Miller iteration so it
764 		 * doesn't hurt to specify a high iteration count.
765 		 */
766 		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
767 			debug("%10u: p is not prime", count_in);
768 			continue;
769 		}
770 		debug("%10u: p is almost certainly prime", count_in);
771 
772 		/* recheck q more rigorously */
773 		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
774 			debug("%10u: q is not prime", count_in);
775 			continue;
776 		}
777 		debug("%10u: q is almost certainly prime", count_in);
778 
779 		if (qfileout(out, MODULI_TYPE_SAFE,
780 		    in_tests | MODULI_TESTS_MILLER_RABIN,
781 		    in_tries, in_size, generator_known, p)) {
782 			res = -1;
783 			break;
784 		}
785 
786 		count_out++;
787 	}
788 
789 	time(&time_stop);
790 	free(lp);
791 	BN_free(p);
792 	BN_free(q);
793 	BN_CTX_free(ctx);
794 
795 	if (checkpoint_file != NULL)
796 		unlink(checkpoint_file);
797 
798 	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
799 	    ctime(&time_stop), count_out, count_possible,
800 	    (long) (time_stop - time_start));
801 
802 	return (res);
803 }
804