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Darren Tuckerf0e792e2005-01-20 11:02:26 +11001/* $OpenBSD: moduli.c,v 1.10 2005/01/17 03:25:46 dtucker Exp $ */
Darren Tuckerb2f9d412003-08-02 23:51:38 +10002/*
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"
Darren Tuckerb2f9d412003-08-02 23:51:38 +100041#include "xmalloc.h"
42#include "log.h"
43
44#include <openssl/bn.h>
45
Darren Tuckerb2f9d412003-08-02 23:51:38 +100046/*
47 * File output defines
48 */
49
50/* need line long enough for largest moduli plus headers */
Darren Tuckerfc959702004-07-17 16:12:08 +100051#define QLINESIZE (100+8192)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100052
53/* Type: decimal.
54 * Specifies the internal structure of the prime modulus.
55 */
Darren Tuckerfc959702004-07-17 16:12:08 +100056#define QTYPE_UNKNOWN (0)
57#define QTYPE_UNSTRUCTURED (1)
58#define QTYPE_SAFE (2)
Darren Tuckerf0e792e2005-01-20 11:02:26 +110059#define QTYPE_SCHNORR (3)
Darren Tuckerfc959702004-07-17 16:12:08 +100060#define QTYPE_SOPHIE_GERMAIN (4)
61#define QTYPE_STRONG (5)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100062
63/* Tests: decimal (bit field).
64 * Specifies the methods used in checking for primality.
65 * Usually, more than one test is used.
66 */
Darren Tuckerfc959702004-07-17 16:12:08 +100067#define QTEST_UNTESTED (0x00)
68#define QTEST_COMPOSITE (0x01)
69#define QTEST_SIEVE (0x02)
70#define QTEST_MILLER_RABIN (0x04)
71#define QTEST_JACOBI (0x08)
72#define QTEST_ELLIPTIC (0x10)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100073
Darren Tucker06930c72003-12-31 11:34:51 +110074/*
75 * Size: decimal.
Darren Tuckerb2f9d412003-08-02 23:51:38 +100076 * Specifies the number of the most significant bit (0 to M).
Darren Tucker06930c72003-12-31 11:34:51 +110077 * WARNING: internally, usually 1 to N.
Darren Tuckerb2f9d412003-08-02 23:51:38 +100078 */
Darren Tuckerfc959702004-07-17 16:12:08 +100079#define QSIZE_MINIMUM (511)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100080
81/*
82 * Prime sieving defines
83 */
84
85/* Constant: assuming 8 bit bytes and 32 bit words */
Darren Tuckerfc959702004-07-17 16:12:08 +100086#define SHIFT_BIT (3)
87#define SHIFT_BYTE (2)
88#define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE)
89#define SHIFT_MEGABYTE (20)
90#define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100091
92/*
Darren Tucker770fc012004-05-13 16:24:32 +100093 * Using virtual memory can cause thrashing. This should be the largest
94 * number that is supported without a large amount of disk activity --
95 * that would increase the run time from hours to days or weeks!
96 */
Darren Tuckerfc959702004-07-17 16:12:08 +100097#define LARGE_MINIMUM (8UL) /* megabytes */
Darren Tucker770fc012004-05-13 16:24:32 +100098
99/*
100 * Do not increase this number beyond the unsigned integer bit size.
101 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
102 */
Darren Tuckerfc959702004-07-17 16:12:08 +1000103#define LARGE_MAXIMUM (127UL) /* megabytes */
Darren Tucker770fc012004-05-13 16:24:32 +1000104
105/*
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000106 * Constant: when used with 32-bit integers, the largest sieve prime
107 * has to be less than 2**32.
108 */
Darren Tuckerfc959702004-07-17 16:12:08 +1000109#define SMALL_MAXIMUM (0xffffffffUL)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000110
111/* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
Darren Tuckerfc959702004-07-17 16:12:08 +1000112#define TINY_NUMBER (1UL<<16)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000113
114/* Ensure enough bit space for testing 2*q. */
115#define TEST_MAXIMUM (1UL<<16)
116#define TEST_MINIMUM (QSIZE_MINIMUM + 1)
117/* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */
118#define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */
119
120/* bit operations on 32-bit words */
121#define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
122#define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
123#define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
124
125/*
126 * Prime testing defines
127 */
128
Darren Tucker770fc012004-05-13 16:24:32 +1000129/* Minimum number of primality tests to perform */
130#define TRIAL_MINIMUM (4)
131
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000132/*
133 * Sieving data (XXX - move to struct)
134 */
135
136/* sieve 2**16 */
137static u_int32_t *TinySieve, tinybits;
138
139/* sieve 2**30 in 2**16 parts */
140static u_int32_t *SmallSieve, smallbits, smallbase;
141
142/* sieve relative to the initial value */
143static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
144static u_int32_t largebits, largememory; /* megabytes */
145static BIGNUM *largebase;
146
Darren Tuckere4ab1152004-05-24 10:14:24 +1000147int gen_candidates(FILE *, int, int, BIGNUM *);
148int prime_test(FILE *, FILE *, u_int32_t, u_int32_t);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000149
150/*
151 * print moduli out in consistent form,
152 */
153static int
154qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
155 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
156{
157 struct tm *gtm;
158 time_t time_now;
159 int res;
160
161 time(&time_now);
162 gtm = gmtime(&time_now);
Damien Miller787b2ec2003-11-21 23:56:47 +1100163
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000164 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
165 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
166 gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
167 otype, otests, otries, osize, ogenerator);
168
169 if (res < 0)
170 return (-1);
171
172 if (BN_print_fp(ofile, omodulus) < 1)
173 return (-1);
174
175 res = fprintf(ofile, "\n");
176 fflush(ofile);
177
178 return (res > 0 ? 0 : -1);
179}
180
181
182/*
183 ** Sieve p's and q's with small factors
184 */
185static void
186sieve_large(u_int32_t s)
187{
188 u_int32_t r, u;
189
Darren Tucker06930c72003-12-31 11:34:51 +1100190 debug3("sieve_large %u", s);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000191 largetries++;
192 /* r = largebase mod s */
193 r = BN_mod_word(largebase, s);
194 if (r == 0)
195 u = 0; /* s divides into largebase exactly */
196 else
197 u = s - r; /* largebase+u is first entry divisible by s */
198
199 if (u < largebits * 2) {
200 /*
201 * The sieve omits p's and q's divisible by 2, so ensure that
202 * largebase+u is odd. Then, step through the sieve in
203 * increments of 2*s
204 */
205 if (u & 0x1)
206 u += s; /* Make largebase+u odd, and u even */
207
208 /* Mark all multiples of 2*s */
209 for (u /= 2; u < largebits; u += s)
210 BIT_SET(LargeSieve, u);
211 }
212
213 /* r = p mod s */
214 r = (2 * r + 1) % s;
215 if (r == 0)
216 u = 0; /* s divides p exactly */
217 else
218 u = s - r; /* p+u is first entry divisible by s */
219
220 if (u < largebits * 4) {
221 /*
222 * The sieve omits p's divisible by 4, so ensure that
223 * largebase+u is not. Then, step through the sieve in
224 * increments of 4*s
225 */
226 while (u & 0x3) {
227 if (SMALL_MAXIMUM - u < s)
228 return;
229 u += s;
230 }
231
232 /* Mark all multiples of 4*s */
233 for (u /= 4; u < largebits; u += s)
234 BIT_SET(LargeSieve, u);
235 }
236}
237
238/*
Darren Tucker47abce42004-05-02 22:09:00 +1000239 * list candidates for Sophie-Germain primes (where q = (p-1)/2)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000240 * to standard output.
241 * The list is checked against small known primes (less than 2**30).
242 */
243int
244gen_candidates(FILE *out, int memory, int power, BIGNUM *start)
245{
246 BIGNUM *q;
247 u_int32_t j, r, s, t;
248 u_int32_t smallwords = TINY_NUMBER >> 6;
249 u_int32_t tinywords = TINY_NUMBER >> 6;
250 time_t time_start, time_stop;
251 int i, ret = 0;
252
253 largememory = memory;
254
Darren Tucker770fc012004-05-13 16:24:32 +1000255 if (memory != 0 &&
256 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
257 error("Invalid memory amount (min %ld, max %ld)",
258 LARGE_MINIMUM, LARGE_MAXIMUM);
259 return (-1);
260 }
261
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000262 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100263 * Set power to the length in bits of the prime to be generated.
264 * This is changed to 1 less than the desired safe prime moduli p.
265 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000266 if (power > TEST_MAXIMUM) {
267 error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
268 return (-1);
269 } else if (power < TEST_MINIMUM) {
270 error("Too few bits: %u < %u", power, TEST_MINIMUM);
271 return (-1);
272 }
273 power--; /* decrement before squaring */
274
275 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100276 * The density of ordinary primes is on the order of 1/bits, so the
277 * density of safe primes should be about (1/bits)**2. Set test range
278 * to something well above bits**2 to be reasonably sure (but not
279 * guaranteed) of catching at least one safe prime.
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000280 */
281 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
282
283 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100284 * Need idea of how much memory is available. We don't have to use all
285 * of it.
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000286 */
287 if (largememory > LARGE_MAXIMUM) {
288 logit("Limited memory: %u MB; limit %lu MB",
289 largememory, LARGE_MAXIMUM);
290 largememory = LARGE_MAXIMUM;
291 }
292
293 if (largewords <= (largememory << SHIFT_MEGAWORD)) {
294 logit("Increased memory: %u MB; need %u bytes",
295 largememory, (largewords << SHIFT_BYTE));
296 largewords = (largememory << SHIFT_MEGAWORD);
297 } else if (largememory > 0) {
298 logit("Decreased memory: %u MB; want %u bytes",
299 largememory, (largewords << SHIFT_BYTE));
300 largewords = (largememory << SHIFT_MEGAWORD);
301 }
302
303 TinySieve = calloc(tinywords, sizeof(u_int32_t));
304 if (TinySieve == NULL) {
305 error("Insufficient memory for tiny sieve: need %u bytes",
306 tinywords << SHIFT_BYTE);
307 exit(1);
308 }
309 tinybits = tinywords << SHIFT_WORD;
310
311 SmallSieve = calloc(smallwords, sizeof(u_int32_t));
312 if (SmallSieve == NULL) {
313 error("Insufficient memory for small sieve: need %u bytes",
314 smallwords << SHIFT_BYTE);
315 xfree(TinySieve);
316 exit(1);
317 }
318 smallbits = smallwords << SHIFT_WORD;
319
320 /*
321 * dynamically determine available memory
322 */
323 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
324 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
325
326 largebits = largewords << SHIFT_WORD;
327 largenumbers = largebits * 2; /* even numbers excluded */
328
329 /* validation check: count the number of primes tried */
330 largetries = 0;
331 q = BN_new();
332
333 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100334 * Generate random starting point for subprime search, or use
335 * specified parameter.
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000336 */
337 largebase = BN_new();
338 if (start == NULL)
339 BN_rand(largebase, power, 1, 1);
340 else
341 BN_copy(largebase, start);
342
343 /* ensure odd */
344 BN_set_bit(largebase, 0);
345
346 time(&time_start);
347
Damien Millera8e06ce2003-11-21 23:48:55 +1100348 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000349 largenumbers, power);
350 debug2("start point: 0x%s", BN_bn2hex(largebase));
351
352 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100353 * TinySieve
354 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000355 for (i = 0; i < tinybits; i++) {
356 if (BIT_TEST(TinySieve, i))
357 continue; /* 2*i+3 is composite */
358
359 /* The next tiny prime */
360 t = 2 * i + 3;
361
362 /* Mark all multiples of t */
363 for (j = i + t; j < tinybits; j += t)
364 BIT_SET(TinySieve, j);
365
366 sieve_large(t);
367 }
368
369 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100370 * Start the small block search at the next possible prime. To avoid
371 * fencepost errors, the last pass is skipped.
372 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000373 for (smallbase = TINY_NUMBER + 3;
374 smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
375 smallbase += TINY_NUMBER) {
376 for (i = 0; i < tinybits; i++) {
377 if (BIT_TEST(TinySieve, i))
378 continue; /* 2*i+3 is composite */
379
380 /* The next tiny prime */
381 t = 2 * i + 3;
382 r = smallbase % t;
383
384 if (r == 0) {
385 s = 0; /* t divides into smallbase exactly */
386 } else {
387 /* smallbase+s is first entry divisible by t */
388 s = t - r;
389 }
390
391 /*
392 * The sieve omits even numbers, so ensure that
393 * smallbase+s is odd. Then, step through the sieve
394 * in increments of 2*t
395 */
396 if (s & 1)
397 s += t; /* Make smallbase+s odd, and s even */
398
399 /* Mark all multiples of 2*t */
400 for (s /= 2; s < smallbits; s += t)
401 BIT_SET(SmallSieve, s);
402 }
403
404 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100405 * SmallSieve
406 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000407 for (i = 0; i < smallbits; i++) {
408 if (BIT_TEST(SmallSieve, i))
409 continue; /* 2*i+smallbase is composite */
410
411 /* The next small prime */
412 sieve_large((2 * i) + smallbase);
413 }
414
415 memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
416 }
417
418 time(&time_stop);
419
420 logit("%.24s Sieved with %u small primes in %ld seconds",
421 ctime(&time_stop), largetries, (long) (time_stop - time_start));
422
423 for (j = r = 0; j < largebits; j++) {
424 if (BIT_TEST(LargeSieve, j))
425 continue; /* Definitely composite, skip */
426
427 debug2("test q = largebase+%u", 2 * j);
428 BN_set_word(q, 2 * j);
429 BN_add(q, q, largebase);
Darren Tucker47abce42004-05-02 22:09:00 +1000430 if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE,
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000431 largetries, (power - 1) /* MSB */, (0), q) == -1) {
432 ret = -1;
433 break;
434 }
435
436 r++; /* count q */
437 }
438
439 time(&time_stop);
440
441 xfree(LargeSieve);
442 xfree(SmallSieve);
443 xfree(TinySieve);
444
445 logit("%.24s Found %u candidates", ctime(&time_stop), r);
446
447 return (ret);
448}
449
450/*
451 * perform a Miller-Rabin primality test
452 * on the list of candidates
453 * (checking both q and p)
454 * The result is a list of so-call "safe" primes
455 */
456int
Darren Tucker770fc012004-05-13 16:24:32 +1000457prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000458{
459 BIGNUM *q, *p, *a;
460 BN_CTX *ctx;
461 char *cp, *lp;
462 u_int32_t count_in = 0, count_out = 0, count_possible = 0;
463 u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
464 time_t time_start, time_stop;
465 int res;
466
Darren Tucker770fc012004-05-13 16:24:32 +1000467 if (trials < TRIAL_MINIMUM) {
468 error("Minimum primality trials is %d", TRIAL_MINIMUM);
469 return (-1);
470 }
471
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000472 time(&time_start);
473
474 p = BN_new();
475 q = BN_new();
476 ctx = BN_CTX_new();
477
478 debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
479 ctime(&time_start), trials, generator_wanted);
480
481 res = 0;
482 lp = xmalloc(QLINESIZE + 1);
483 while (fgets(lp, QLINESIZE, in) != NULL) {
484 int ll = strlen(lp);
485
486 count_in++;
487 if (ll < 14 || *lp == '!' || *lp == '#') {
488 debug2("%10u: comment or short line", count_in);
489 continue;
490 }
491
492 /* XXX - fragile parser */
493 /* time */
494 cp = &lp[14]; /* (skip) */
495
496 /* type */
497 in_type = strtoul(cp, &cp, 10);
498
499 /* tests */
500 in_tests = strtoul(cp, &cp, 10);
501
502 if (in_tests & QTEST_COMPOSITE) {
503 debug2("%10u: known composite", count_in);
504 continue;
505 }
Darren Tucker06930c72003-12-31 11:34:51 +1100506
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000507 /* tries */
508 in_tries = strtoul(cp, &cp, 10);
509
510 /* size (most significant bit) */
511 in_size = strtoul(cp, &cp, 10);
512
513 /* generator (hex) */
514 generator_known = strtoul(cp, &cp, 16);
515
516 /* Skip white space */
517 cp += strspn(cp, " ");
518
519 /* modulus (hex) */
520 switch (in_type) {
Darren Tucker47abce42004-05-02 22:09:00 +1000521 case QTYPE_SOPHIE_GERMAIN:
522 debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000523 a = q;
524 BN_hex2bn(&a, cp);
525 /* p = 2*q + 1 */
526 BN_lshift(p, q, 1);
527 BN_add_word(p, 1);
528 in_size += 1;
529 generator_known = 0;
530 break;
Darren Tucker06930c72003-12-31 11:34:51 +1100531 case QTYPE_UNSTRUCTURED:
532 case QTYPE_SAFE:
Darren Tuckerf0e792e2005-01-20 11:02:26 +1100533 case QTYPE_SCHNORR:
Darren Tucker06930c72003-12-31 11:34:51 +1100534 case QTYPE_STRONG:
535 case QTYPE_UNKNOWN:
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000536 debug2("%10u: (%u)", count_in, in_type);
537 a = p;
538 BN_hex2bn(&a, cp);
539 /* q = (p-1) / 2 */
540 BN_rshift(q, p, 1);
541 break;
Darren Tucker06930c72003-12-31 11:34:51 +1100542 default:
543 debug2("Unknown prime type");
544 break;
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000545 }
546
547 /*
548 * due to earlier inconsistencies in interpretation, check
549 * the proposed bit size.
550 */
551 if (BN_num_bits(p) != (in_size + 1)) {
552 debug2("%10u: bit size %u mismatch", count_in, in_size);
553 continue;
554 }
555 if (in_size < QSIZE_MINIMUM) {
556 debug2("%10u: bit size %u too short", count_in, in_size);
557 continue;
558 }
559
560 if (in_tests & QTEST_MILLER_RABIN)
561 in_tries += trials;
562 else
563 in_tries = trials;
Darren Tucker06930c72003-12-31 11:34:51 +1100564
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000565 /*
566 * guess unknown generator
567 */
568 if (generator_known == 0) {
569 if (BN_mod_word(p, 24) == 11)
570 generator_known = 2;
571 else if (BN_mod_word(p, 12) == 5)
572 generator_known = 3;
573 else {
574 u_int32_t r = BN_mod_word(p, 10);
575
Darren Tucker06930c72003-12-31 11:34:51 +1100576 if (r == 3 || r == 7)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000577 generator_known = 5;
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000578 }
579 }
580 /*
581 * skip tests when desired generator doesn't match
582 */
583 if (generator_wanted > 0 &&
584 generator_wanted != generator_known) {
585 debug2("%10u: generator %d != %d",
586 count_in, generator_known, generator_wanted);
587 continue;
588 }
589
Darren Tucker5cd9d442003-12-10 00:54:38 +1100590 /*
591 * Primes with no known generator are useless for DH, so
592 * skip those.
593 */
594 if (generator_known == 0) {
595 debug2("%10u: no known generator", count_in);
596 continue;
597 }
598
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000599 count_possible++;
600
601 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100602 * The (1/4)^N performance bound on Miller-Rabin is
603 * extremely pessimistic, so don't spend a lot of time
604 * really verifying that q is prime until after we know
605 * that p is also prime. A single pass will weed out the
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000606 * vast majority of composite q's.
607 */
608 if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) {
Darren Tucker06930c72003-12-31 11:34:51 +1100609 debug("%10u: q failed first possible prime test",
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000610 count_in);
611 continue;
612 }
Damien Miller787b2ec2003-11-21 23:56:47 +1100613
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000614 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100615 * q is possibly prime, so go ahead and really make sure
616 * that p is prime. If it is, then we can go back and do
617 * the same for q. If p is composite, chances are that
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000618 * will show up on the first Rabin-Miller iteration so it
619 * doesn't hurt to specify a high iteration count.
620 */
621 if (!BN_is_prime(p, trials, NULL, ctx, NULL)) {
Darren Tucker06930c72003-12-31 11:34:51 +1100622 debug("%10u: p is not prime", count_in);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000623 continue;
624 }
625 debug("%10u: p is almost certainly prime", count_in);
626
627 /* recheck q more rigorously */
628 if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) {
629 debug("%10u: q is not prime", count_in);
630 continue;
631 }
632 debug("%10u: q is almost certainly prime", count_in);
633
Damien Millera8e06ce2003-11-21 23:48:55 +1100634 if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN),
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000635 in_tries, in_size, generator_known, p)) {
636 res = -1;
637 break;
638 }
639
640 count_out++;
641 }
642
643 time(&time_stop);
644 xfree(lp);
645 BN_free(p);
646 BN_free(q);
647 BN_CTX_free(ctx);
648
649 logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
Damien Millera8e06ce2003-11-21 23:48:55 +1100650 ctime(&time_stop), count_out, count_possible,
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000651 (long) (time_stop - time_start));
652
653 return (res);
654}