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1b56ff3d | 1 | /* $OpenBSD: moduli.c,v 1.9 2004/07/11 17:48:47 deraadt Exp $ */ |
70791e56 | 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" | |
70791e56 | 41 | #include "xmalloc.h" |
42 | #include "log.h" | |
43 | ||
44 | #include <openssl/bn.h> | |
45 | ||
70791e56 | 46 | /* |
47 | * File output defines | |
48 | */ | |
49 | ||
50 | /* need line long enough for largest moduli plus headers */ | |
1b56ff3d | 51 | #define QLINESIZE (100+8192) |
70791e56 | 52 | |
53 | /* Type: decimal. | |
54 | * Specifies the internal structure of the prime modulus. | |
55 | */ | |
1b56ff3d | 56 | #define QTYPE_UNKNOWN (0) |
57 | #define QTYPE_UNSTRUCTURED (1) | |
58 | #define QTYPE_SAFE (2) | |
59 | #define QTYPE_SCHNOOR (3) | |
60 | #define QTYPE_SOPHIE_GERMAIN (4) | |
61 | #define QTYPE_STRONG (5) | |
70791e56 | 62 | |
63 | /* Tests: decimal (bit field). | |
64 | * Specifies the methods used in checking for primality. | |
65 | * Usually, more than one test is used. | |
66 | */ | |
1b56ff3d | 67 | #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) | |
70791e56 | 73 | |
416fd2a8 | 74 | /* |
75 | * Size: decimal. | |
70791e56 | 76 | * Specifies the number of the most significant bit (0 to M). |
416fd2a8 | 77 | * WARNING: internally, usually 1 to N. |
70791e56 | 78 | */ |
1b56ff3d | 79 | #define QSIZE_MINIMUM (511) |
70791e56 | 80 | |
81 | /* | |
82 | * Prime sieving defines | |
83 | */ | |
84 | ||
85 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
1b56ff3d | 86 | #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) | |
91 | ||
92 | /* | |
93 | * 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 | */ | |
97 | #define LARGE_MINIMUM (8UL) /* megabytes */ | |
98 | ||
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 | */ | |
103 | #define LARGE_MAXIMUM (127UL) /* megabytes */ | |
70791e56 | 104 | |
105 | /* | |
106 | * Constant: when used with 32-bit integers, the largest sieve prime | |
107 | * has to be less than 2**32. | |
108 | */ | |
1b56ff3d | 109 | #define SMALL_MAXIMUM (0xffffffffUL) |
70791e56 | 110 | |
111 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
1b56ff3d | 112 | #define TINY_NUMBER (1UL<<16) |
70791e56 | 113 | |
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 | ||
1b56ff3d | 129 | /* Minimum number of primality tests to perform */ |
130 | #define TRIAL_MINIMUM (4) | |
131 | ||
70791e56 | 132 | /* |
133 | * Sieving data (XXX - move to struct) | |
134 | */ | |
135 | ||
136 | /* sieve 2**16 */ | |
137 | static u_int32_t *TinySieve, tinybits; | |
138 | ||
139 | /* sieve 2**30 in 2**16 parts */ | |
140 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
141 | ||
142 | /* sieve relative to the initial value */ | |
143 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
144 | static u_int32_t largebits, largememory; /* megabytes */ | |
145 | static BIGNUM *largebase; | |
146 | ||
1b56ff3d | 147 | int gen_candidates(FILE *, int, int, BIGNUM *); |
148 | int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); | |
70791e56 | 149 | |
150 | /* | |
151 | * print moduli out in consistent form, | |
152 | */ | |
153 | static int | |
154 | qfileout(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); | |
416fd2a8 | 163 | |
70791e56 | 164 | 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 | */ | |
185 | static void | |
186 | sieve_large(u_int32_t s) | |
187 | { | |
188 | u_int32_t r, u; | |
189 | ||
416fd2a8 | 190 | debug3("sieve_large %u", s); |
70791e56 | 191 | 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 | /* | |
1b56ff3d | 239 | * list candidates for Sophie-Germain primes (where q = (p-1)/2) |
70791e56 | 240 | * to standard output. |
241 | * The list is checked against small known primes (less than 2**30). | |
242 | */ | |
243 | int | |
244 | gen_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 | ||
1b56ff3d | 255 | 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 | ||
70791e56 | 262 | /* |
416fd2a8 | 263 | * 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 | */ | |
70791e56 | 266 | 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 | /* | |
416fd2a8 | 276 | * 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. | |
70791e56 | 280 | */ |
281 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
282 | ||
283 | /* | |
416fd2a8 | 284 | * Need idea of how much memory is available. We don't have to use all |
285 | * of it. | |
70791e56 | 286 | */ |
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 | /* | |
416fd2a8 | 334 | * Generate random starting point for subprime search, or use |
335 | * specified parameter. | |
70791e56 | 336 | */ |
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 | ||
416fd2a8 | 348 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
70791e56 | 349 | largenumbers, power); |
350 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
351 | ||
352 | /* | |
416fd2a8 | 353 | * TinySieve |
354 | */ | |
70791e56 | 355 | 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 | /* | |
416fd2a8 | 370 | * Start the small block search at the next possible prime. To avoid |
371 | * fencepost errors, the last pass is skipped. | |
372 | */ | |
70791e56 | 373 | 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 | /* | |
416fd2a8 | 405 | * SmallSieve |
406 | */ | |
70791e56 | 407 | 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); | |
1b56ff3d | 430 | if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE, |
70791e56 | 431 | 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 | */ | |
456 | int | |
1b56ff3d | 457 | prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) |
70791e56 | 458 | { |
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 | ||
1b56ff3d | 467 | if (trials < TRIAL_MINIMUM) { |
468 | error("Minimum primality trials is %d", TRIAL_MINIMUM); | |
469 | return (-1); | |
470 | } | |
471 | ||
70791e56 | 472 | 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 | } | |
416fd2a8 | 506 | |
70791e56 | 507 | /* 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) { | |
1b56ff3d | 521 | case QTYPE_SOPHIE_GERMAIN: |
522 | debug2("%10u: (%u) Sophie-Germain", count_in, in_type); | |
70791e56 | 523 | 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; | |
416fd2a8 | 531 | case QTYPE_UNSTRUCTURED: |
532 | case QTYPE_SAFE: | |
533 | case QTYPE_SCHNOOR: | |
534 | case QTYPE_STRONG: | |
535 | case QTYPE_UNKNOWN: | |
70791e56 | 536 | 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; | |
416fd2a8 | 542 | default: |
543 | debug2("Unknown prime type"); | |
544 | break; | |
70791e56 | 545 | } |
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; | |
416fd2a8 | 564 | |
70791e56 | 565 | /* |
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 | ||
416fd2a8 | 576 | if (r == 3 || r == 7) |
70791e56 | 577 | generator_known = 5; |
70791e56 | 578 | } |
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 | ||
416fd2a8 | 590 | /* |
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 | ||
70791e56 | 599 | count_possible++; |
600 | ||
601 | /* | |
416fd2a8 | 602 | * 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 | |
70791e56 | 606 | * vast majority of composite q's. |
607 | */ | |
608 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
416fd2a8 | 609 | debug("%10u: q failed first possible prime test", |
70791e56 | 610 | count_in); |
611 | continue; | |
612 | } | |
416fd2a8 | 613 | |
70791e56 | 614 | /* |
416fd2a8 | 615 | * 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 | |
70791e56 | 618 | * 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)) { | |
416fd2a8 | 622 | debug("%10u: p is not prime", count_in); |
70791e56 | 623 | 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 | ||
416fd2a8 | 634 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
70791e56 | 635 | 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", | |
416fd2a8 | 650 | ctime(&time_stop), count_out, count_possible, |
70791e56 | 651 | (long) (time_stop - time_start)); |
652 | ||
653 | return (res); | |
654 | } |