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30460aeb | 1 | /* $OpenBSD: moduli.c,v 1.18 2006/08/03 03:34:42 deraadt Exp $ */ |
c9307018 | 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" | |
30460aeb | 41 | |
42 | #include <sys/types.h> | |
c9307018 | 43 | |
44 | #include <openssl/bn.h> | |
45 | ||
30460aeb | 46 | #include <stdio.h> |
47 | #include <stdlib.h> | |
48 | #include <string.h> | |
49 | #include <stdarg.h> | |
50 | #include <time.h> | |
51 | ||
52 | #include "xmalloc.h" | |
53 | #include "log.h" | |
54 | ||
c9307018 | 55 | /* |
56 | * File output defines | |
57 | */ | |
58 | ||
59 | /* need line long enough for largest moduli plus headers */ | |
7e82606e | 60 | #define QLINESIZE (100+8192) |
c9307018 | 61 | |
62 | /* Type: decimal. | |
63 | * Specifies the internal structure of the prime modulus. | |
64 | */ | |
7e82606e | 65 | #define QTYPE_UNKNOWN (0) |
66 | #define QTYPE_UNSTRUCTURED (1) | |
67 | #define QTYPE_SAFE (2) | |
dfddba3d | 68 | #define QTYPE_SCHNORR (3) |
7e82606e | 69 | #define QTYPE_SOPHIE_GERMAIN (4) |
70 | #define QTYPE_STRONG (5) | |
c9307018 | 71 | |
72 | /* Tests: decimal (bit field). | |
73 | * Specifies the methods used in checking for primality. | |
74 | * Usually, more than one test is used. | |
75 | */ | |
7e82606e | 76 | #define QTEST_UNTESTED (0x00) |
77 | #define QTEST_COMPOSITE (0x01) | |
78 | #define QTEST_SIEVE (0x02) | |
79 | #define QTEST_MILLER_RABIN (0x04) | |
80 | #define QTEST_JACOBI (0x08) | |
81 | #define QTEST_ELLIPTIC (0x10) | |
c9307018 | 82 | |
540d72c3 | 83 | /* |
84 | * Size: decimal. | |
c9307018 | 85 | * Specifies the number of the most significant bit (0 to M). |
540d72c3 | 86 | * WARNING: internally, usually 1 to N. |
c9307018 | 87 | */ |
7e82606e | 88 | #define QSIZE_MINIMUM (511) |
c9307018 | 89 | |
90 | /* | |
91 | * Prime sieving defines | |
92 | */ | |
93 | ||
94 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
7e82606e | 95 | #define SHIFT_BIT (3) |
96 | #define SHIFT_BYTE (2) | |
97 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
98 | #define SHIFT_MEGABYTE (20) | |
99 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
100 | ||
101 | /* | |
102 | * Using virtual memory can cause thrashing. This should be the largest | |
103 | * number that is supported without a large amount of disk activity -- | |
104 | * that would increase the run time from hours to days or weeks! | |
105 | */ | |
106 | #define LARGE_MINIMUM (8UL) /* megabytes */ | |
107 | ||
108 | /* | |
109 | * Do not increase this number beyond the unsigned integer bit size. | |
110 | * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). | |
111 | */ | |
112 | #define LARGE_MAXIMUM (127UL) /* megabytes */ | |
c9307018 | 113 | |
114 | /* | |
115 | * Constant: when used with 32-bit integers, the largest sieve prime | |
116 | * has to be less than 2**32. | |
117 | */ | |
7e82606e | 118 | #define SMALL_MAXIMUM (0xffffffffUL) |
c9307018 | 119 | |
120 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
7e82606e | 121 | #define TINY_NUMBER (1UL<<16) |
c9307018 | 122 | |
123 | /* Ensure enough bit space for testing 2*q. */ | |
2ce0bfe4 | 124 | #define TEST_MAXIMUM (1UL<<16) |
125 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
126 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
127 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
c9307018 | 128 | |
129 | /* bit operations on 32-bit words */ | |
2ce0bfe4 | 130 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) |
131 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
132 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
c9307018 | 133 | |
134 | /* | |
135 | * Prime testing defines | |
136 | */ | |
137 | ||
7e82606e | 138 | /* Minimum number of primality tests to perform */ |
2ce0bfe4 | 139 | #define TRIAL_MINIMUM (4) |
7e82606e | 140 | |
c9307018 | 141 | /* |
142 | * Sieving data (XXX - move to struct) | |
143 | */ | |
144 | ||
145 | /* sieve 2**16 */ | |
146 | static u_int32_t *TinySieve, tinybits; | |
147 | ||
148 | /* sieve 2**30 in 2**16 parts */ | |
149 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
150 | ||
151 | /* sieve relative to the initial value */ | |
152 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
153 | static u_int32_t largebits, largememory; /* megabytes */ | |
154 | static BIGNUM *largebase; | |
155 | ||
2ce0bfe4 | 156 | int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); |
7e82606e | 157 | int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); |
c9307018 | 158 | |
159 | /* | |
160 | * print moduli out in consistent form, | |
161 | */ | |
162 | static int | |
163 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
164 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
165 | { | |
166 | struct tm *gtm; | |
167 | time_t time_now; | |
168 | int res; | |
169 | ||
170 | time(&time_now); | |
171 | gtm = gmtime(&time_now); | |
540d72c3 | 172 | |
c9307018 | 173 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", |
174 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
175 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
176 | otype, otests, otries, osize, ogenerator); | |
177 | ||
178 | if (res < 0) | |
179 | return (-1); | |
180 | ||
181 | if (BN_print_fp(ofile, omodulus) < 1) | |
182 | return (-1); | |
183 | ||
184 | res = fprintf(ofile, "\n"); | |
185 | fflush(ofile); | |
186 | ||
187 | return (res > 0 ? 0 : -1); | |
188 | } | |
189 | ||
190 | ||
191 | /* | |
192 | ** Sieve p's and q's with small factors | |
193 | */ | |
194 | static void | |
195 | sieve_large(u_int32_t s) | |
196 | { | |
197 | u_int32_t r, u; | |
198 | ||
540d72c3 | 199 | debug3("sieve_large %u", s); |
c9307018 | 200 | largetries++; |
201 | /* r = largebase mod s */ | |
202 | r = BN_mod_word(largebase, s); | |
203 | if (r == 0) | |
204 | u = 0; /* s divides into largebase exactly */ | |
205 | else | |
206 | u = s - r; /* largebase+u is first entry divisible by s */ | |
207 | ||
208 | if (u < largebits * 2) { | |
209 | /* | |
210 | * The sieve omits p's and q's divisible by 2, so ensure that | |
211 | * largebase+u is odd. Then, step through the sieve in | |
212 | * increments of 2*s | |
213 | */ | |
214 | if (u & 0x1) | |
215 | u += s; /* Make largebase+u odd, and u even */ | |
216 | ||
217 | /* Mark all multiples of 2*s */ | |
218 | for (u /= 2; u < largebits; u += s) | |
219 | BIT_SET(LargeSieve, u); | |
220 | } | |
221 | ||
222 | /* r = p mod s */ | |
223 | r = (2 * r + 1) % s; | |
224 | if (r == 0) | |
225 | u = 0; /* s divides p exactly */ | |
226 | else | |
227 | u = s - r; /* p+u is first entry divisible by s */ | |
228 | ||
229 | if (u < largebits * 4) { | |
230 | /* | |
231 | * The sieve omits p's divisible by 4, so ensure that | |
232 | * largebase+u is not. Then, step through the sieve in | |
233 | * increments of 4*s | |
234 | */ | |
235 | while (u & 0x3) { | |
236 | if (SMALL_MAXIMUM - u < s) | |
237 | return; | |
238 | u += s; | |
239 | } | |
240 | ||
241 | /* Mark all multiples of 4*s */ | |
242 | for (u /= 4; u < largebits; u += s) | |
243 | BIT_SET(LargeSieve, u); | |
244 | } | |
245 | } | |
246 | ||
247 | /* | |
7e82606e | 248 | * list candidates for Sophie-Germain primes (where q = (p-1)/2) |
c9307018 | 249 | * to standard output. |
250 | * The list is checked against small known primes (less than 2**30). | |
251 | */ | |
252 | int | |
2ce0bfe4 | 253 | gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) |
c9307018 | 254 | { |
255 | BIGNUM *q; | |
256 | u_int32_t j, r, s, t; | |
257 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
258 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
259 | time_t time_start, time_stop; | |
2ce0bfe4 | 260 | u_int32_t i; |
261 | int ret = 0; | |
c9307018 | 262 | |
263 | largememory = memory; | |
264 | ||
7e82606e | 265 | if (memory != 0 && |
2ce0bfe4 | 266 | (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { |
7e82606e | 267 | error("Invalid memory amount (min %ld, max %ld)", |
268 | LARGE_MINIMUM, LARGE_MAXIMUM); | |
269 | return (-1); | |
270 | } | |
271 | ||
c9307018 | 272 | /* |
540d72c3 | 273 | * Set power to the length in bits of the prime to be generated. |
274 | * This is changed to 1 less than the desired safe prime moduli p. | |
275 | */ | |
c9307018 | 276 | if (power > TEST_MAXIMUM) { |
277 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
278 | return (-1); | |
279 | } else if (power < TEST_MINIMUM) { | |
280 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
281 | return (-1); | |
282 | } | |
283 | power--; /* decrement before squaring */ | |
284 | ||
285 | /* | |
540d72c3 | 286 | * The density of ordinary primes is on the order of 1/bits, so the |
287 | * density of safe primes should be about (1/bits)**2. Set test range | |
288 | * to something well above bits**2 to be reasonably sure (but not | |
289 | * guaranteed) of catching at least one safe prime. | |
c9307018 | 290 | */ |
291 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
292 | ||
293 | /* | |
540d72c3 | 294 | * Need idea of how much memory is available. We don't have to use all |
295 | * of it. | |
c9307018 | 296 | */ |
297 | if (largememory > LARGE_MAXIMUM) { | |
298 | logit("Limited memory: %u MB; limit %lu MB", | |
299 | largememory, LARGE_MAXIMUM); | |
300 | largememory = LARGE_MAXIMUM; | |
301 | } | |
302 | ||
303 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
304 | logit("Increased memory: %u MB; need %u bytes", | |
305 | largememory, (largewords << SHIFT_BYTE)); | |
306 | largewords = (largememory << SHIFT_MEGAWORD); | |
307 | } else if (largememory > 0) { | |
308 | logit("Decreased memory: %u MB; want %u bytes", | |
309 | largememory, (largewords << SHIFT_BYTE)); | |
310 | largewords = (largememory << SHIFT_MEGAWORD); | |
311 | } | |
312 | ||
30460aeb | 313 | TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); |
c9307018 | 314 | tinybits = tinywords << SHIFT_WORD; |
315 | ||
30460aeb | 316 | SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); |
c9307018 | 317 | smallbits = smallwords << SHIFT_WORD; |
318 | ||
319 | /* | |
320 | * dynamically determine available memory | |
321 | */ | |
322 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
323 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
324 | ||
325 | largebits = largewords << SHIFT_WORD; | |
326 | largenumbers = largebits * 2; /* even numbers excluded */ | |
327 | ||
328 | /* validation check: count the number of primes tried */ | |
329 | largetries = 0; | |
330 | q = BN_new(); | |
331 | ||
332 | /* | |
540d72c3 | 333 | * Generate random starting point for subprime search, or use |
334 | * specified parameter. | |
c9307018 | 335 | */ |
336 | largebase = BN_new(); | |
337 | if (start == NULL) | |
338 | BN_rand(largebase, power, 1, 1); | |
339 | else | |
340 | BN_copy(largebase, start); | |
341 | ||
342 | /* ensure odd */ | |
343 | BN_set_bit(largebase, 0); | |
344 | ||
345 | time(&time_start); | |
346 | ||
540d72c3 | 347 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
c9307018 | 348 | largenumbers, power); |
349 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
350 | ||
351 | /* | |
540d72c3 | 352 | * TinySieve |
353 | */ | |
c9307018 | 354 | for (i = 0; i < tinybits; i++) { |
355 | if (BIT_TEST(TinySieve, i)) | |
356 | continue; /* 2*i+3 is composite */ | |
357 | ||
358 | /* The next tiny prime */ | |
359 | t = 2 * i + 3; | |
360 | ||
361 | /* Mark all multiples of t */ | |
362 | for (j = i + t; j < tinybits; j += t) | |
363 | BIT_SET(TinySieve, j); | |
364 | ||
365 | sieve_large(t); | |
366 | } | |
367 | ||
368 | /* | |
540d72c3 | 369 | * Start the small block search at the next possible prime. To avoid |
370 | * fencepost errors, the last pass is skipped. | |
371 | */ | |
c9307018 | 372 | for (smallbase = TINY_NUMBER + 3; |
2ce0bfe4 | 373 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); |
374 | smallbase += TINY_NUMBER) { | |
c9307018 | 375 | for (i = 0; i < tinybits; i++) { |
376 | if (BIT_TEST(TinySieve, i)) | |
377 | continue; /* 2*i+3 is composite */ | |
378 | ||
379 | /* The next tiny prime */ | |
380 | t = 2 * i + 3; | |
381 | r = smallbase % t; | |
382 | ||
383 | if (r == 0) { | |
384 | s = 0; /* t divides into smallbase exactly */ | |
385 | } else { | |
386 | /* smallbase+s is first entry divisible by t */ | |
387 | s = t - r; | |
388 | } | |
389 | ||
390 | /* | |
391 | * The sieve omits even numbers, so ensure that | |
392 | * smallbase+s is odd. Then, step through the sieve | |
393 | * in increments of 2*t | |
394 | */ | |
395 | if (s & 1) | |
396 | s += t; /* Make smallbase+s odd, and s even */ | |
397 | ||
398 | /* Mark all multiples of 2*t */ | |
399 | for (s /= 2; s < smallbits; s += t) | |
400 | BIT_SET(SmallSieve, s); | |
401 | } | |
402 | ||
403 | /* | |
540d72c3 | 404 | * SmallSieve |
405 | */ | |
c9307018 | 406 | for (i = 0; i < smallbits; i++) { |
407 | if (BIT_TEST(SmallSieve, i)) | |
408 | continue; /* 2*i+smallbase is composite */ | |
409 | ||
410 | /* The next small prime */ | |
411 | sieve_large((2 * i) + smallbase); | |
412 | } | |
413 | ||
414 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
415 | } | |
416 | ||
417 | time(&time_stop); | |
418 | ||
419 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
420 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
421 | ||
422 | for (j = r = 0; j < largebits; j++) { | |
423 | if (BIT_TEST(LargeSieve, j)) | |
424 | continue; /* Definitely composite, skip */ | |
425 | ||
426 | debug2("test q = largebase+%u", 2 * j); | |
427 | BN_set_word(q, 2 * j); | |
428 | BN_add(q, q, largebase); | |
7e82606e | 429 | if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE, |
c9307018 | 430 | largetries, (power - 1) /* MSB */, (0), q) == -1) { |
431 | ret = -1; | |
432 | break; | |
433 | } | |
434 | ||
435 | r++; /* count q */ | |
436 | } | |
437 | ||
438 | time(&time_stop); | |
439 | ||
440 | xfree(LargeSieve); | |
441 | xfree(SmallSieve); | |
442 | xfree(TinySieve); | |
443 | ||
444 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
445 | ||
446 | return (ret); | |
447 | } | |
448 | ||
449 | /* | |
450 | * perform a Miller-Rabin primality test | |
451 | * on the list of candidates | |
452 | * (checking both q and p) | |
453 | * The result is a list of so-call "safe" primes | |
454 | */ | |
455 | int | |
7e82606e | 456 | prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) |
c9307018 | 457 | { |
458 | BIGNUM *q, *p, *a; | |
459 | BN_CTX *ctx; | |
460 | char *cp, *lp; | |
461 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
462 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
463 | time_t time_start, time_stop; | |
464 | int res; | |
465 | ||
7e82606e | 466 | if (trials < TRIAL_MINIMUM) { |
467 | error("Minimum primality trials is %d", TRIAL_MINIMUM); | |
468 | return (-1); | |
469 | } | |
470 | ||
c9307018 | 471 | time(&time_start); |
472 | ||
473 | p = BN_new(); | |
474 | q = BN_new(); | |
475 | ctx = BN_CTX_new(); | |
476 | ||
477 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
478 | ctime(&time_start), trials, generator_wanted); | |
479 | ||
480 | res = 0; | |
481 | lp = xmalloc(QLINESIZE + 1); | |
482 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
483 | int ll = strlen(lp); | |
484 | ||
485 | count_in++; | |
486 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
487 | debug2("%10u: comment or short line", count_in); | |
488 | continue; | |
489 | } | |
490 | ||
491 | /* XXX - fragile parser */ | |
492 | /* time */ | |
493 | cp = &lp[14]; /* (skip) */ | |
494 | ||
495 | /* type */ | |
496 | in_type = strtoul(cp, &cp, 10); | |
497 | ||
498 | /* tests */ | |
499 | in_tests = strtoul(cp, &cp, 10); | |
500 | ||
501 | if (in_tests & QTEST_COMPOSITE) { | |
502 | debug2("%10u: known composite", count_in); | |
503 | continue; | |
504 | } | |
540d72c3 | 505 | |
c9307018 | 506 | /* tries */ |
507 | in_tries = strtoul(cp, &cp, 10); | |
508 | ||
509 | /* size (most significant bit) */ | |
510 | in_size = strtoul(cp, &cp, 10); | |
511 | ||
512 | /* generator (hex) */ | |
513 | generator_known = strtoul(cp, &cp, 16); | |
514 | ||
515 | /* Skip white space */ | |
516 | cp += strspn(cp, " "); | |
517 | ||
518 | /* modulus (hex) */ | |
519 | switch (in_type) { | |
7e82606e | 520 | case QTYPE_SOPHIE_GERMAIN: |
521 | debug2("%10u: (%u) Sophie-Germain", count_in, in_type); | |
c9307018 | 522 | a = q; |
523 | BN_hex2bn(&a, cp); | |
524 | /* p = 2*q + 1 */ | |
525 | BN_lshift(p, q, 1); | |
526 | BN_add_word(p, 1); | |
527 | in_size += 1; | |
528 | generator_known = 0; | |
529 | break; | |
540d72c3 | 530 | case QTYPE_UNSTRUCTURED: |
531 | case QTYPE_SAFE: | |
dfddba3d | 532 | case QTYPE_SCHNORR: |
540d72c3 | 533 | case QTYPE_STRONG: |
534 | case QTYPE_UNKNOWN: | |
c9307018 | 535 | debug2("%10u: (%u)", count_in, in_type); |
536 | a = p; | |
537 | BN_hex2bn(&a, cp); | |
538 | /* q = (p-1) / 2 */ | |
539 | BN_rshift(q, p, 1); | |
540 | break; | |
540d72c3 | 541 | default: |
542 | debug2("Unknown prime type"); | |
543 | break; | |
c9307018 | 544 | } |
545 | ||
546 | /* | |
547 | * due to earlier inconsistencies in interpretation, check | |
548 | * the proposed bit size. | |
549 | */ | |
2ce0bfe4 | 550 | if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { |
c9307018 | 551 | debug2("%10u: bit size %u mismatch", count_in, in_size); |
552 | continue; | |
553 | } | |
554 | if (in_size < QSIZE_MINIMUM) { | |
555 | debug2("%10u: bit size %u too short", count_in, in_size); | |
556 | continue; | |
557 | } | |
558 | ||
559 | if (in_tests & QTEST_MILLER_RABIN) | |
560 | in_tries += trials; | |
561 | else | |
562 | in_tries = trials; | |
540d72c3 | 563 | |
c9307018 | 564 | /* |
565 | * guess unknown generator | |
566 | */ | |
567 | if (generator_known == 0) { | |
568 | if (BN_mod_word(p, 24) == 11) | |
569 | generator_known = 2; | |
570 | else if (BN_mod_word(p, 12) == 5) | |
571 | generator_known = 3; | |
572 | else { | |
573 | u_int32_t r = BN_mod_word(p, 10); | |
574 | ||
540d72c3 | 575 | if (r == 3 || r == 7) |
c9307018 | 576 | generator_known = 5; |
c9307018 | 577 | } |
578 | } | |
579 | /* | |
580 | * skip tests when desired generator doesn't match | |
581 | */ | |
582 | if (generator_wanted > 0 && | |
583 | generator_wanted != generator_known) { | |
584 | debug2("%10u: generator %d != %d", | |
585 | count_in, generator_known, generator_wanted); | |
586 | continue; | |
587 | } | |
588 | ||
540d72c3 | 589 | /* |
590 | * Primes with no known generator are useless for DH, so | |
591 | * skip those. | |
592 | */ | |
593 | if (generator_known == 0) { | |
594 | debug2("%10u: no known generator", count_in); | |
595 | continue; | |
596 | } | |
597 | ||
c9307018 | 598 | count_possible++; |
599 | ||
600 | /* | |
540d72c3 | 601 | * The (1/4)^N performance bound on Miller-Rabin is |
602 | * extremely pessimistic, so don't spend a lot of time | |
603 | * really verifying that q is prime until after we know | |
604 | * that p is also prime. A single pass will weed out the | |
c9307018 | 605 | * vast majority of composite q's. |
606 | */ | |
607 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
540d72c3 | 608 | debug("%10u: q failed first possible prime test", |
c9307018 | 609 | count_in); |
610 | continue; | |
611 | } | |
540d72c3 | 612 | |
c9307018 | 613 | /* |
540d72c3 | 614 | * q is possibly prime, so go ahead and really make sure |
615 | * that p is prime. If it is, then we can go back and do | |
616 | * the same for q. If p is composite, chances are that | |
c9307018 | 617 | * will show up on the first Rabin-Miller iteration so it |
618 | * doesn't hurt to specify a high iteration count. | |
619 | */ | |
620 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
540d72c3 | 621 | debug("%10u: p is not prime", count_in); |
c9307018 | 622 | continue; |
623 | } | |
624 | debug("%10u: p is almost certainly prime", count_in); | |
625 | ||
626 | /* recheck q more rigorously */ | |
627 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
628 | debug("%10u: q is not prime", count_in); | |
629 | continue; | |
630 | } | |
631 | debug("%10u: q is almost certainly prime", count_in); | |
632 | ||
540d72c3 | 633 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
c9307018 | 634 | in_tries, in_size, generator_known, p)) { |
635 | res = -1; | |
636 | break; | |
637 | } | |
638 | ||
639 | count_out++; | |
640 | } | |
641 | ||
642 | time(&time_stop); | |
643 | xfree(lp); | |
644 | BN_free(p); | |
645 | BN_free(q); | |
646 | BN_CTX_free(ctx); | |
647 | ||
648 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
540d72c3 | 649 | ctime(&time_stop), count_out, count_possible, |
c9307018 | 650 | (long) (time_stop - time_start)); |
651 | ||
652 | return (res); | |
653 | } |