blob: eb2c0fd18e8a27e28e842436a465d496e2c86cfb [file] [log] [blame]
Darren Tuckerb2f9d412003-08-02 23:51:38 +10001/* $OpenBSD: moduli.c,v 1.1 2003/07/28 09:49:56 djm 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#include "moduli.h"
42#include "xmalloc.h"
43#include "log.h"
44
45#include <openssl/bn.h>
46
47
48/*
49 * Debugging defines
50 */
51
52/* define DEBUG_LARGE 1 */
53/* define DEBUG_SMALL 1 */
54/* define DEBUG_TEST 1 */
55
56/*
57 * File output defines
58 */
59
60/* need line long enough for largest moduli plus headers */
61#define QLINESIZE (100+8192)
62
63/* Type: decimal.
64 * Specifies the internal structure of the prime modulus.
65 */
66#define QTYPE_UNKNOWN (0)
67#define QTYPE_UNSTRUCTURED (1)
68#define QTYPE_SAFE (2)
69#define QTYPE_SCHNOOR (3)
70#define QTYPE_SOPHIE_GERMAINE (4)
71#define QTYPE_STRONG (5)
72
73/* Tests: decimal (bit field).
74 * Specifies the methods used in checking for primality.
75 * Usually, more than one test is used.
76 */
77#define QTEST_UNTESTED (0x00)
78#define QTEST_COMPOSITE (0x01)
79#define QTEST_SIEVE (0x02)
80#define QTEST_MILLER_RABIN (0x04)
81#define QTEST_JACOBI (0x08)
82#define QTEST_ELLIPTIC (0x10)
83
84/* Size: decimal.
85 * Specifies the number of the most significant bit (0 to M).
86 ** WARNING: internally, usually 1 to N.
87 */
88#define QSIZE_MINIMUM (511)
89
90/*
91 * Prime sieving defines
92 */
93
94/* Constant: assuming 8 bit bytes and 32 bit words */
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 * 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/*
126 * Sieving data (XXX - move to struct)
127 */
128
129/* sieve 2**16 */
130static u_int32_t *TinySieve, tinybits;
131
132/* sieve 2**30 in 2**16 parts */
133static u_int32_t *SmallSieve, smallbits, smallbase;
134
135/* sieve relative to the initial value */
136static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
137static u_int32_t largebits, largememory; /* megabytes */
138static BIGNUM *largebase;
139
140
141/*
142 * print moduli out in consistent form,
143 */
144static int
145qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
146 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
147{
148 struct tm *gtm;
149 time_t time_now;
150 int res;
151
152 time(&time_now);
153 gtm = gmtime(&time_now);
154
155 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
156 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
157 gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
158 otype, otests, otries, osize, ogenerator);
159
160 if (res < 0)
161 return (-1);
162
163 if (BN_print_fp(ofile, omodulus) < 1)
164 return (-1);
165
166 res = fprintf(ofile, "\n");
167 fflush(ofile);
168
169 return (res > 0 ? 0 : -1);
170}
171
172
173/*
174 ** Sieve p's and q's with small factors
175 */
176static void
177sieve_large(u_int32_t s)
178{
179 u_int32_t r, u;
180
181 debug2("sieve_large %u", s);
182 largetries++;
183 /* r = largebase mod s */
184 r = BN_mod_word(largebase, s);
185 if (r == 0)
186 u = 0; /* s divides into largebase exactly */
187 else
188 u = s - r; /* largebase+u is first entry divisible by s */
189
190 if (u < largebits * 2) {
191 /*
192 * The sieve omits p's and q's divisible by 2, so ensure that
193 * largebase+u is odd. Then, step through the sieve in
194 * increments of 2*s
195 */
196 if (u & 0x1)
197 u += s; /* Make largebase+u odd, and u even */
198
199 /* Mark all multiples of 2*s */
200 for (u /= 2; u < largebits; u += s)
201 BIT_SET(LargeSieve, u);
202 }
203
204 /* r = p mod s */
205 r = (2 * r + 1) % s;
206 if (r == 0)
207 u = 0; /* s divides p exactly */
208 else
209 u = s - r; /* p+u is first entry divisible by s */
210
211 if (u < largebits * 4) {
212 /*
213 * The sieve omits p's divisible by 4, so ensure that
214 * largebase+u is not. Then, step through the sieve in
215 * increments of 4*s
216 */
217 while (u & 0x3) {
218 if (SMALL_MAXIMUM - u < s)
219 return;
220 u += s;
221 }
222
223 /* Mark all multiples of 4*s */
224 for (u /= 4; u < largebits; u += s)
225 BIT_SET(LargeSieve, u);
226 }
227}
228
229/*
230 * list candidates for Sophie-Germaine primes (where q = (p-1)/2)
231 * to standard output.
232 * The list is checked against small known primes (less than 2**30).
233 */
234int
235gen_candidates(FILE *out, int memory, int power, BIGNUM *start)
236{
237 BIGNUM *q;
238 u_int32_t j, r, s, t;
239 u_int32_t smallwords = TINY_NUMBER >> 6;
240 u_int32_t tinywords = TINY_NUMBER >> 6;
241 time_t time_start, time_stop;
242 int i, ret = 0;
243
244 largememory = memory;
245
246 /*
247 * Set power to the length in bits of the prime to be generated.
248 * This is changed to 1 less than the desired safe prime moduli p.
249 */
250 if (power > TEST_MAXIMUM) {
251 error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
252 return (-1);
253 } else if (power < TEST_MINIMUM) {
254 error("Too few bits: %u < %u", power, TEST_MINIMUM);
255 return (-1);
256 }
257 power--; /* decrement before squaring */
258
259 /*
260 * The density of ordinary primes is on the order of 1/bits, so the
261 * density of safe primes should be about (1/bits)**2. Set test range
262 * to something well above bits**2 to be reasonably sure (but not
263 * guaranteed) of catching at least one safe prime.
264 */
265 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
266
267 /*
268 * Need idea of how much memory is available. We don't have to use all
269 * of it.
270 */
271 if (largememory > LARGE_MAXIMUM) {
272 logit("Limited memory: %u MB; limit %lu MB",
273 largememory, LARGE_MAXIMUM);
274 largememory = LARGE_MAXIMUM;
275 }
276
277 if (largewords <= (largememory << SHIFT_MEGAWORD)) {
278 logit("Increased memory: %u MB; need %u bytes",
279 largememory, (largewords << SHIFT_BYTE));
280 largewords = (largememory << SHIFT_MEGAWORD);
281 } else if (largememory > 0) {
282 logit("Decreased memory: %u MB; want %u bytes",
283 largememory, (largewords << SHIFT_BYTE));
284 largewords = (largememory << SHIFT_MEGAWORD);
285 }
286
287 TinySieve = calloc(tinywords, sizeof(u_int32_t));
288 if (TinySieve == NULL) {
289 error("Insufficient memory for tiny sieve: need %u bytes",
290 tinywords << SHIFT_BYTE);
291 exit(1);
292 }
293 tinybits = tinywords << SHIFT_WORD;
294
295 SmallSieve = calloc(smallwords, sizeof(u_int32_t));
296 if (SmallSieve == NULL) {
297 error("Insufficient memory for small sieve: need %u bytes",
298 smallwords << SHIFT_BYTE);
299 xfree(TinySieve);
300 exit(1);
301 }
302 smallbits = smallwords << SHIFT_WORD;
303
304 /*
305 * dynamically determine available memory
306 */
307 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
308 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
309
310 largebits = largewords << SHIFT_WORD;
311 largenumbers = largebits * 2; /* even numbers excluded */
312
313 /* validation check: count the number of primes tried */
314 largetries = 0;
315 q = BN_new();
316
317 /*
318 * Generate random starting point for subprime search, or use
319 * specified parameter.
320 */
321 largebase = BN_new();
322 if (start == NULL)
323 BN_rand(largebase, power, 1, 1);
324 else
325 BN_copy(largebase, start);
326
327 /* ensure odd */
328 BN_set_bit(largebase, 0);
329
330 time(&time_start);
331
332 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
333 largenumbers, power);
334 debug2("start point: 0x%s", BN_bn2hex(largebase));
335
336 /*
337 * TinySieve
338 */
339 for (i = 0; i < tinybits; i++) {
340 if (BIT_TEST(TinySieve, i))
341 continue; /* 2*i+3 is composite */
342
343 /* The next tiny prime */
344 t = 2 * i + 3;
345
346 /* Mark all multiples of t */
347 for (j = i + t; j < tinybits; j += t)
348 BIT_SET(TinySieve, j);
349
350 sieve_large(t);
351 }
352
353 /*
354 * Start the small block search at the next possible prime. To avoid
355 * fencepost errors, the last pass is skipped.
356 */
357 for (smallbase = TINY_NUMBER + 3;
358 smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
359 smallbase += TINY_NUMBER) {
360 for (i = 0; i < tinybits; i++) {
361 if (BIT_TEST(TinySieve, i))
362 continue; /* 2*i+3 is composite */
363
364 /* The next tiny prime */
365 t = 2 * i + 3;
366 r = smallbase % t;
367
368 if (r == 0) {
369 s = 0; /* t divides into smallbase exactly */
370 } else {
371 /* smallbase+s is first entry divisible by t */
372 s = t - r;
373 }
374
375 /*
376 * The sieve omits even numbers, so ensure that
377 * smallbase+s is odd. Then, step through the sieve
378 * in increments of 2*t
379 */
380 if (s & 1)
381 s += t; /* Make smallbase+s odd, and s even */
382
383 /* Mark all multiples of 2*t */
384 for (s /= 2; s < smallbits; s += t)
385 BIT_SET(SmallSieve, s);
386 }
387
388 /*
389 * SmallSieve
390 */
391 for (i = 0; i < smallbits; i++) {
392 if (BIT_TEST(SmallSieve, i))
393 continue; /* 2*i+smallbase is composite */
394
395 /* The next small prime */
396 sieve_large((2 * i) + smallbase);
397 }
398
399 memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
400 }
401
402 time(&time_stop);
403
404 logit("%.24s Sieved with %u small primes in %ld seconds",
405 ctime(&time_stop), largetries, (long) (time_stop - time_start));
406
407 for (j = r = 0; j < largebits; j++) {
408 if (BIT_TEST(LargeSieve, j))
409 continue; /* Definitely composite, skip */
410
411 debug2("test q = largebase+%u", 2 * j);
412 BN_set_word(q, 2 * j);
413 BN_add(q, q, largebase);
414 if (qfileout(out, QTYPE_SOPHIE_GERMAINE, QTEST_SIEVE,
415 largetries, (power - 1) /* MSB */, (0), q) == -1) {
416 ret = -1;
417 break;
418 }
419
420 r++; /* count q */
421 }
422
423 time(&time_stop);
424
425 xfree(LargeSieve);
426 xfree(SmallSieve);
427 xfree(TinySieve);
428
429 logit("%.24s Found %u candidates", ctime(&time_stop), r);
430
431 return (ret);
432}
433
434/*
435 * perform a Miller-Rabin primality test
436 * on the list of candidates
437 * (checking both q and p)
438 * The result is a list of so-call "safe" primes
439 */
440int
441prime_test(FILE *in, FILE *out, u_int32_t trials,
442 u_int32_t generator_wanted)
443{
444 BIGNUM *q, *p, *a;
445 BN_CTX *ctx;
446 char *cp, *lp;
447 u_int32_t count_in = 0, count_out = 0, count_possible = 0;
448 u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
449 time_t time_start, time_stop;
450 int res;
451
452 time(&time_start);
453
454 p = BN_new();
455 q = BN_new();
456 ctx = BN_CTX_new();
457
458 debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
459 ctime(&time_start), trials, generator_wanted);
460
461 res = 0;
462 lp = xmalloc(QLINESIZE + 1);
463 while (fgets(lp, QLINESIZE, in) != NULL) {
464 int ll = strlen(lp);
465
466 count_in++;
467 if (ll < 14 || *lp == '!' || *lp == '#') {
468 debug2("%10u: comment or short line", count_in);
469 continue;
470 }
471
472 /* XXX - fragile parser */
473 /* time */
474 cp = &lp[14]; /* (skip) */
475
476 /* type */
477 in_type = strtoul(cp, &cp, 10);
478
479 /* tests */
480 in_tests = strtoul(cp, &cp, 10);
481
482 if (in_tests & QTEST_COMPOSITE) {
483 debug2("%10u: known composite", count_in);
484 continue;
485 }
486 /* tries */
487 in_tries = strtoul(cp, &cp, 10);
488
489 /* size (most significant bit) */
490 in_size = strtoul(cp, &cp, 10);
491
492 /* generator (hex) */
493 generator_known = strtoul(cp, &cp, 16);
494
495 /* Skip white space */
496 cp += strspn(cp, " ");
497
498 /* modulus (hex) */
499 switch (in_type) {
500 case QTYPE_SOPHIE_GERMAINE:
501 debug2("%10u: (%u) Sophie-Germaine", count_in, in_type);
502 a = q;
503 BN_hex2bn(&a, cp);
504 /* p = 2*q + 1 */
505 BN_lshift(p, q, 1);
506 BN_add_word(p, 1);
507 in_size += 1;
508 generator_known = 0;
509 break;
510 default:
511 debug2("%10u: (%u)", count_in, in_type);
512 a = p;
513 BN_hex2bn(&a, cp);
514 /* q = (p-1) / 2 */
515 BN_rshift(q, p, 1);
516 break;
517 }
518
519 /*
520 * due to earlier inconsistencies in interpretation, check
521 * the proposed bit size.
522 */
523 if (BN_num_bits(p) != (in_size + 1)) {
524 debug2("%10u: bit size %u mismatch", count_in, in_size);
525 continue;
526 }
527 if (in_size < QSIZE_MINIMUM) {
528 debug2("%10u: bit size %u too short", count_in, in_size);
529 continue;
530 }
531
532 if (in_tests & QTEST_MILLER_RABIN)
533 in_tries += trials;
534 else
535 in_tries = trials;
536 /*
537 * guess unknown generator
538 */
539 if (generator_known == 0) {
540 if (BN_mod_word(p, 24) == 11)
541 generator_known = 2;
542 else if (BN_mod_word(p, 12) == 5)
543 generator_known = 3;
544 else {
545 u_int32_t r = BN_mod_word(p, 10);
546
547 if (r == 3 || r == 7) {
548 generator_known = 5;
549 }
550 }
551 }
552 /*
553 * skip tests when desired generator doesn't match
554 */
555 if (generator_wanted > 0 &&
556 generator_wanted != generator_known) {
557 debug2("%10u: generator %d != %d",
558 count_in, generator_known, generator_wanted);
559 continue;
560 }
561
562 count_possible++;
563
564 /*
565 * The (1/4)^N performance bound on Miller-Rabin is
566 * extremely pessimistic, so don't spend a lot of time
567 * really verifying that q is prime until after we know
568 * that p is also prime. A single pass will weed out the
569 * vast majority of composite q's.
570 */
571 if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) {
572 debug2("%10u: q failed first possible prime test",
573 count_in);
574 continue;
575 }
576
577 /*
578 * q is possibly prime, so go ahead and really make sure
579 * that p is prime. If it is, then we can go back and do
580 * the same for q. If p is composite, chances are that
581 * will show up on the first Rabin-Miller iteration so it
582 * doesn't hurt to specify a high iteration count.
583 */
584 if (!BN_is_prime(p, trials, NULL, ctx, NULL)) {
585 debug2("%10u: p is not prime", count_in);
586 continue;
587 }
588 debug("%10u: p is almost certainly prime", count_in);
589
590 /* recheck q more rigorously */
591 if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) {
592 debug("%10u: q is not prime", count_in);
593 continue;
594 }
595 debug("%10u: q is almost certainly prime", count_in);
596
597 if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN),
598 in_tries, in_size, generator_known, p)) {
599 res = -1;
600 break;
601 }
602
603 count_out++;
604 }
605
606 time(&time_stop);
607 xfree(lp);
608 BN_free(p);
609 BN_free(q);
610 BN_CTX_free(ctx);
611
612 logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
613 ctime(&time_stop), count_out, count_possible,
614 (long) (time_stop - time_start));
615
616 return (res);
617}