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[dragonfly.git] / crypto / openssh-5 / moduli.c
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1 /* $OpenBSD: moduli.c,v 1.20 2007/02/24 03:30:11 ray 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.
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.
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.
30 * Two-step process to generate safe primes for DHGEX
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.
36 * First step: generate candidate primes (memory intensive)
37 * Second step: test primes' safety (processor intensive)
40 #include "includes.h"
42 #include <sys/types.h>
44 #include <openssl/bn.h>
46 #include <stdio.h>
47 #include <stdlib.h>
48 #include <string.h>
49 #include <stdarg.h>
50 #include <time.h>
52 #include "xmalloc.h"
53 #include "log.h"
56 * File output defines
59 /* need line long enough for largest moduli plus headers */
60 #define QLINESIZE (100+8192)
62 /* Type: decimal.
63 * Specifies the internal structure of the prime modulus.
65 #define QTYPE_UNKNOWN (0)
66 #define QTYPE_UNSTRUCTURED (1)
67 #define QTYPE_SAFE (2)
68 #define QTYPE_SCHNORR (3)
69 #define QTYPE_SOPHIE_GERMAIN (4)
70 #define QTYPE_STRONG (5)
72 /* Tests: decimal (bit field).
73 * Specifies the methods used in checking for primality.
74 * Usually, more than one test is used.
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)
84 * Size: decimal.
85 * Specifies the number of the most significant bit (0 to M).
86 * WARNING: internally, usually 1 to N.
88 #define QSIZE_MINIMUM (511)
91 * Prime sieving defines
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)
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!
106 #define LARGE_MINIMUM (8UL) /* megabytes */
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).
112 #define LARGE_MAXIMUM (127UL) /* megabytes */
115 * Constant: when used with 32-bit integers, the largest sieve prime
116 * has to be less than 2**32.
118 #define SMALL_MAXIMUM (0xffffffffUL)
120 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
121 #define TINY_NUMBER (1UL<<16)
123 /* Ensure enough bit space for testing 2*q. */
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 */
129 /* bit operations on 32-bit words */
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)))
135 * Prime testing defines
138 /* Minimum number of primality tests to perform */
139 #define TRIAL_MINIMUM (4)
142 * Sieving data (XXX - move to struct)
145 /* sieve 2**16 */
146 static u_int32_t *TinySieve, tinybits;
148 /* sieve 2**30 in 2**16 parts */
149 static u_int32_t *SmallSieve, smallbits, smallbase;
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;
156 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
157 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t);
160 * print moduli out in consistent form,
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)
166 struct tm *gtm;
167 time_t time_now;
168 int res;
170 time(&time_now);
171 gtm = gmtime(&time_now);
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);
178 if (res < 0)
179 return (-1);
181 if (BN_print_fp(ofile, omodulus) < 1)
182 return (-1);
184 res = fprintf(ofile, "\n");
185 fflush(ofile);
187 return (res > 0 ? 0 : -1);
192 ** Sieve p's and q's with small factors
194 static void
195 sieve_large(u_int32_t s)
197 u_int32_t r, u;
199 debug3("sieve_large %u", s);
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 */
208 if (u < largebits * 2) {
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
214 if (u & 0x1)
215 u += s; /* Make largebase+u odd, and u even */
217 /* Mark all multiples of 2*s */
218 for (u /= 2; u < largebits; u += s)
219 BIT_SET(LargeSieve, u);
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 */
229 if (u < largebits * 4) {
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
235 while (u & 0x3) {
236 if (SMALL_MAXIMUM - u < s)
237 return;
238 u += s;
241 /* Mark all multiples of 4*s */
242 for (u /= 4; u < largebits; u += s)
243 BIT_SET(LargeSieve, u);
248 * list candidates for Sophie-Germain primes (where q = (p-1)/2)
249 * to standard output.
250 * The list is checked against small known primes (less than 2**30).
253 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
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;
260 u_int32_t i;
261 int ret = 0;
263 largememory = memory;
265 if (memory != 0 &&
266 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
267 error("Invalid memory amount (min %ld, max %ld)",
268 LARGE_MINIMUM, LARGE_MAXIMUM);
269 return (-1);
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.
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);
283 power--; /* decrement before squaring */
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.
291 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
294 * Need idea of how much memory is available. We don't have to use all
295 * of it.
297 if (largememory > LARGE_MAXIMUM) {
298 logit("Limited memory: %u MB; limit %lu MB",
299 largememory, LARGE_MAXIMUM);
300 largememory = LARGE_MAXIMUM;
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);
313 TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
314 tinybits = tinywords << SHIFT_WORD;
316 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
317 smallbits = smallwords << SHIFT_WORD;
320 * dynamically determine available memory
322 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
323 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
325 largebits = largewords << SHIFT_WORD;
326 largenumbers = largebits * 2; /* even numbers excluded */
328 /* validation check: count the number of primes tried */
329 largetries = 0;
330 if ((q = BN_new()) == NULL)
331 fatal("BN_new failed");
334 * Generate random starting point for subprime search, or use
335 * specified parameter.
337 if ((largebase = BN_new()) == NULL)
338 fatal("BN_new failed");
339 if (start == NULL) {
340 if (BN_rand(largebase, power, 1, 1) == 0)
341 fatal("BN_rand failed");
342 } else {
343 if (BN_copy(largebase, start) == NULL)
344 fatal("BN_copy: failed");
347 /* ensure odd */
348 if (BN_set_bit(largebase, 0) == 0)
349 fatal("BN_set_bit: failed");
351 time(&time_start);
353 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
354 largenumbers, power);
355 debug2("start point: 0x%s", BN_bn2hex(largebase));
358 * TinySieve
360 for (i = 0; i < tinybits; i++) {
361 if (BIT_TEST(TinySieve, i))
362 continue; /* 2*i+3 is composite */
364 /* The next tiny prime */
365 t = 2 * i + 3;
367 /* Mark all multiples of t */
368 for (j = i + t; j < tinybits; j += t)
369 BIT_SET(TinySieve, j);
371 sieve_large(t);
375 * Start the small block search at the next possible prime. To avoid
376 * fencepost errors, the last pass is skipped.
378 for (smallbase = TINY_NUMBER + 3;
379 smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
380 smallbase += TINY_NUMBER) {
381 for (i = 0; i < tinybits; i++) {
382 if (BIT_TEST(TinySieve, i))
383 continue; /* 2*i+3 is composite */
385 /* The next tiny prime */
386 t = 2 * i + 3;
387 r = smallbase % t;
389 if (r == 0) {
390 s = 0; /* t divides into smallbase exactly */
391 } else {
392 /* smallbase+s is first entry divisible by t */
393 s = t - r;
397 * The sieve omits even numbers, so ensure that
398 * smallbase+s is odd. Then, step through the sieve
399 * in increments of 2*t
401 if (s & 1)
402 s += t; /* Make smallbase+s odd, and s even */
404 /* Mark all multiples of 2*t */
405 for (s /= 2; s < smallbits; s += t)
406 BIT_SET(SmallSieve, s);
410 * SmallSieve
412 for (i = 0; i < smallbits; i++) {
413 if (BIT_TEST(SmallSieve, i))
414 continue; /* 2*i+smallbase is composite */
416 /* The next small prime */
417 sieve_large((2 * i) + smallbase);
420 memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
423 time(&time_stop);
425 logit("%.24s Sieved with %u small primes in %ld seconds",
426 ctime(&time_stop), largetries, (long) (time_stop - time_start));
428 for (j = r = 0; j < largebits; j++) {
429 if (BIT_TEST(LargeSieve, j))
430 continue; /* Definitely composite, skip */
432 debug2("test q = largebase+%u", 2 * j);
433 if (BN_set_word(q, 2 * j) == 0)
434 fatal("BN_set_word failed");
435 if (BN_add(q, q, largebase) == 0)
436 fatal("BN_add failed");
437 if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE,
438 largetries, (power - 1) /* MSB */, (0), q) == -1) {
439 ret = -1;
440 break;
443 r++; /* count q */
446 time(&time_stop);
448 xfree(LargeSieve);
449 xfree(SmallSieve);
450 xfree(TinySieve);
452 logit("%.24s Found %u candidates", ctime(&time_stop), r);
454 return (ret);
458 * perform a Miller-Rabin primality test
459 * on the list of candidates
460 * (checking both q and p)
461 * The result is a list of so-call "safe" primes
464 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted)
466 BIGNUM *q, *p, *a;
467 BN_CTX *ctx;
468 char *cp, *lp;
469 u_int32_t count_in = 0, count_out = 0, count_possible = 0;
470 u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
471 time_t time_start, time_stop;
472 int res;
474 if (trials < TRIAL_MINIMUM) {
475 error("Minimum primality trials is %d", TRIAL_MINIMUM);
476 return (-1);
479 time(&time_start);
481 if ((p = BN_new()) == NULL)
482 fatal("BN_new failed");
483 if ((q = BN_new()) == NULL)
484 fatal("BN_new failed");
485 if ((ctx = BN_CTX_new()) == NULL)
486 fatal("BN_CTX_new failed");
488 debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
489 ctime(&time_start), trials, generator_wanted);
491 res = 0;
492 lp = xmalloc(QLINESIZE + 1);
493 while (fgets(lp, QLINESIZE + 1, in) != NULL) {
494 count_in++;
495 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
496 debug2("%10u: comment or short line", count_in);
497 continue;
500 /* XXX - fragile parser */
501 /* time */
502 cp = &lp[14]; /* (skip) */
504 /* type */
505 in_type = strtoul(cp, &cp, 10);
507 /* tests */
508 in_tests = strtoul(cp, &cp, 10);
510 if (in_tests & QTEST_COMPOSITE) {
511 debug2("%10u: known composite", count_in);
512 continue;
515 /* tries */
516 in_tries = strtoul(cp, &cp, 10);
518 /* size (most significant bit) */
519 in_size = strtoul(cp, &cp, 10);
521 /* generator (hex) */
522 generator_known = strtoul(cp, &cp, 16);
524 /* Skip white space */
525 cp += strspn(cp, " ");
527 /* modulus (hex) */
528 switch (in_type) {
529 case QTYPE_SOPHIE_GERMAIN:
530 debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
531 a = q;
532 if (BN_hex2bn(&a, cp) == 0)
533 fatal("BN_hex2bn failed");
534 /* p = 2*q + 1 */
535 if (BN_lshift(p, q, 1) == 0)
536 fatal("BN_lshift failed");
537 if (BN_add_word(p, 1) == 0)
538 fatal("BN_add_word failed");
539 in_size += 1;
540 generator_known = 0;
541 break;
542 case QTYPE_UNSTRUCTURED:
543 case QTYPE_SAFE:
544 case QTYPE_SCHNORR:
545 case QTYPE_STRONG:
546 case QTYPE_UNKNOWN:
547 debug2("%10u: (%u)", count_in, in_type);
548 a = p;
549 if (BN_hex2bn(&a, cp) == 0)
550 fatal("BN_hex2bn failed");
551 /* q = (p-1) / 2 */
552 if (BN_rshift(q, p, 1) == 0)
553 fatal("BN_rshift failed");
554 break;
555 default:
556 debug2("Unknown prime type");
557 break;
561 * due to earlier inconsistencies in interpretation, check
562 * the proposed bit size.
564 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
565 debug2("%10u: bit size %u mismatch", count_in, in_size);
566 continue;
568 if (in_size < QSIZE_MINIMUM) {
569 debug2("%10u: bit size %u too short", count_in, in_size);
570 continue;
573 if (in_tests & QTEST_MILLER_RABIN)
574 in_tries += trials;
575 else
576 in_tries = trials;
579 * guess unknown generator
581 if (generator_known == 0) {
582 if (BN_mod_word(p, 24) == 11)
583 generator_known = 2;
584 else if (BN_mod_word(p, 12) == 5)
585 generator_known = 3;
586 else {
587 u_int32_t r = BN_mod_word(p, 10);
589 if (r == 3 || r == 7)
590 generator_known = 5;
594 * skip tests when desired generator doesn't match
596 if (generator_wanted > 0 &&
597 generator_wanted != generator_known) {
598 debug2("%10u: generator %d != %d",
599 count_in, generator_known, generator_wanted);
600 continue;
604 * Primes with no known generator are useless for DH, so
605 * skip those.
607 if (generator_known == 0) {
608 debug2("%10u: no known generator", count_in);
609 continue;
612 count_possible++;
615 * The (1/4)^N performance bound on Miller-Rabin is
616 * extremely pessimistic, so don't spend a lot of time
617 * really verifying that q is prime until after we know
618 * that p is also prime. A single pass will weed out the
619 * vast majority of composite q's.
621 if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) {
622 debug("%10u: q failed first possible prime test",
623 count_in);
624 continue;
628 * q is possibly prime, so go ahead and really make sure
629 * that p is prime. If it is, then we can go back and do
630 * the same for q. If p is composite, chances are that
631 * will show up on the first Rabin-Miller iteration so it
632 * doesn't hurt to specify a high iteration count.
634 if (!BN_is_prime(p, trials, NULL, ctx, NULL)) {
635 debug("%10u: p is not prime", count_in);
636 continue;
638 debug("%10u: p is almost certainly prime", count_in);
640 /* recheck q more rigorously */
641 if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) {
642 debug("%10u: q is not prime", count_in);
643 continue;
645 debug("%10u: q is almost certainly prime", count_in);
647 if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN),
648 in_tries, in_size, generator_known, p)) {
649 res = -1;
650 break;
653 count_out++;
656 time(&time_stop);
657 xfree(lp);
658 BN_free(p);
659 BN_free(q);
660 BN_CTX_free(ctx);
662 logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
663 ctime(&time_stop), count_out, count_possible,
664 (long) (time_stop - time_start));
666 return (res);