Annotation of src/usr.bin/ssh/moduli.c, Revision 1.2
1.2 ! djm 1: /* $OpenBSD: moduli.c,v 1.1 2003/07/28 09:49:56 djm Exp $ */
1.1 djm 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: /*
1.2 ! djm 49: * Debugging defines
1.1 djm 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 */
130: static u_int32_t *TinySieve, tinybits;
131:
132: /* sieve 2**30 in 2**16 parts */
133: static u_int32_t *SmallSieve, smallbits, smallbase;
134:
135: /* sieve relative to the initial value */
136: static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
137: static u_int32_t largebits, largememory; /* megabytes */
138: static BIGNUM *largebase;
139:
140:
141: /*
142: * print moduli out in consistent form,
143: */
144: static int
145: qfileout(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);
1.2 ! djm 154:
1.1 djm 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: */
176: static void
177: sieve_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: */
234: int
235: gen_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: /*
1.2 ! djm 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: */
1.1 djm 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: /*
1.2 ! djm 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.
1.1 djm 264: */
265: largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
266:
267: /*
1.2 ! djm 268: * Need idea of how much memory is available. We don't have to use all
! 269: * of it.
1.1 djm 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: /*
1.2 ! djm 318: * Generate random starting point for subprime search, or use
! 319: * specified parameter.
1.1 djm 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:
1.2 ! djm 332: logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
1.1 djm 333: largenumbers, power);
334: debug2("start point: 0x%s", BN_bn2hex(largebase));
335:
336: /*
1.2 ! djm 337: * TinySieve
! 338: */
1.1 djm 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: /*
1.2 ! djm 354: * Start the small block search at the next possible prime. To avoid
! 355: * fencepost errors, the last pass is skipped.
! 356: */
1.1 djm 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: /*
1.2 ! djm 389: * SmallSieve
! 390: */
1.1 djm 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: */
440: int
1.2 ! djm 441: prime_test(FILE *in, FILE *out, u_int32_t trials,
1.1 djm 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: /*
1.2 ! djm 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
1.1 djm 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: }
1.2 ! djm 576:
1.1 djm 577: /*
1.2 ! djm 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
1.1 djm 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:
1.2 ! djm 597: if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN),
1.1 djm 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",
1.2 ! djm 613: ctime(&time_stop), count_out, count_possible,
1.1 djm 614: (long) (time_stop - time_start));
615:
616: return (res);
617: }
![[BACK]](/icons/back.gif){kind=icon}
Return to moduli.c CVS log ![[TXT]](/icons/text.gif){kind=icon}
![[DIR]](/icons/dir.gif){kind=icon}
Up to [local] / src / usr.bin / ssh