Annotation of src/usr.bin/ssh/moduli.c, Revision 1.4
1.4 ! dtucker 1: /* $OpenBSD: moduli.c,v 1.3 2003/12/07 06:34:18 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: * File output defines
49: */
50:
51: /* need line long enough for largest moduli plus headers */
52: #define QLINESIZE (100+8192)
53:
54: /* Type: decimal.
55: * Specifies the internal structure of the prime modulus.
56: */
57: #define QTYPE_UNKNOWN (0)
58: #define QTYPE_UNSTRUCTURED (1)
59: #define QTYPE_SAFE (2)
60: #define QTYPE_SCHNOOR (3)
61: #define QTYPE_SOPHIE_GERMAINE (4)
62: #define QTYPE_STRONG (5)
63:
64: /* Tests: decimal (bit field).
65: * Specifies the methods used in checking for primality.
66: * Usually, more than one test is used.
67: */
68: #define QTEST_UNTESTED (0x00)
69: #define QTEST_COMPOSITE (0x01)
70: #define QTEST_SIEVE (0x02)
71: #define QTEST_MILLER_RABIN (0x04)
72: #define QTEST_JACOBI (0x08)
73: #define QTEST_ELLIPTIC (0x10)
74:
75: /* Size: decimal.
76: * Specifies the number of the most significant bit (0 to M).
77: ** WARNING: internally, usually 1 to N.
78: */
79: #define QSIZE_MINIMUM (511)
80:
81: /*
82: * Prime sieving defines
83: */
84:
85: /* Constant: assuming 8 bit bytes and 32 bit words */
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: * Constant: when used with 32-bit integers, the largest sieve prime
94: * has to be less than 2**32.
95: */
96: #define SMALL_MAXIMUM (0xffffffffUL)
97:
98: /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
99: #define TINY_NUMBER (1UL<<16)
100:
101: /* Ensure enough bit space for testing 2*q. */
102: #define TEST_MAXIMUM (1UL<<16)
103: #define TEST_MINIMUM (QSIZE_MINIMUM + 1)
104: /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */
105: #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */
106:
107: /* bit operations on 32-bit words */
108: #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
109: #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
110: #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
111:
112: /*
113: * Prime testing defines
114: */
115:
116: /*
117: * Sieving data (XXX - move to struct)
118: */
119:
120: /* sieve 2**16 */
121: static u_int32_t *TinySieve, tinybits;
122:
123: /* sieve 2**30 in 2**16 parts */
124: static u_int32_t *SmallSieve, smallbits, smallbase;
125:
126: /* sieve relative to the initial value */
127: static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
128: static u_int32_t largebits, largememory; /* megabytes */
129: static BIGNUM *largebase;
130:
131:
132: /*
133: * print moduli out in consistent form,
134: */
135: static int
136: qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
137: u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
138: {
139: struct tm *gtm;
140: time_t time_now;
141: int res;
142:
143: time(&time_now);
144: gtm = gmtime(&time_now);
1.2 djm 145:
1.1 djm 146: res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
147: gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
148: gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
149: otype, otests, otries, osize, ogenerator);
150:
151: if (res < 0)
152: return (-1);
153:
154: if (BN_print_fp(ofile, omodulus) < 1)
155: return (-1);
156:
157: res = fprintf(ofile, "\n");
158: fflush(ofile);
159:
160: return (res > 0 ? 0 : -1);
161: }
162:
163:
164: /*
165: ** Sieve p's and q's with small factors
166: */
167: static void
168: sieve_large(u_int32_t s)
169: {
170: u_int32_t r, u;
171:
172: debug2("sieve_large %u", s);
173: largetries++;
174: /* r = largebase mod s */
175: r = BN_mod_word(largebase, s);
176: if (r == 0)
177: u = 0; /* s divides into largebase exactly */
178: else
179: u = s - r; /* largebase+u is first entry divisible by s */
180:
181: if (u < largebits * 2) {
182: /*
183: * The sieve omits p's and q's divisible by 2, so ensure that
184: * largebase+u is odd. Then, step through the sieve in
185: * increments of 2*s
186: */
187: if (u & 0x1)
188: u += s; /* Make largebase+u odd, and u even */
189:
190: /* Mark all multiples of 2*s */
191: for (u /= 2; u < largebits; u += s)
192: BIT_SET(LargeSieve, u);
193: }
194:
195: /* r = p mod s */
196: r = (2 * r + 1) % s;
197: if (r == 0)
198: u = 0; /* s divides p exactly */
199: else
200: u = s - r; /* p+u is first entry divisible by s */
201:
202: if (u < largebits * 4) {
203: /*
204: * The sieve omits p's divisible by 4, so ensure that
205: * largebase+u is not. Then, step through the sieve in
206: * increments of 4*s
207: */
208: while (u & 0x3) {
209: if (SMALL_MAXIMUM - u < s)
210: return;
211: u += s;
212: }
213:
214: /* Mark all multiples of 4*s */
215: for (u /= 4; u < largebits; u += s)
216: BIT_SET(LargeSieve, u);
217: }
218: }
219:
220: /*
221: * list candidates for Sophie-Germaine primes (where q = (p-1)/2)
222: * to standard output.
223: * The list is checked against small known primes (less than 2**30).
224: */
225: int
226: gen_candidates(FILE *out, int memory, int power, BIGNUM *start)
227: {
228: BIGNUM *q;
229: u_int32_t j, r, s, t;
230: u_int32_t smallwords = TINY_NUMBER >> 6;
231: u_int32_t tinywords = TINY_NUMBER >> 6;
232: time_t time_start, time_stop;
233: int i, ret = 0;
234:
235: largememory = memory;
236:
237: /*
1.2 djm 238: * Set power to the length in bits of the prime to be generated.
239: * This is changed to 1 less than the desired safe prime moduli p.
240: */
1.1 djm 241: if (power > TEST_MAXIMUM) {
242: error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
243: return (-1);
244: } else if (power < TEST_MINIMUM) {
245: error("Too few bits: %u < %u", power, TEST_MINIMUM);
246: return (-1);
247: }
248: power--; /* decrement before squaring */
249:
250: /*
1.2 djm 251: * The density of ordinary primes is on the order of 1/bits, so the
252: * density of safe primes should be about (1/bits)**2. Set test range
253: * to something well above bits**2 to be reasonably sure (but not
254: * guaranteed) of catching at least one safe prime.
1.1 djm 255: */
256: largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
257:
258: /*
1.2 djm 259: * Need idea of how much memory is available. We don't have to use all
260: * of it.
1.1 djm 261: */
262: if (largememory > LARGE_MAXIMUM) {
263: logit("Limited memory: %u MB; limit %lu MB",
264: largememory, LARGE_MAXIMUM);
265: largememory = LARGE_MAXIMUM;
266: }
267:
268: if (largewords <= (largememory << SHIFT_MEGAWORD)) {
269: logit("Increased memory: %u MB; need %u bytes",
270: largememory, (largewords << SHIFT_BYTE));
271: largewords = (largememory << SHIFT_MEGAWORD);
272: } else if (largememory > 0) {
273: logit("Decreased memory: %u MB; want %u bytes",
274: largememory, (largewords << SHIFT_BYTE));
275: largewords = (largememory << SHIFT_MEGAWORD);
276: }
277:
278: TinySieve = calloc(tinywords, sizeof(u_int32_t));
279: if (TinySieve == NULL) {
280: error("Insufficient memory for tiny sieve: need %u bytes",
281: tinywords << SHIFT_BYTE);
282: exit(1);
283: }
284: tinybits = tinywords << SHIFT_WORD;
285:
286: SmallSieve = calloc(smallwords, sizeof(u_int32_t));
287: if (SmallSieve == NULL) {
288: error("Insufficient memory for small sieve: need %u bytes",
289: smallwords << SHIFT_BYTE);
290: xfree(TinySieve);
291: exit(1);
292: }
293: smallbits = smallwords << SHIFT_WORD;
294:
295: /*
296: * dynamically determine available memory
297: */
298: while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
299: largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
300:
301: largebits = largewords << SHIFT_WORD;
302: largenumbers = largebits * 2; /* even numbers excluded */
303:
304: /* validation check: count the number of primes tried */
305: largetries = 0;
306: q = BN_new();
307:
308: /*
1.2 djm 309: * Generate random starting point for subprime search, or use
310: * specified parameter.
1.1 djm 311: */
312: largebase = BN_new();
313: if (start == NULL)
314: BN_rand(largebase, power, 1, 1);
315: else
316: BN_copy(largebase, start);
317:
318: /* ensure odd */
319: BN_set_bit(largebase, 0);
320:
321: time(&time_start);
322:
1.2 djm 323: logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
1.1 djm 324: largenumbers, power);
325: debug2("start point: 0x%s", BN_bn2hex(largebase));
326:
327: /*
1.2 djm 328: * TinySieve
329: */
1.1 djm 330: for (i = 0; i < tinybits; i++) {
331: if (BIT_TEST(TinySieve, i))
332: continue; /* 2*i+3 is composite */
333:
334: /* The next tiny prime */
335: t = 2 * i + 3;
336:
337: /* Mark all multiples of t */
338: for (j = i + t; j < tinybits; j += t)
339: BIT_SET(TinySieve, j);
340:
341: sieve_large(t);
342: }
343:
344: /*
1.2 djm 345: * Start the small block search at the next possible prime. To avoid
346: * fencepost errors, the last pass is skipped.
347: */
1.1 djm 348: for (smallbase = TINY_NUMBER + 3;
349: smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
350: smallbase += TINY_NUMBER) {
351: for (i = 0; i < tinybits; i++) {
352: if (BIT_TEST(TinySieve, i))
353: continue; /* 2*i+3 is composite */
354:
355: /* The next tiny prime */
356: t = 2 * i + 3;
357: r = smallbase % t;
358:
359: if (r == 0) {
360: s = 0; /* t divides into smallbase exactly */
361: } else {
362: /* smallbase+s is first entry divisible by t */
363: s = t - r;
364: }
365:
366: /*
367: * The sieve omits even numbers, so ensure that
368: * smallbase+s is odd. Then, step through the sieve
369: * in increments of 2*t
370: */
371: if (s & 1)
372: s += t; /* Make smallbase+s odd, and s even */
373:
374: /* Mark all multiples of 2*t */
375: for (s /= 2; s < smallbits; s += t)
376: BIT_SET(SmallSieve, s);
377: }
378:
379: /*
1.2 djm 380: * SmallSieve
381: */
1.1 djm 382: for (i = 0; i < smallbits; i++) {
383: if (BIT_TEST(SmallSieve, i))
384: continue; /* 2*i+smallbase is composite */
385:
386: /* The next small prime */
387: sieve_large((2 * i) + smallbase);
388: }
389:
390: memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
391: }
392:
393: time(&time_stop);
394:
395: logit("%.24s Sieved with %u small primes in %ld seconds",
396: ctime(&time_stop), largetries, (long) (time_stop - time_start));
397:
398: for (j = r = 0; j < largebits; j++) {
399: if (BIT_TEST(LargeSieve, j))
400: continue; /* Definitely composite, skip */
401:
402: debug2("test q = largebase+%u", 2 * j);
403: BN_set_word(q, 2 * j);
404: BN_add(q, q, largebase);
405: if (qfileout(out, QTYPE_SOPHIE_GERMAINE, QTEST_SIEVE,
406: largetries, (power - 1) /* MSB */, (0), q) == -1) {
407: ret = -1;
408: break;
409: }
410:
411: r++; /* count q */
412: }
413:
414: time(&time_stop);
415:
416: xfree(LargeSieve);
417: xfree(SmallSieve);
418: xfree(TinySieve);
419:
420: logit("%.24s Found %u candidates", ctime(&time_stop), r);
421:
422: return (ret);
423: }
424:
425: /*
426: * perform a Miller-Rabin primality test
427: * on the list of candidates
428: * (checking both q and p)
429: * The result is a list of so-call "safe" primes
430: */
431: int
1.2 djm 432: prime_test(FILE *in, FILE *out, u_int32_t trials,
1.1 djm 433: u_int32_t generator_wanted)
434: {
435: BIGNUM *q, *p, *a;
436: BN_CTX *ctx;
437: char *cp, *lp;
438: u_int32_t count_in = 0, count_out = 0, count_possible = 0;
439: u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
440: time_t time_start, time_stop;
441: int res;
442:
443: time(&time_start);
444:
445: p = BN_new();
446: q = BN_new();
447: ctx = BN_CTX_new();
448:
449: debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
450: ctime(&time_start), trials, generator_wanted);
451:
452: res = 0;
453: lp = xmalloc(QLINESIZE + 1);
454: while (fgets(lp, QLINESIZE, in) != NULL) {
455: int ll = strlen(lp);
456:
457: count_in++;
458: if (ll < 14 || *lp == '!' || *lp == '#') {
459: debug2("%10u: comment or short line", count_in);
460: continue;
461: }
462:
463: /* XXX - fragile parser */
464: /* time */
465: cp = &lp[14]; /* (skip) */
466:
467: /* type */
468: in_type = strtoul(cp, &cp, 10);
469:
470: /* tests */
471: in_tests = strtoul(cp, &cp, 10);
472:
473: if (in_tests & QTEST_COMPOSITE) {
474: debug2("%10u: known composite", count_in);
475: continue;
476: }
477: /* tries */
478: in_tries = strtoul(cp, &cp, 10);
479:
480: /* size (most significant bit) */
481: in_size = strtoul(cp, &cp, 10);
482:
483: /* generator (hex) */
484: generator_known = strtoul(cp, &cp, 16);
485:
486: /* Skip white space */
487: cp += strspn(cp, " ");
488:
489: /* modulus (hex) */
490: switch (in_type) {
491: case QTYPE_SOPHIE_GERMAINE:
492: debug2("%10u: (%u) Sophie-Germaine", count_in, in_type);
493: a = q;
494: BN_hex2bn(&a, cp);
495: /* p = 2*q + 1 */
496: BN_lshift(p, q, 1);
497: BN_add_word(p, 1);
498: in_size += 1;
499: generator_known = 0;
500: break;
501: default:
502: debug2("%10u: (%u)", count_in, in_type);
503: a = p;
504: BN_hex2bn(&a, cp);
505: /* q = (p-1) / 2 */
506: BN_rshift(q, p, 1);
507: break;
508: }
509:
510: /*
511: * due to earlier inconsistencies in interpretation, check
512: * the proposed bit size.
513: */
514: if (BN_num_bits(p) != (in_size + 1)) {
515: debug2("%10u: bit size %u mismatch", count_in, in_size);
516: continue;
517: }
518: if (in_size < QSIZE_MINIMUM) {
519: debug2("%10u: bit size %u too short", count_in, in_size);
520: continue;
521: }
522:
523: if (in_tests & QTEST_MILLER_RABIN)
524: in_tries += trials;
525: else
526: in_tries = trials;
527: /*
528: * guess unknown generator
529: */
530: if (generator_known == 0) {
531: if (BN_mod_word(p, 24) == 11)
532: generator_known = 2;
533: else if (BN_mod_word(p, 12) == 5)
534: generator_known = 3;
535: else {
536: u_int32_t r = BN_mod_word(p, 10);
537:
538: if (r == 3 || r == 7) {
539: generator_known = 5;
540: }
541: }
542: }
543: /*
544: * skip tests when desired generator doesn't match
545: */
546: if (generator_wanted > 0 &&
547: generator_wanted != generator_known) {
548: debug2("%10u: generator %d != %d",
549: count_in, generator_known, generator_wanted);
1.4 ! dtucker 550: continue;
! 551: }
! 552:
! 553: /*
! 554: * Primes with no known generator are useless for DH, so
! 555: * skip those.
! 556: */
! 557: if (generator_known == 0) {
! 558: debug2("%10u: no known generator", count_in);
1.1 djm 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: }
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