Annotation of src/usr.bin/ssh/moduli.c, Revision 1.1.4.2
1.1.4.2 ! brad 1: /* $OpenBSD: moduli.c,v 1.5 2003/12/22 09:16:57 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:
1.1.4.2 ! brad 75: /*
! 76: * Size: decimal.
1.1 djm 77: * Specifies the number of the most significant bit (0 to M).
1.1.4.2 ! brad 78: * WARNING: internally, usually 1 to N.
1.1 djm 79: */
80: #define QSIZE_MINIMUM (511)
81:
82: /*
83: * Prime sieving defines
84: */
85:
86: /* Constant: assuming 8 bit bytes and 32 bit words */
87: #define SHIFT_BIT (3)
88: #define SHIFT_BYTE (2)
89: #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE)
90: #define SHIFT_MEGABYTE (20)
91: #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE)
92:
93: /*
94: * Constant: when used with 32-bit integers, the largest sieve prime
95: * has to be less than 2**32.
96: */
97: #define SMALL_MAXIMUM (0xffffffffUL)
98:
99: /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
100: #define TINY_NUMBER (1UL<<16)
101:
102: /* Ensure enough bit space for testing 2*q. */
103: #define TEST_MAXIMUM (1UL<<16)
104: #define TEST_MINIMUM (QSIZE_MINIMUM + 1)
105: /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */
106: #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */
107:
108: /* bit operations on 32-bit words */
109: #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
110: #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
111: #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
112:
113: /*
114: * Prime testing defines
115: */
116:
117: /*
118: * Sieving data (XXX - move to struct)
119: */
120:
121: /* sieve 2**16 */
122: static u_int32_t *TinySieve, tinybits;
123:
124: /* sieve 2**30 in 2**16 parts */
125: static u_int32_t *SmallSieve, smallbits, smallbase;
126:
127: /* sieve relative to the initial value */
128: static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
129: static u_int32_t largebits, largememory; /* megabytes */
130: static BIGNUM *largebase;
131:
132:
133: /*
134: * print moduli out in consistent form,
135: */
136: static int
137: qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
138: u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
139: {
140: struct tm *gtm;
141: time_t time_now;
142: int res;
143:
144: time(&time_now);
145: gtm = gmtime(&time_now);
1.1.4.2 ! brad 146:
1.1 djm 147: res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
148: gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
149: gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
150: otype, otests, otries, osize, ogenerator);
151:
152: if (res < 0)
153: return (-1);
154:
155: if (BN_print_fp(ofile, omodulus) < 1)
156: return (-1);
157:
158: res = fprintf(ofile, "\n");
159: fflush(ofile);
160:
161: return (res > 0 ? 0 : -1);
162: }
163:
164:
165: /*
166: ** Sieve p's and q's with small factors
167: */
168: static void
169: sieve_large(u_int32_t s)
170: {
171: u_int32_t r, u;
172:
1.1.4.2 ! brad 173: debug3("sieve_large %u", s);
1.1 djm 174: largetries++;
175: /* r = largebase mod s */
176: r = BN_mod_word(largebase, s);
177: if (r == 0)
178: u = 0; /* s divides into largebase exactly */
179: else
180: u = s - r; /* largebase+u is first entry divisible by s */
181:
182: if (u < largebits * 2) {
183: /*
184: * The sieve omits p's and q's divisible by 2, so ensure that
185: * largebase+u is odd. Then, step through the sieve in
186: * increments of 2*s
187: */
188: if (u & 0x1)
189: u += s; /* Make largebase+u odd, and u even */
190:
191: /* Mark all multiples of 2*s */
192: for (u /= 2; u < largebits; u += s)
193: BIT_SET(LargeSieve, u);
194: }
195:
196: /* r = p mod s */
197: r = (2 * r + 1) % s;
198: if (r == 0)
199: u = 0; /* s divides p exactly */
200: else
201: u = s - r; /* p+u is first entry divisible by s */
202:
203: if (u < largebits * 4) {
204: /*
205: * The sieve omits p's divisible by 4, so ensure that
206: * largebase+u is not. Then, step through the sieve in
207: * increments of 4*s
208: */
209: while (u & 0x3) {
210: if (SMALL_MAXIMUM - u < s)
211: return;
212: u += s;
213: }
214:
215: /* Mark all multiples of 4*s */
216: for (u /= 4; u < largebits; u += s)
217: BIT_SET(LargeSieve, u);
218: }
219: }
220:
221: /*
222: * list candidates for Sophie-Germaine primes (where q = (p-1)/2)
223: * to standard output.
224: * The list is checked against small known primes (less than 2**30).
225: */
226: int
227: gen_candidates(FILE *out, int memory, int power, BIGNUM *start)
228: {
229: BIGNUM *q;
230: u_int32_t j, r, s, t;
231: u_int32_t smallwords = TINY_NUMBER >> 6;
232: u_int32_t tinywords = TINY_NUMBER >> 6;
233: time_t time_start, time_stop;
234: int i, ret = 0;
235:
236: largememory = memory;
237:
238: /*
1.1.4.2 ! brad 239: * Set power to the length in bits of the prime to be generated.
! 240: * This is changed to 1 less than the desired safe prime moduli p.
! 241: */
1.1 djm 242: if (power > TEST_MAXIMUM) {
243: error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
244: return (-1);
245: } else if (power < TEST_MINIMUM) {
246: error("Too few bits: %u < %u", power, TEST_MINIMUM);
247: return (-1);
248: }
249: power--; /* decrement before squaring */
250:
251: /*
1.1.4.2 ! brad 252: * The density of ordinary primes is on the order of 1/bits, so the
! 253: * density of safe primes should be about (1/bits)**2. Set test range
! 254: * to something well above bits**2 to be reasonably sure (but not
! 255: * guaranteed) of catching at least one safe prime.
1.1 djm 256: */
257: largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
258:
259: /*
1.1.4.2 ! brad 260: * Need idea of how much memory is available. We don't have to use all
! 261: * of it.
1.1 djm 262: */
263: if (largememory > LARGE_MAXIMUM) {
264: logit("Limited memory: %u MB; limit %lu MB",
265: largememory, LARGE_MAXIMUM);
266: largememory = LARGE_MAXIMUM;
267: }
268:
269: if (largewords <= (largememory << SHIFT_MEGAWORD)) {
270: logit("Increased memory: %u MB; need %u bytes",
271: largememory, (largewords << SHIFT_BYTE));
272: largewords = (largememory << SHIFT_MEGAWORD);
273: } else if (largememory > 0) {
274: logit("Decreased memory: %u MB; want %u bytes",
275: largememory, (largewords << SHIFT_BYTE));
276: largewords = (largememory << SHIFT_MEGAWORD);
277: }
278:
279: TinySieve = calloc(tinywords, sizeof(u_int32_t));
280: if (TinySieve == NULL) {
281: error("Insufficient memory for tiny sieve: need %u bytes",
282: tinywords << SHIFT_BYTE);
283: exit(1);
284: }
285: tinybits = tinywords << SHIFT_WORD;
286:
287: SmallSieve = calloc(smallwords, sizeof(u_int32_t));
288: if (SmallSieve == NULL) {
289: error("Insufficient memory for small sieve: need %u bytes",
290: smallwords << SHIFT_BYTE);
291: xfree(TinySieve);
292: exit(1);
293: }
294: smallbits = smallwords << SHIFT_WORD;
295:
296: /*
297: * dynamically determine available memory
298: */
299: while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
300: largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
301:
302: largebits = largewords << SHIFT_WORD;
303: largenumbers = largebits * 2; /* even numbers excluded */
304:
305: /* validation check: count the number of primes tried */
306: largetries = 0;
307: q = BN_new();
308:
309: /*
1.1.4.2 ! brad 310: * Generate random starting point for subprime search, or use
! 311: * specified parameter.
1.1 djm 312: */
313: largebase = BN_new();
314: if (start == NULL)
315: BN_rand(largebase, power, 1, 1);
316: else
317: BN_copy(largebase, start);
318:
319: /* ensure odd */
320: BN_set_bit(largebase, 0);
321:
322: time(&time_start);
323:
1.1.4.2 ! brad 324: logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
1.1 djm 325: largenumbers, power);
326: debug2("start point: 0x%s", BN_bn2hex(largebase));
327:
328: /*
1.1.4.2 ! brad 329: * TinySieve
! 330: */
1.1 djm 331: for (i = 0; i < tinybits; i++) {
332: if (BIT_TEST(TinySieve, i))
333: continue; /* 2*i+3 is composite */
334:
335: /* The next tiny prime */
336: t = 2 * i + 3;
337:
338: /* Mark all multiples of t */
339: for (j = i + t; j < tinybits; j += t)
340: BIT_SET(TinySieve, j);
341:
342: sieve_large(t);
343: }
344:
345: /*
1.1.4.2 ! brad 346: * Start the small block search at the next possible prime. To avoid
! 347: * fencepost errors, the last pass is skipped.
! 348: */
1.1 djm 349: for (smallbase = TINY_NUMBER + 3;
350: smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
351: smallbase += TINY_NUMBER) {
352: for (i = 0; i < tinybits; i++) {
353: if (BIT_TEST(TinySieve, i))
354: continue; /* 2*i+3 is composite */
355:
356: /* The next tiny prime */
357: t = 2 * i + 3;
358: r = smallbase % t;
359:
360: if (r == 0) {
361: s = 0; /* t divides into smallbase exactly */
362: } else {
363: /* smallbase+s is first entry divisible by t */
364: s = t - r;
365: }
366:
367: /*
368: * The sieve omits even numbers, so ensure that
369: * smallbase+s is odd. Then, step through the sieve
370: * in increments of 2*t
371: */
372: if (s & 1)
373: s += t; /* Make smallbase+s odd, and s even */
374:
375: /* Mark all multiples of 2*t */
376: for (s /= 2; s < smallbits; s += t)
377: BIT_SET(SmallSieve, s);
378: }
379:
380: /*
1.1.4.2 ! brad 381: * SmallSieve
! 382: */
1.1 djm 383: for (i = 0; i < smallbits; i++) {
384: if (BIT_TEST(SmallSieve, i))
385: continue; /* 2*i+smallbase is composite */
386:
387: /* The next small prime */
388: sieve_large((2 * i) + smallbase);
389: }
390:
391: memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
392: }
393:
394: time(&time_stop);
395:
396: logit("%.24s Sieved with %u small primes in %ld seconds",
397: ctime(&time_stop), largetries, (long) (time_stop - time_start));
398:
399: for (j = r = 0; j < largebits; j++) {
400: if (BIT_TEST(LargeSieve, j))
401: continue; /* Definitely composite, skip */
402:
403: debug2("test q = largebase+%u", 2 * j);
404: BN_set_word(q, 2 * j);
405: BN_add(q, q, largebase);
406: if (qfileout(out, QTYPE_SOPHIE_GERMAINE, QTEST_SIEVE,
407: largetries, (power - 1) /* MSB */, (0), q) == -1) {
408: ret = -1;
409: break;
410: }
411:
412: r++; /* count q */
413: }
414:
415: time(&time_stop);
416:
417: xfree(LargeSieve);
418: xfree(SmallSieve);
419: xfree(TinySieve);
420:
421: logit("%.24s Found %u candidates", ctime(&time_stop), r);
422:
423: return (ret);
424: }
425:
426: /*
427: * perform a Miller-Rabin primality test
428: * on the list of candidates
429: * (checking both q and p)
430: * The result is a list of so-call "safe" primes
431: */
432: int
1.1.4.2 ! brad 433: prime_test(FILE *in, FILE *out, u_int32_t trials,
1.1 djm 434: u_int32_t generator_wanted)
435: {
436: BIGNUM *q, *p, *a;
437: BN_CTX *ctx;
438: char *cp, *lp;
439: u_int32_t count_in = 0, count_out = 0, count_possible = 0;
440: u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
441: time_t time_start, time_stop;
442: int res;
443:
444: time(&time_start);
445:
446: p = BN_new();
447: q = BN_new();
448: ctx = BN_CTX_new();
449:
450: debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
451: ctime(&time_start), trials, generator_wanted);
452:
453: res = 0;
454: lp = xmalloc(QLINESIZE + 1);
455: while (fgets(lp, QLINESIZE, in) != NULL) {
456: int ll = strlen(lp);
457:
458: count_in++;
459: if (ll < 14 || *lp == '!' || *lp == '#') {
460: debug2("%10u: comment or short line", count_in);
461: continue;
462: }
463:
464: /* XXX - fragile parser */
465: /* time */
466: cp = &lp[14]; /* (skip) */
467:
468: /* type */
469: in_type = strtoul(cp, &cp, 10);
470:
471: /* tests */
472: in_tests = strtoul(cp, &cp, 10);
473:
474: if (in_tests & QTEST_COMPOSITE) {
475: debug2("%10u: known composite", count_in);
476: continue;
477: }
1.1.4.2 ! brad 478:
1.1 djm 479: /* tries */
480: in_tries = strtoul(cp, &cp, 10);
481:
482: /* size (most significant bit) */
483: in_size = strtoul(cp, &cp, 10);
484:
485: /* generator (hex) */
486: generator_known = strtoul(cp, &cp, 16);
487:
488: /* Skip white space */
489: cp += strspn(cp, " ");
490:
491: /* modulus (hex) */
492: switch (in_type) {
493: case QTYPE_SOPHIE_GERMAINE:
494: debug2("%10u: (%u) Sophie-Germaine", count_in, in_type);
495: a = q;
496: BN_hex2bn(&a, cp);
497: /* p = 2*q + 1 */
498: BN_lshift(p, q, 1);
499: BN_add_word(p, 1);
500: in_size += 1;
501: generator_known = 0;
502: break;
1.1.4.2 ! brad 503: case QTYPE_UNSTRUCTURED:
! 504: case QTYPE_SAFE:
! 505: case QTYPE_SCHNOOR:
! 506: case QTYPE_STRONG:
! 507: case QTYPE_UNKNOWN:
1.1 djm 508: debug2("%10u: (%u)", count_in, in_type);
509: a = p;
510: BN_hex2bn(&a, cp);
511: /* q = (p-1) / 2 */
512: BN_rshift(q, p, 1);
513: break;
1.1.4.2 ! brad 514: default:
! 515: debug2("Unknown prime type");
! 516: break;
1.1 djm 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;
1.1.4.2 ! brad 536:
1.1 djm 537: /*
538: * guess unknown generator
539: */
540: if (generator_known == 0) {
541: if (BN_mod_word(p, 24) == 11)
542: generator_known = 2;
543: else if (BN_mod_word(p, 12) == 5)
544: generator_known = 3;
545: else {
546: u_int32_t r = BN_mod_word(p, 10);
547:
1.1.4.2 ! brad 548: if (r == 3 || r == 7)
1.1 djm 549: generator_known = 5;
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:
1.1.4.2 ! brad 562: /*
! 563: * Primes with no known generator are useless for DH, so
! 564: * skip those.
! 565: */
! 566: if (generator_known == 0) {
! 567: debug2("%10u: no known generator", count_in);
! 568: continue;
! 569: }
! 570:
1.1 djm 571: count_possible++;
572:
573: /*
1.1.4.2 ! brad 574: * The (1/4)^N performance bound on Miller-Rabin is
! 575: * extremely pessimistic, so don't spend a lot of time
! 576: * really verifying that q is prime until after we know
! 577: * that p is also prime. A single pass will weed out the
1.1 djm 578: * vast majority of composite q's.
579: */
580: if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) {
1.1.4.2 ! brad 581: debug("%10u: q failed first possible prime test",
1.1 djm 582: count_in);
583: continue;
584: }
1.1.4.2 ! brad 585:
1.1 djm 586: /*
1.1.4.2 ! brad 587: * q is possibly prime, so go ahead and really make sure
! 588: * that p is prime. If it is, then we can go back and do
! 589: * the same for q. If p is composite, chances are that
1.1 djm 590: * will show up on the first Rabin-Miller iteration so it
591: * doesn't hurt to specify a high iteration count.
592: */
593: if (!BN_is_prime(p, trials, NULL, ctx, NULL)) {
1.1.4.2 ! brad 594: debug("%10u: p is not prime", count_in);
1.1 djm 595: continue;
596: }
597: debug("%10u: p is almost certainly prime", count_in);
598:
599: /* recheck q more rigorously */
600: if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) {
601: debug("%10u: q is not prime", count_in);
602: continue;
603: }
604: debug("%10u: q is almost certainly prime", count_in);
605:
1.1.4.2 ! brad 606: if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN),
1.1 djm 607: in_tries, in_size, generator_known, p)) {
608: res = -1;
609: break;
610: }
611:
612: count_out++;
613: }
614:
615: time(&time_stop);
616: xfree(lp);
617: BN_free(p);
618: BN_free(q);
619: BN_CTX_free(ctx);
620:
621: logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
1.1.4.2 ! brad 622: ctime(&time_stop), count_out, count_possible,
1.1 djm 623: (long) (time_stop - time_start));
624:
625: return (res);
626: }
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