1/* $NetBSD: qsieve.c,v 1.2 2009/01/18 01:34:30 lukem Exp $ */
2
3/*-
4 * Copyright 1994 Phil Karn <karn@qualcomm.com>
5 * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com>
6 * Copyright 2000 Niels Provos <provos@citi.umich.edu>
7 * All rights reserved.
8 *
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions
11 * are met:
12 * 1. Redistributions of source code must retain the above copyright
13 *    notice, this list of conditions and the following disclaimer.
14 * 2. Redistributions in binary form must reproduce the above copyright
15 *    notice, this list of conditions and the following disclaimer in the
16 *    documentation and/or other materials provided with the distribution.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
19 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
20 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
21 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
22 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
23 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
24 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
25 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
26 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
27 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29
30/*
31 * Sieve candidates for "safe" primes,
32 *  suitable for use as Diffie-Hellman moduli;
33 *  that is, where q = (p-1)/2 is also prime.
34 *
35 * This is the first of two steps.
36 * This step is memory intensive.
37 *
38 * 1996 May     William Allen Simpson
39 *              extracted from earlier code by Phil Karn, April 1994.
40 *              save large primes list for later processing.
41 * 1998 May     William Allen Simpson
42 *              parameterized.
43 * 2000 Dec     Niels Provos
44 *              convert from GMP to openssl BN.
45 * 2003 Jun     William Allen Simpson
46 *              change outfile definition slightly to match openssh mistake.
47 *              move common file i/o to own file for better documentation.
48 *              redo memory again.
49 */
50
51#include <stdio.h>
52#include <stdlib.h>
53#include <time.h>
54#include <openssl/bn.h>
55#include <string.h>
56#include <err.h>
57#include "qfile.h"
58
59/* define DEBUG_LARGE 1 */
60/* define DEBUG_SMALL 1 */
61
62/*
63 * Using virtual memory can cause thrashing.  This should be the largest
64 * number that is supported without a large amount of disk activity --
65 * that would increase the run time from hours to days or weeks!
66 */
67#define LARGE_MINIMUM   (8UL)	/* megabytes */
68
69/*
70 * Do not increase this number beyond the unsigned integer bit size.
71 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
72 */
73#define LARGE_MAXIMUM   (127UL)	/* megabytes */
74
75/*
76 * Constant: assuming 8 bit bytes and 32 bit words
77 */
78#define SHIFT_BIT       (3)
79#define SHIFT_BYTE      (2)
80#define SHIFT_WORD      (SHIFT_BIT+SHIFT_BYTE)
81#define SHIFT_MEGABYTE  (20)
82#define SHIFT_MEGAWORD  (SHIFT_MEGABYTE-SHIFT_BYTE)
83
84/*
85 * Constant: when used with 32-bit integers, the largest sieve prime
86 * has to be less than 2**32.
87 */
88#define SMALL_MAXIMUM   (0xffffffffUL)
89
90/*
91 * Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1.
92 */
93#define TINY_NUMBER     (1UL<<16)
94
95/*
96 * Ensure enough bit space for testing 2*q.
97 */
98#define TEST_MAXIMUM    (1UL<<16)
99#define TEST_MINIMUM    (QSIZE_MINIMUM + 1)
100/* real TEST_MINIMUM    (1UL << (SHIFT_WORD - TEST_POWER)) */
101#define TEST_POWER      (3)	/* 2**n, n < SHIFT_WORD */
102
103/*
104 * bit operations on 32-bit words
105 */
106#define BIT_CLEAR(a,n)  ((a)[(n)>>SHIFT_WORD] &= ~(1U << ((n) & 31)))
107#define BIT_SET(a,n)    ((a)[(n)>>SHIFT_WORD] |= (1U << ((n) & 31)))
108#define BIT_TEST(a,n)   ((a)[(n)>>SHIFT_WORD] & (1U << ((n) & 31)))
109
110/*
111 * sieve relative to the initial value
112 */
113static uint32_t       *LargeSieve;
114static uint32_t        largewords;
115static uint32_t        largetries;
116static uint32_t        largenumbers;
117static uint32_t        largememory;	/* megabytes */
118static uint32_t        largebits;
119static BIGNUM         *largebase;
120
121/*
122 * sieve 2**30 in 2**16 parts
123 */
124static uint32_t       *SmallSieve;
125static uint32_t        smallbits;
126static uint32_t        smallbase;
127
128/*
129 * sieve 2**16
130 */
131static uint32_t       *TinySieve;
132static uint32_t        tinybits;
133
134__dead static void     usage(void);
135static void            sieve_large(uint32_t);
136
137/*
138 * Sieve p's and q's with small factors
139 */
140static void
141sieve_large(uint32_t s)
142{
143	BN_ULONG        r;
144	BN_ULONG        u;
145
146#ifdef  DEBUG_SMALL
147	(void)fprintf(stderr, "%lu\n", s);
148#endif
149	largetries++;
150	/* r = largebase mod s */
151	r = BN_mod_word(largebase, (BN_ULONG) s);
152	if (r == 0) {
153		/* s divides into largebase exactly */
154		u = 0;
155	} else {
156		/* largebase+u is first entry divisible by s */
157		u = s - r;
158	}
159
160	if (u < largebits * 2) {
161		/*
162		 * The sieve omits p's and q's divisible by 2, so ensure that
163		 * largebase+u is odd. Then, step through the sieve in
164		 * increments of 2*s
165		 */
166		if (u & 0x1) {
167			/* Make largebase+u odd, and u even */
168			u += s;
169		}
170
171		/* Mark all multiples of 2*s */
172		for (u /= 2; u < largebits; u += s) {
173			BIT_SET(LargeSieve, (uint32_t)u);
174		}
175	}
176
177	/* r = p mod s */
178	r = (2 * r + 1) % s;
179
180	if (r == 0) {
181		/* s divides p exactly */
182		u = 0;
183	} else {
184		/* p+u is first entry divisible by s */
185		u = s - r;
186	}
187
188	if (u < largebits * 4) {
189		/*
190		 * The sieve omits p's divisible by 4, so ensure that
191		 * largebase+u is not. Then, step through the sieve in
192		 * increments of 4*s
193		 */
194		while (u & 0x3) {
195			if (SMALL_MAXIMUM - u < s) {
196				return;
197			}
198
199			u += s;
200		}
201
202		/* Mark all multiples of 4*s */
203		for (u /= 4; u < largebits; u += s) {
204			BIT_SET(LargeSieve, (uint32_t)u);
205		}
206	}
207}
208
209/*
210 * list candidates for Sophie-Germaine primes
211 * (where q = (p-1)/2)
212 * to standard output.
213 * The list is checked against small known primes
214 * (less than 2**30).
215 */
216int
217main(int argc, char *argv[])
218{
219	BIGNUM         *q;
220	uint32_t        j;
221	int             power;
222	uint32_t        r;
223	uint32_t        s;
224	uint32_t        smallwords = TINY_NUMBER >> 6;
225	uint32_t        t;
226	time_t          time_start;
227	time_t          time_stop;
228	uint32_t        tinywords = TINY_NUMBER >> 6;
229	unsigned int    i;
230
231	setprogname(argv[0]);
232
233	if (argc < 3) {
234		usage();
235	}
236
237	/*
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         */
241	power = (int) strtoul(argv[2], NULL, 10);
242	if ((unsigned)power > TEST_MAXIMUM) {
243		errx(1, "Too many bits: %d > %lu.", power,
244		     (unsigned long)TEST_MAXIMUM);
245	} else if (power < TEST_MINIMUM) {
246		errx(1, "Too few bits: %d < %lu.", power,
247		     (unsigned long)TEST_MINIMUM);
248	}
249
250	power--;		/* decrement before squaring */
251
252	/*
253         * The density of ordinary primes is on the order of 1/bits, so the
254         * density of safe primes should be about (1/bits)**2. Set test range
255         * to something well above bits**2 to be reasonably sure (but not
256         * guaranteed) of catching at least one safe prime.
257	 */
258	largewords = (uint32_t)((unsigned long)
259			(power * power) >> (SHIFT_WORD - TEST_POWER));
260
261	/*
262         * Need idea of how much memory is available. We don't have to use all
263         * of it.
264	 */
265	largememory = (uint32_t)strtoul(argv[1], NULL, 10);
266	if (largememory > LARGE_MAXIMUM) {
267		warnx("Limited memory: %u MB; limit %lu MB.", largememory,
268		      LARGE_MAXIMUM);
269		largememory = LARGE_MAXIMUM;
270	}
271
272	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
273		warnx("Increased memory: %u MB; need %u bytes.",
274		      largememory, (largewords << SHIFT_BYTE));
275		largewords = (largememory << SHIFT_MEGAWORD);
276	} else if (largememory > 0) {
277		warnx("Decreased memory: %u MB; want %u bytes.",
278		      largememory, (largewords << SHIFT_BYTE));
279		largewords = (largememory << SHIFT_MEGAWORD);
280	}
281
282	if ((TinySieve = (uint32_t *) calloc((size_t) tinywords, sizeof(uint32_t))) == NULL) {
283		errx(1, "Insufficient memory for tiny sieve: need %u byts.",
284		     tinywords << SHIFT_BYTE);
285	}
286	tinybits = tinywords << SHIFT_WORD;
287
288	if ((SmallSieve = (uint32_t *) calloc((size_t) smallwords, sizeof(uint32_t))) == NULL) {
289		errx(1, "Insufficient memory for small sieve: need %u bytes.",
290		     smallwords << SHIFT_BYTE);
291	}
292	smallbits = smallwords << SHIFT_WORD;
293
294	/*
295	 * dynamically determine available memory
296	 */
297	while ((LargeSieve = (uint32_t *)calloc((size_t)largewords,
298						sizeof(uint32_t))) == NULL) {
299		/* 1/4 MB chunks */
300		largewords -= (1L << (SHIFT_MEGAWORD - 2));
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
308	q = BN_new();
309	largebase = BN_new();
310
311	/*
312         * Generate random starting point for subprime search, or use
313         * specified parameter.
314	 */
315	if (argc < 4) {
316		BN_rand(largebase, power, 1, 1);
317	} else {
318		BIGNUM         *a;
319
320		a = largebase;
321		BN_hex2bn(&a, argv[2]);
322	}
323
324	/* ensure odd */
325	if (!BN_is_odd(largebase)) {
326		BN_set_bit(largebase, 0);
327	}
328
329	time(&time_start);
330	(void)fprintf(stderr,
331		"%.24s Sieve next %u plus %d-bit start point:\n# ",
332		ctime(&time_start), largenumbers, power);
333	BN_print_fp(stderr, largebase);
334	(void)fprintf(stderr, "\n");
335
336	/*
337         * TinySieve
338         */
339	for (i = 0; i < tinybits; i++) {
340		if (BIT_TEST(TinySieve, i)) {
341			/* 2*i+3 is composite */
342			continue;
343		}
344
345		/* The next tiny prime */
346		t = 2 * i + 3;
347
348		/* Mark all multiples of t */
349		for (j = i + t; j < tinybits; j += t) {
350			BIT_SET(TinySieve, j);
351		}
352
353		sieve_large(t);
354	}
355
356	/*
357         * Start the small block search at the next possible prime. To avoid
358         * fencepost errors, the last pass is skipped.
359         */
360	for (smallbase = TINY_NUMBER + 3;
361	     smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
362	     smallbase += TINY_NUMBER) {
363		for (i = 0; i < tinybits; i++) {
364			if (BIT_TEST(TinySieve, i)) {
365				/* 2*i+3 is composite */
366				continue;
367			}
368
369			/* The next tiny prime */
370			t = 2 * i + 3;
371			r = smallbase % t;
372
373			if (r == 0) {
374				/* t divides into smallbase exactly */
375				s = 0;
376			} else {
377				/* smallbase+s is first entry divisible by t */
378				s = t - r;
379			}
380
381			/*
382			 * The sieve omits even numbers, so ensure that
383			 * smallbase+s is odd. Then, step through the sieve in
384			 * increments of 2*t
385			 */
386			if (s & 1) {
387				/* Make smallbase+s odd, and s even */
388				s += t;
389			}
390
391			/* Mark all multiples of 2*t */
392			for (s /= 2; s < smallbits; s += t) {
393				BIT_SET(SmallSieve, s);
394			}
395		}
396
397		/*
398                 * SmallSieve
399                 */
400		for (i = 0; i < smallbits; i++) {
401			if (BIT_TEST(SmallSieve, i)) {
402				/* 2*i+smallbase is composite */
403				continue;
404			}
405
406			/* The next small prime */
407			sieve_large((2 * i) + smallbase);
408		}
409
410		memset(SmallSieve, 0, (size_t)(smallwords << SHIFT_BYTE));
411	}
412
413	time(&time_stop);
414	(void)fprintf(stderr,
415		"%.24s Sieved with %u small primes in %lu seconds\n",
416		ctime(&time_stop), largetries,
417		(long) (time_stop - time_start));
418
419	for (j = r = 0; j < largebits; j++) {
420		if (BIT_TEST(LargeSieve, j)) {
421			/* Definitely composite, skip */
422			continue;
423		}
424
425#ifdef  DEBUG_LARGE
426		(void)fprintf(stderr, "test q = largebase+%lu\n", 2 * j);
427#endif
428
429		BN_set_word(q, (unsigned long)(2 * j));
430		BN_add(q, q, largebase);
431
432		if (0 > qfileout(stdout,
433				 (uint32_t) QTYPE_SOPHIE_GERMAINE,
434				 (uint32_t) QTEST_SIEVE,
435				 largetries,
436				 (uint32_t) (power - 1), /* MSB */
437				 (uint32_t) (0), /* generator unknown */
438				 q)) {
439			break;
440		}
441
442		r++;		/* count q */
443	}
444
445	time(&time_stop);
446
447	free(LargeSieve);
448	free(SmallSieve);
449	free(TinySieve);
450
451	fflush(stdout);
452	/* fclose(stdout); */
453
454	(void) fprintf(stderr, "%.24s Found %u candidates\n",
455	    ctime(&time_stop), r);
456
457	return (0);
458}
459
460static void
461usage(void)
462{
463	(void)fprintf(stderr, "Usage: %s <megabytes> <bits> [initial]\n"
464		"Possible values for <megabytes>: 0, %lu to %lu\n"
465		"Possible values for <bits>: %lu to %lu\n",
466		getprogname(),
467		LARGE_MINIMUM,
468		LARGE_MAXIMUM,
469		(unsigned long) TEST_MINIMUM,
470		(unsigned long) TEST_MAXIMUM);
471
472	exit(1);
473}
474