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[u/mdw/catacomb] / pfilt.c
1 /* -*-c-*-
2 *
3 * $Id: pfilt.c,v 1.4 2000/10/08 12:14:57 mdw Exp $
4 *
5 * Finding and testing prime numbers
6 *
7 * (c) 1999 Straylight/Edgeware
8 */
9
10 /*----- Licensing notice --------------------------------------------------*
11 *
12 * This file is part of Catacomb.
13 *
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
18 *
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
23 *
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
27 * MA 02111-1307, USA.
28 */
29
30 /*----- Revision history --------------------------------------------------*
31 *
32 * $Log: pfilt.c,v $
33 * Revision 1.4 2000/10/08 12:14:57 mdw
34 * Remove vestiges of @primorial@.
35 *
36 * Revision 1.3 2000/08/15 21:44:27 mdw
37 * (pfilt_smallfactor): New function for doing trial division the hard
38 * way.
39 *
40 * (pfilt_create): Use @mpx_udivn@ for computing residues, for improved
41 * performance.
42 *
43 * Pull the `small prime' test into a separate function, and do it
44 * properly.
45 *
46 * Revision 1.2 2000/06/17 11:54:27 mdw
47 * Use new MP memory management functions.
48 *
49 * Revision 1.1 1999/12/22 15:49:39 mdw
50 * Renamed from `pgen'. Reworking for new prime-search system.
51 *
52 * Revision 1.3 1999/12/10 23:28:35 mdw
53 * Track suggested destination changes.
54 *
55 * Revision 1.2 1999/11/20 22:23:05 mdw
56 * Add multiply-and-add function for Diffie-Hellman safe prime generation.
57 *
58 * Revision 1.1 1999/11/19 13:17:57 mdw
59 * Prime number generator and tester.
60 *
61 */
62
63 /*----- Header files ------------------------------------------------------*/
64
65 #include "mp.h"
66 #include "mpint.h"
67 #include "pfilt.h"
68 #include "pgen.h"
69 #include "primetab.h"
70
71 /*----- Main code ---------------------------------------------------------*/
72
73 /* --- @smallenough@ --- *
74 *
75 * Arguments: @mp *m@ = integer to test
76 *
77 * Returns: One of the @PGEN@ result codes.
78 *
79 * Use: Assuming that @m@ has been tested by trial division on every
80 * prime in the small-primes array, this function will return
81 * @PGEN_DONE@ if the number is less than the square of the
82 * largest small prime.
83 */
84
85 static int smallenough(mp *m)
86 {
87 static mp *max = 0;
88 int rc = PGEN_TRY;
89
90 if (!max) {
91 max = mp_fromuint(MP_NEW, MAXPRIME);
92 max = mp_sqr(max, max);
93 max->a->n--; /* Permanent allocation */
94 }
95 if (MP_CMP(m, <, max))
96 rc = PGEN_DONE;
97 return (rc);
98 }
99
100 /* --- @pfilt_smallfactor@ --- *
101 *
102 * Arguments: @mp *m@ = integer to test
103 *
104 * Returns: One of the @PGEN@ result codes.
105 *
106 * Use: Tests a number by dividing by a number of small primes. This
107 * is a useful first step if you're testing random primes; for
108 * sequential searches, @pfilt_create@ works better.
109 */
110
111 int pfilt_smallfactor(mp *m)
112 {
113 int rc = PGEN_TRY;
114 int i;
115 size_t sz = MP_LEN(m);
116 mpw *v = mpalloc(m->a, sz);
117
118 /* --- Fill in the residues --- */
119
120 for (i = 0; i < NPRIME; i++) {
121 if (!mpx_udivn(v, v + sz, m->v, m->vl, primetab[i])) {
122 if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
123 rc = PGEN_DONE;
124 else
125 rc = PGEN_FAIL;
126 }
127 }
128
129 /* --- Check for small primes --- */
130
131 if (rc == PGEN_TRY)
132 rc = smallenough(m);
133
134 /* --- Done --- */
135
136 mpfree(m->a, v);
137 return (rc);
138 }
139
140 /* --- @pfilt_create@ --- *
141 *
142 * Arguments: @pfilt *p@ = pointer to prime filtering context
143 * @mp *m@ = pointer to initial number to test
144 *
145 * Returns: One of the @PGEN@ result codes.
146 *
147 * Use: Tests an initial number for primality by computing its
148 * residue modulo various small prime numbers. This is fairly
149 * quick, but not particularly certain. If a @PGEN_TRY@
150 * result is returned, perform Rabin-Miller tests to confirm.
151 */
152
153 int pfilt_create(pfilt *p, mp *m)
154 {
155 int rc = PGEN_TRY;
156 int i;
157 size_t sz = MP_LEN(m);
158 mpw *v = mpalloc(m->a, sz);
159
160 /* --- Take a copy of the number --- */
161
162 mp_shrink(m);
163 p->m = MP_COPY(m);
164
165 /* --- Fill in the residues --- */
166
167 for (i = 0; i < NPRIME; i++) {
168 p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]);
169 if (!p->r[i] && rc == PGEN_TRY) {
170 if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
171 rc = PGEN_DONE;
172 else
173 rc = PGEN_FAIL;
174 }
175 }
176
177 /* --- Check for small primes --- */
178
179 if (rc == PGEN_TRY)
180 rc = smallenough(m);
181
182 /* --- Done --- */
183
184 mpfree(m->a, v);
185 return (rc);
186 }
187
188 /* --- @pfilt_destroy@ --- *
189 *
190 * Arguments: @pfilt *p@ = pointer to prime filtering context
191 *
192 * Returns: ---
193 *
194 * Use: Discards a context and all the resources it holds.
195 */
196
197 void pfilt_destroy(pfilt *p)
198 {
199 mp_drop(p->m);
200 }
201
202 /* --- @pfilt_step@ --- *
203 *
204 * Arguments: @pfilt *p@ = pointer to prime filtering context
205 * @mpw step@ = how much to step the number
206 *
207 * Returns: One of the @PGEN@ result codes.
208 *
209 * Use: Steps a number by a small amount. Stepping is much faster
210 * than initializing with a new number. The test performed is
211 * the same simple one used by @primetab_create@, so @PGEN_TRY@
212 * results should be followed up by a Rabin-Miller test.
213 */
214
215 int pfilt_step(pfilt *p, mpw step)
216 {
217 int rc = PGEN_TRY;
218 int i;
219
220 /* --- Add the step on to the number --- */
221
222 p->m = mp_split(p->m);
223 mp_ensure(p->m, MP_LEN(p->m) + 1);
224 mpx_uaddn(p->m->v, p->m->vl, step);
225 mp_shrink(p->m);
226
227 /* --- Update the residue table --- */
228
229 for (i = 0; i < NPRIME; i++) {
230 p->r[i] = (p->r[i] + step) % primetab[i];
231 if (!p->r[i] && rc == PGEN_TRY) {
232 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
233 rc = PGEN_DONE;
234 else
235 rc = PGEN_FAIL;
236 }
237 }
238
239 /* --- Check for small primes --- */
240
241 if (rc == PGEN_TRY)
242 rc = smallenough(p->m);
243
244 /* --- Done --- */
245
246 return (rc);
247 }
248
249 /* --- @pfilt_muladd@ --- *
250 *
251 * Arguments: @pfilt *p@ = destination prime filtering context
252 * @const pfilt *q@ = source prime filtering context
253 * @mpw m@ = number to multiply by
254 * @mpw a@ = number to add
255 *
256 * Returns: One of the @PGEN@ result codes.
257 *
258 * Use: Multiplies the number in a prime filtering context by a
259 * small value and then adds a small value. The destination
260 * should either be uninitialized or the same as the source.
261 *
262 * Common things to do include multiplying by 2 and adding 0 to
263 * turn a prime into a jump for finding other primes with @q@ as
264 * a factor of @p - 1@, or multiplying by 2 and adding 1.
265 */
266
267 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
268 {
269 int rc = PGEN_TRY;
270 int i;
271
272 /* --- Multiply the big number --- */
273
274 {
275 mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f);
276 mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
277 mpx_uaddn(d->v, d->vl, a);
278 if (p == q)
279 mp_drop(p->m);
280 mp_shrink(d);
281 p->m = d;
282 }
283
284 /* --- Gallivant through the residue table --- */
285
286 for (i = 0; i < NPRIME; i++) {
287 p->r[i] = (q->r[i] * m + a) % primetab[i];
288 if (!p->r[i] && rc == PGEN_TRY) {
289 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
290 rc = PGEN_DONE;
291 else
292 rc = PGEN_FAIL;
293 }
294 }
295
296 /* --- Check for small primes --- */
297
298 if (rc == PGEN_TRY)
299 rc = smallenough(p->m);
300
301 /* --- Finished --- */
302
303 return (rc);
304 }
305
306 /* --- @pfilt_jump@ --- *
307 *
308 * Arguments: @pfilt *p@ = pointer to prime filtering context
309 * @const pfilt *j@ = pointer to another filtering context
310 *
311 * Returns: One of the @PGEN@ result codes.
312 *
313 * Use: Steps a number by a large amount. Even so, jumping is much
314 * faster than initializing a new number. The test peformed is
315 * the same simple one used by @primetab_create@, so @PGEN_TRY@
316 * results should be followed up by a Rabin-Miller test.
317 *
318 * Note that the number stored in the @j@ context is probably
319 * better off being even than prime. The important thing is
320 * that all of the residues for the number have already been
321 * computed.
322 */
323
324 int pfilt_jump(pfilt *p, const pfilt *j)
325 {
326 int rc = PGEN_TRY;
327 int i;
328
329 /* --- Add the step on --- */
330
331 p->m = mp_add(p->m, p->m, j->m);
332
333 /* --- Update the residue table --- */
334
335 for (i = 0; i < NPRIME; i++) {
336 p->r[i] = p->r[i] + j->r[i];
337 if (p->r[i] > primetab[i])
338 p->r[i] -= primetab[i];
339 if (!p->r[i] && rc == PGEN_TRY) {
340 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
341 rc = PGEN_DONE;
342 else
343 rc = PGEN_FAIL;
344 }
345 }
346
347 /* --- Check for small primes --- */
348
349 if (rc == PGEN_TRY)
350 rc = smallenough(p->m);
351
352 /* --- Done --- */
353
354 return (rc);
355 }
356
357 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)