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(pfilt_smallfactor): New function for doing trial division the hard
[u/mdw/catacomb] / pfilt.c
1 /* -*-c-*-
2 *
3 * $Id: pfilt.c,v 1.3 2000/08/15 21:44:27 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 1.3 2000/08/15 21:44:27 mdw
34 * (pfilt_smallfactor): New function for doing trial division the hard
35 * way.
36 *
37 * (pfilt_create): Use @mpx_udivn@ for computing residues, for improved
38 * performance.
39 *
40 * Pull the `small prime' test into a separate function, and do it
41 * properly.
42 *
43 * Revision 1.2 2000/06/17 11:54:27 mdw
44 * Use new MP memory management functions.
45 *
46 * Revision 1.1 1999/12/22 15:49:39 mdw
47 * Renamed from `pgen'. Reworking for new prime-search system.
48 *
49 * Revision 1.3 1999/12/10 23:28:35 mdw
50 * Track suggested destination changes.
51 *
52 * Revision 1.2 1999/11/20 22:23:05 mdw
53 * Add multiply-and-add function for Diffie-Hellman safe prime generation.
54 *
55 * Revision 1.1 1999/11/19 13:17:57 mdw
56 * Prime number generator and tester.
57 *
58 */
59
60 /*----- Header files ------------------------------------------------------*/
61
62 #include "mp.h"
63 #include "mpint.h"
64 #include "pfilt.h"
65 #include "pgen.h"
66 #include "primetab.h"
67 #include "primorial.h"
68
69 /*----- Main code ---------------------------------------------------------*/
70
71 /* --- @smallenough@ --- *
72 *
73 * Arguments: @mp *m@ = integer to test
74 *
75 * Returns: One of the @PGEN@ result codes.
76 *
77 * Use: Assuming that @m@ has been tested by trial division on every
78 * prime in the small-primes array, this function will return
79 * @PGEN_DONE@ if the number is less than the square of the
80 * largest small prime.
81 */
82
83 static int smallenough(mp *m)
84 {
85 static mp *max = 0;
86 int rc = PGEN_TRY;
87
88 if (!max) {
89 max = mp_fromuint(MP_NEW, MAXPRIME);
90 max = mp_sqr(max, max);
91 max->a->n--; /* Permanent allocation */
92 }
93 if (MP_CMP(m, <, max))
94 rc = PGEN_DONE;
95 return (rc);
96 }
97
98 /* --- @pfilt_smallfactor@ --- *
99 *
100 * Arguments: @mp *m@ = integer to test
101 *
102 * Returns: One of the @PGEN@ result codes.
103 *
104 * Use: Tests a number by dividing by a number of small primes. This
105 * is a useful first step if you're testing random primes; for
106 * sequential searches, @pfilt_create@ works better.
107 */
108
109 int pfilt_smallfactor(mp *m)
110 {
111 int rc = PGEN_TRY;
112 int i;
113 size_t sz = MP_LEN(m);
114 mpw *v = mpalloc(m->a, sz);
115
116 /* --- Fill in the residues --- */
117
118 for (i = 0; i < NPRIME; i++) {
119 if (!mpx_udivn(v, v + sz, m->v, m->vl, primetab[i])) {
120 if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
121 rc = PGEN_DONE;
122 else
123 rc = PGEN_FAIL;
124 }
125 }
126
127 /* --- Check for small primes --- */
128
129 if (rc == PGEN_TRY)
130 rc = smallenough(m);
131
132 /* --- Done --- */
133
134 mpfree(m->a, v);
135 return (rc);
136 }
137
138 /* --- @pfilt_create@ --- *
139 *
140 * Arguments: @pfilt *p@ = pointer to prime filtering context
141 * @mp *m@ = pointer to initial number to test
142 *
143 * Returns: One of the @PGEN@ result codes.
144 *
145 * Use: Tests an initial number for primality by computing its
146 * residue modulo various small prime numbers. This is fairly
147 * quick, but not particularly certain. If a @PGEN_TRY@
148 * result is returned, perform Rabin-Miller tests to confirm.
149 */
150
151 int pfilt_create(pfilt *p, mp *m)
152 {
153 int rc = PGEN_TRY;
154 int i;
155 size_t sz = MP_LEN(m);
156 mpw *v = mpalloc(m->a, sz);
157
158 /* --- Take a copy of the number --- */
159
160 mp_shrink(m);
161 p->m = MP_COPY(m);
162
163 /* --- Fill in the residues --- */
164
165 for (i = 0; i < NPRIME; i++) {
166 p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]);
167 if (!p->r[i] && rc == PGEN_TRY) {
168 if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
169 rc = PGEN_DONE;
170 else
171 rc = PGEN_FAIL;
172 }
173 }
174
175 /* --- Check for small primes --- */
176
177 if (rc == PGEN_TRY)
178 rc = smallenough(m);
179
180 /* --- Done --- */
181
182 mpfree(m->a, v);
183 return (rc);
184 }
185
186 /* --- @pfilt_destroy@ --- *
187 *
188 * Arguments: @pfilt *p@ = pointer to prime filtering context
189 *
190 * Returns: ---
191 *
192 * Use: Discards a context and all the resources it holds.
193 */
194
195 void pfilt_destroy(pfilt *p)
196 {
197 mp_drop(p->m);
198 }
199
200 /* --- @pfilt_step@ --- *
201 *
202 * Arguments: @pfilt *p@ = pointer to prime filtering context
203 * @mpw step@ = how much to step the number
204 *
205 * Returns: One of the @PGEN@ result codes.
206 *
207 * Use: Steps a number by a small amount. Stepping is much faster
208 * than initializing with a new number. The test performed is
209 * the same simple one used by @primetab_create@, so @PGEN_TRY@
210 * results should be followed up by a Rabin-Miller test.
211 */
212
213 int pfilt_step(pfilt *p, mpw step)
214 {
215 int rc = PGEN_TRY;
216 int i;
217
218 /* --- Add the step on to the number --- */
219
220 p->m = mp_split(p->m);
221 mp_ensure(p->m, MP_LEN(p->m) + 1);
222 mpx_uaddn(p->m->v, p->m->vl, step);
223 mp_shrink(p->m);
224
225 /* --- Update the residue table --- */
226
227 for (i = 0; i < NPRIME; i++) {
228 p->r[i] = (p->r[i] + step) % primetab[i];
229 if (!p->r[i] && rc == PGEN_TRY) {
230 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
231 rc = PGEN_DONE;
232 else
233 rc = PGEN_FAIL;
234 }
235 }
236
237 /* --- Check for small primes --- */
238
239 if (rc == PGEN_TRY)
240 rc = smallenough(p->m);
241
242 /* --- Done --- */
243
244 return (rc);
245 }
246
247 /* --- @pfilt_muladd@ --- *
248 *
249 * Arguments: @pfilt *p@ = destination prime filtering context
250 * @const pfilt *q@ = source prime filtering context
251 * @mpw m@ = number to multiply by
252 * @mpw a@ = number to add
253 *
254 * Returns: One of the @PGEN@ result codes.
255 *
256 * Use: Multiplies the number in a prime filtering context by a
257 * small value and then adds a small value. The destination
258 * should either be uninitialized or the same as the source.
259 *
260 * Common things to do include multiplying by 2 and adding 0 to
261 * turn a prime into a jump for finding other primes with @q@ as
262 * a factor of @p - 1@, or multiplying by 2 and adding 1.
263 */
264
265 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
266 {
267 int rc = PGEN_TRY;
268 int i;
269
270 /* --- Multiply the big number --- */
271
272 {
273 mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f);
274 mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
275 mpx_uaddn(d->v, d->vl, a);
276 if (p == q)
277 mp_drop(p->m);
278 mp_shrink(d);
279 p->m = d;
280 }
281
282 /* --- Gallivant through the residue table --- */
283
284 for (i = 0; i < NPRIME; i++) {
285 p->r[i] = (q->r[i] * m + a) % primetab[i];
286 if (!p->r[i] && rc == PGEN_TRY) {
287 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
288 rc = PGEN_DONE;
289 else
290 rc = PGEN_FAIL;
291 }
292 }
293
294 /* --- Check for small primes --- */
295
296 if (rc == PGEN_TRY)
297 rc = smallenough(p->m);
298
299 /* --- Finished --- */
300
301 return (rc);
302 }
303
304 /* --- @pfilt_jump@ --- *
305 *
306 * Arguments: @pfilt *p@ = pointer to prime filtering context
307 * @const pfilt *j@ = pointer to another filtering context
308 *
309 * Returns: One of the @PGEN@ result codes.
310 *
311 * Use: Steps a number by a large amount. Even so, jumping is much
312 * faster than initializing a new number. The test peformed is
313 * the same simple one used by @primetab_create@, so @PGEN_TRY@
314 * results should be followed up by a Rabin-Miller test.
315 *
316 * Note that the number stored in the @j@ context is probably
317 * better off being even than prime. The important thing is
318 * that all of the residues for the number have already been
319 * computed.
320 */
321
322 int pfilt_jump(pfilt *p, const pfilt *j)
323 {
324 int rc = PGEN_TRY;
325 int i;
326
327 /* --- Add the step on --- */
328
329 p->m = mp_add(p->m, p->m, j->m);
330
331 /* --- Update the residue table --- */
332
333 for (i = 0; i < NPRIME; i++) {
334 p->r[i] = p->r[i] + j->r[i];
335 if (p->r[i] > primetab[i])
336 p->r[i] -= primetab[i];
337 if (!p->r[i] && rc == PGEN_TRY) {
338 if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
339 rc = PGEN_DONE;
340 else
341 rc = PGEN_FAIL;
342 }
343 }
344
345 /* --- Check for small primes --- */
346
347 if (rc == PGEN_TRY)
348 rc = smallenough(p->m);
349
350 /* --- Done --- */
351
352 return (rc);
353 }
354
355 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)