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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: pfilt.c,v 1.4 2000/10/08 12:14:57 mdw Exp $ |
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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 $ |
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33 | * Revision 1.4 2000/10/08 12:14:57 mdw |
34 | * Remove vestiges of @primorial@. |
35 | * |
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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 | * |
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46 | * Revision 1.2 2000/06/17 11:54:27 mdw |
47 | * Use new MP memory management functions. |
48 | * |
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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" |
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66 | #include "mpint.h" |
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67 | #include "pfilt.h" |
68 | #include "pgen.h" |
69 | #include "primetab.h" |
70 | |
71 | /*----- Main code ---------------------------------------------------------*/ |
72 | |
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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 | |
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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; |
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157 | size_t sz = MP_LEN(m); |
158 | mpw *v = mpalloc(m->a, sz); |
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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 | |
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167 | for (i = 0; i < NPRIME; i++) { |
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168 | p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]); |
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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 | |
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177 | /* --- Check for small primes --- */ |
178 | |
179 | if (rc == PGEN_TRY) |
180 | rc = smallenough(m); |
181 | |
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182 | /* --- Done --- */ |
183 | |
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184 | mpfree(m->a, v); |
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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 | |
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239 | /* --- Check for small primes --- */ |
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240 | |
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241 | if (rc == PGEN_TRY) |
242 | rc = smallenough(p->m); |
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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 | { |
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275 | mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f); |
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276 | mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m); |
277 | mpx_uaddn(d->v, d->vl, a); |
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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 | |
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296 | /* --- Check for small primes --- */ |
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297 | |
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298 | if (rc == PGEN_TRY) |
299 | rc = smallenough(p->m); |
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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 | |
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347 | /* --- Check for small primes --- */ |
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348 | |
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349 | if (rc == PGEN_TRY) |
350 | rc = smallenough(p->m); |
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351 | |
352 | /* --- Done --- */ |
353 | |
354 | return (rc); |
355 | } |
356 | |
357 | /*----- That's all, folks -------------------------------------------------*/ |