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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: pfilt.c,v 1.3 2000/08/15 21:44:27 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 1.3 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 | * |
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43 | * Revision 1.2 2000/06/17 11:54:27 mdw |
44 | * Use new MP memory management functions. |
45 | * |
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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" |
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63 | #include "mpint.h" |
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64 | #include "pfilt.h" |
65 | #include "pgen.h" |
66 | #include "primetab.h" |
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67 | #include "primorial.h" |
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68 | |
69 | /*----- Main code ---------------------------------------------------------*/ |
70 | |
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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 | |
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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; |
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155 | size_t sz = MP_LEN(m); |
156 | mpw *v = mpalloc(m->a, sz); |
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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 | |
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165 | for (i = 0; i < NPRIME; i++) { |
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166 | p->r[i] = mpx_udivn(v, v + sz, m->v, m->vl, primetab[i]); |
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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 | |
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175 | /* --- Check for small primes --- */ |
176 | |
177 | if (rc == PGEN_TRY) |
178 | rc = smallenough(m); |
179 | |
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180 | /* --- Done --- */ |
181 | |
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182 | mpfree(m->a, v); |
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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 | |
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237 | /* --- Check for small primes --- */ |
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238 | |
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239 | if (rc == PGEN_TRY) |
240 | rc = smallenough(p->m); |
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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 | { |
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273 | mp *d = mp_new(MP_LEN(q->m) + 2, q->m->f); |
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274 | mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m); |
275 | mpx_uaddn(d->v, d->vl, a); |
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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 | |
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294 | /* --- Check for small primes --- */ |
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295 | |
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296 | if (rc == PGEN_TRY) |
297 | rc = smallenough(p->m); |
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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 | |
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345 | /* --- Check for small primes --- */ |
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346 | |
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347 | if (rc == PGEN_TRY) |
348 | rc = smallenough(p->m); |
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349 | |
350 | /* --- Done --- */ |
351 | |
352 | return (rc); |
353 | } |
354 | |
355 | /*----- That's all, folks -------------------------------------------------*/ |