| 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 -------------------------------------------------*/ |