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   1 /* -*-c-*-
   2  *
   3  * $Id: pfilt.c,v 1.1 1999/12/22 15:49:39 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 1.1  1999/12/22 15:49:39  mdw
  34  * Renamed from `pgen'.  Reworking for new prime-search system.
  35  *
  36  * Revision 1.3  1999/12/10 23:28:35  mdw
  37  * Track suggested destination changes.
  38  *
  39  * Revision 1.2  1999/11/20 22:23:05  mdw
  40  * Add multiply-and-add function for Diffie-Hellman safe prime generation.
  41  *
  42  * Revision 1.1  1999/11/19 13:17:57  mdw
  43  * Prime number generator and tester.
  44  *
  45  */
  46
  47 /*----- Header files ------------------------------------------------------*/
  48
  49 #include "mp.h"
  50 #include "mpmont.h"
  51 #include "pfilt.h"
  52 #include "pgen.h"
  53 #include "primetab.h"
  54
  55 /*----- Main code ---------------------------------------------------------*/
  56
  57 /* --- @pfilt_create@ --- *
  58  *
  59  * Arguments:   @pfilt *p@ = pointer to prime filtering context
  60  *              @mp *m@ = pointer to initial number to test
  61  *
  62  * Returns:     One of the @PGEN@ result codes.
  63  *
  64  * Use:         Tests an initial number for primality by computing its
  65  *              residue modulo various small prime numbers.  This is fairly
  66  *              quick, but not particularly certain.  If a @PGEN_TRY@
  67  *              result is returned, perform Rabin-Miller tests to confirm.
  68  */
  69
  70 int pfilt_create(pfilt *p, mp *m)
  71 {
  72   int rc = PGEN_TRY;
  73   int i;
  74   mp *r = MP_NEW;
  75   mpw qw;
  76   mp q;
  77
  78   /* --- Take a copy of the number --- */
  79
  80   mp_shrink(m);
  81   p->m = MP_COPY(m);
  82
  83   /* --- Fill in the residues --- */
  84
  85   mp_build(&q, &qw, &qw + 1);
  86   for (i = 0; i < NPRIME; i++) {
  87     qw = primetab[i];
  88     mp_div(0, &r, m, &q);
  89     p->r[i] = r->v[0];
  90     if (!p->r[i] && rc == PGEN_TRY) {
  91       if (MP_LEN(m) == 1 && m->v[0] == primetab[i])
  92         rc = PGEN_DONE;
  93       else
  94         rc = PGEN_FAIL;
  95     }
  96   }
  97
  98   /* --- Done --- */
  99
 100   mp_drop(r);
 101   return (rc);
 102 }
 103
 104 /* --- @pfilt_destroy@ --- *
 105  *
 106  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 107  *
 108  * Returns:     ---
 109  *
 110  * Use:         Discards a context and all the resources it holds.
 111  */
 112
 113 void pfilt_destroy(pfilt *p)
 114 {
 115   mp_drop(p->m);
 116 }
 117
 118 /* --- @pfilt_step@ --- *
 119  *
 120  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 121  *              @mpw step@ = how much to step the number
 122  *
 123  * Returns:     One of the @PGEN@ result codes.
 124  *
 125  * Use:         Steps a number by a small amount.  Stepping is much faster
 126  *              than initializing with a new number.  The test performed is
 127  *              the same simple one used by @primetab_create@, so @PGEN_TRY@
 128  *              results should be followed up by a Rabin-Miller test.
 129  */
 130
 131 int pfilt_step(pfilt *p, mpw step)
 132 {
 133   int rc = PGEN_TRY;
 134   int i;
 135
 136   /* --- Add the step on to the number --- */
 137
 138   p->m = mp_split(p->m);
 139   mp_ensure(p->m, MP_LEN(p->m) + 1);
 140   mpx_uaddn(p->m->v, p->m->vl, step);
 141   mp_shrink(p->m);
 142
 143   /* --- Update the residue table --- */
 144
 145   for (i = 0; i < NPRIME; i++) {
 146     p->r[i] = (p->r[i] + step) % primetab[i];
 147     if (!p->r[i] && rc == PGEN_TRY) {
 148       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 149         rc = PGEN_DONE;
 150       else
 151         rc = PGEN_FAIL;
 152     }
 153   }
 154
 155   /* --- Small numbers must be prime --- */
 156
 157   if (rc == PGEN_TRY && MP_LEN(p->m) == 1 &&
 158       p->m->v[0] < MAXPRIME * MAXPRIME)
 159     rc = PGEN_DONE;
 160
 161   /* --- Done --- */
 162
 163   return (rc);
 164 }
 165
 166 /* --- @pfilt_muladd@ --- *
 167  *
 168  * Arguments:   @pfilt *p@ = destination prime filtering context
 169  *              @const pfilt *q@ = source prime filtering context
 170  *              @mpw m@ = number to multiply by
 171  *              @mpw a@ = number to add
 172  *
 173  * Returns:     One of the @PGEN@ result codes.
 174  *
 175  * Use:         Multiplies the number in a prime filtering context by a
 176  *              small value and then adds a small value.  The destination
 177  *              should either be uninitialized or the same as the source.
 178  *
 179  *              Common things to do include multiplying by 2 and adding 0 to
 180  *              turn a prime into a jump for finding other primes with @q@ as
 181  *              a factor of @p - 1@, or multiplying by 2 and adding 1.
 182  */
 183
 184 int pfilt_muladd(pfilt *p, const pfilt *q, mpw m, mpw a)
 185 {
 186   int rc = PGEN_TRY;
 187   int i;
 188
 189   /* --- Multiply the big number --- */
 190
 191   {
 192     mp *d = mp_create(MP_LEN(q->m) + 2);
 193     mpx_umuln(d->v, d->vl, q->m->v, q->m->vl, m);
 194     mpx_uaddn(d->v, d->vl, a);
 195     d->f = q->m->f;
 196     if (p == q)
 197       mp_drop(p->m);
 198     mp_shrink(d);
 199     p->m = d;
 200   }
 201
 202   /* --- Gallivant through the residue table --- */
 203
 204   for (i = 0; i < NPRIME; i++) {
 205     p->r[i] = (q->r[i] * m + a) % primetab[i];
 206     if (!p->r[i] && rc == PGEN_TRY) {
 207       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 208         rc = PGEN_DONE;
 209       else
 210         rc = PGEN_FAIL;
 211     }
 212   }
 213
 214   /* --- Small numbers must be prime --- */
 215
 216   if (rc == PGEN_TRY && MP_LEN(p->m) == 1 &&
 217       p->m->v[0] < MAXPRIME * MAXPRIME)
 218     rc = PGEN_DONE;
 219
 220   /* --- Finished --- */
 221
 222   return (rc);
 223 }
 224
 225 /* --- @pfilt_jump@ --- *
 226  *
 227  * Arguments:   @pfilt *p@ = pointer to prime filtering context
 228  *              @const pfilt *j@ = pointer to another filtering context
 229  *
 230  * Returns:     One of the @PGEN@ result codes.
 231  *
 232  * Use:         Steps a number by a large amount.  Even so, jumping is much
 233  *              faster than initializing a new number.  The test peformed is
 234  *              the same simple one used by @primetab_create@, so @PGEN_TRY@
 235  *              results should be followed up by a Rabin-Miller test.
 236  *
 237  *              Note that the number stored in the @j@ context is probably
 238  *              better off being even than prime.  The important thing is
 239  *              that all of the residues for the number have already been
 240  *              computed.
 241  */
 242
 243 int pfilt_jump(pfilt *p, const pfilt *j)
 244 {
 245   int rc = PGEN_TRY;
 246   int i;
 247
 248   /* --- Add the step on --- */
 249
 250   p->m = mp_add(p->m, p->m, j->m);
 251
 252   /* --- Update the residue table --- */
 253
 254   for (i = 0; i < NPRIME; i++) {
 255     p->r[i] = p->r[i] + j->r[i];
 256     if (p->r[i] > primetab[i])
 257       p->r[i] -= primetab[i];
 258     if (!p->r[i] && rc == PGEN_TRY) {
 259       if (MP_LEN(p->m) == 1 && p->m->v[0] == primetab[i])
 260         rc = PGEN_DONE;
 261       else
 262         rc = PGEN_FAIL;
 263     }
 264   }
 265
 266   /* --- Small numbers must be prime --- */
 267
 268   if (rc == PGEN_TRY && MP_LEN(p->m) == 1 &&
 269       p->m->v[0] < MAXPRIME * MAXPRIME)
 270     rc = PGEN_DONE;
 271
 272   /* --- Done --- */
 273
 274   return (rc);
 275 }
 276
 277 /*----- That's all, folks -------------------------------------------------*/