git.distorted.org.uk Git - u/mdw/catacomb/blob - gf-gcd.c

   1 /* -*-c-*-
   2  *
   3  * $Id: gf-gcd.c,v 1.1.2.1 2004/03/21 22:39:46 mdw Exp $
   4  *
   5  * Euclidian algorithm on binary polynomials
   6  *
   7  * (c) 2004 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: gf-gcd.c,v $
  33  * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
  34  * Elliptic curves on binary fields work.
  35  *
  36  */
  37
  38 /*----- Header files ------------------------------------------------------*/
  39
  40 #include "gf.h"
  41
  42 /*----- Main code ---------------------------------------------------------*/
  43
  44 /* --- @gf_gcd@ --- *
  45  *
  46  * Arguments:   @mp **gcd, **xx, **yy@ = where to write the results
  47  *              @mp *a, *b@ = sources (must be nonzero)
  48  *
  49  *
  50  * Returns:     ---
  51  *
  52  * Use:         Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
  53  *              @ax + by = gcd(a, b)@.  This is useful for computing modular
  54  *              inverses.
  55  */
  56
  57 void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
  58 {
  59   mp *x = MP_ONE, *X = MP_ZERO;
  60   mp *y = MP_ZERO, *Y = MP_ONE;
  61   mp *u, *v;
  62   mp *q = MP_NEW;
  63   unsigned f = 0;
  64
  65 #define f_swap 1u
  66 #define f_ext 2u
  67
  68   /* --- Sort out some initial flags --- */
  69
  70   if (xx || yy)
  71     f |= f_ext;
  72
  73   /* --- Ensure that @a@ is larger than @b@ --- *
  74    *
  75    * If they're the same length we don't care which order they're in, so this
  76    * unsigned comparison is fine.
  77    */
  78
  79   if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
  80     { mp *t = a; a = b; b = t; }
  81     f |= f_swap;
  82   }
  83
  84   /* --- Check for zeroness --- */
  85
  86   if (MP_EQ(b, MP_ZERO)) {
  87
  88     /* --- Store %$|a|$% as the GCD --- */
  89
  90     if (gcd) {
  91       if (*gcd) MP_DROP(*gcd);
  92       a = MP_COPY(a);
  93       *gcd = a;
  94     }
  95
  96     /* --- Store %$1$% and %$0$% in the appropriate bins --- */
  97
  98     if (f & f_ext) {
  99       if (f & f_swap) {
 100         mp **t = xx; xx = yy; yy = t;
 101       }
 102       if (xx) {
 103         if (*xx) MP_DROP(*xx);
 104         if (MP_EQ(a, MP_ZERO))
 105           *xx = MP_ZERO;
 106         else
 107           *xx = MP_ONE;
 108       }
 109       if (yy) {
 110         if (*yy) MP_DROP(*yy);
 111         *yy = MP_ZERO;
 112       }
 113     }
 114     return;
 115   }
 116
 117   /* --- Take a reference to the arguments --- */
 118
 119   a = MP_COPY(a);
 120   b = MP_COPY(b);
 121
 122   /* --- Make sure @a@ and @b@ are not both even --- */
 123
 124   MP_SPLIT(a); a->f &= ~MP_NEG;
 125   MP_SPLIT(b); b->f &= ~MP_NEG;
 126
 127   u = MP_COPY(a);
 128   v = MP_COPY(b);
 129
 130   while (MP_LEN(v)) {
 131     mp *t;
 132     gf_div(&q, &u, u, v);
 133     if (f & f_ext) {
 134       t = gf_mul(MP_NEW, X, q);
 135       t = gf_add(t, x, t);
 136       MP_DROP(x); x = X; X = t;
 137       t = gf_mul(MP_NEW, Y, q);
 138       t = gf_add(t, y, t);
 139       MP_DROP(y); y = Y; Y = t;
 140     }
 141     t = u; u = v; v = t;
 142   }
 143
 144   MP_DROP(q);
 145   if (!gcd)
 146     MP_DROP(u);
 147   else {
 148     if (*gcd) MP_DROP(*gcd);
 149     u->f &= ~MP_NEG;
 150     *gcd = u;
 151   }
 152
 153   /* --- Perform a little normalization --- */
 154
 155   if (f & f_ext) {
 156
 157     /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
 158
 159     if (f & f_swap) {
 160       mp *t = x; x = y; y = t;
 161       t = a; a = b; b = t;
 162     }
 163
 164     /* --- Store the results --- */
 165
 166     if (!xx)
 167       MP_DROP(x);
 168     else {
 169       if (*xx) MP_DROP(*xx);
 170       *xx = x;
 171     }
 172
 173     if (!yy)
 174       MP_DROP(y);
 175     else {
 176       if (*yy) MP_DROP(*yy);
 177       *yy = y;
 178     }
 179   }
 180
 181   MP_DROP(v);
 182   MP_DROP(X); MP_DROP(Y);
 183   MP_DROP(a); MP_DROP(b);
 184 }
 185
 186 /*----- Test rig ----------------------------------------------------------*/
 187
 188 #ifdef TEST_RIG
 189
 190 static int gcd(dstr *v)
 191 {
 192   int ok = 1;
 193   mp *a = *(mp **)v[0].buf;
 194   mp *b = *(mp **)v[1].buf;
 195   mp *g = *(mp **)v[2].buf;
 196   mp *x = *(mp **)v[3].buf;
 197   mp *y = *(mp **)v[4].buf;
 198
 199   mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
 200   gf_gcd(&gg, &xx, &yy, a, b);
 201   if (!MP_EQ(x, xx)) {
 202     fputs("\n*** mp_gcd(x) failed", stderr);
 203     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 204     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 205     fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 16);
 206     fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 16);
 207     fputc('\n', stderr);
 208     ok = 0;
 209   }
 210   if (!MP_EQ(y, yy)) {
 211     fputs("\n*** mp_gcd(y) failed", stderr);
 212     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 213     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 214     fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 16);
 215     fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 16);
 216     fputc('\n', stderr);
 217     ok = 0;
 218   }
 219
 220   if (!ok) {
 221     mp *ax = gf_mul(MP_NEW, a, xx);
 222     mp *by = gf_mul(MP_NEW, b, yy);
 223     ax = gf_add(ax, ax, by);
 224     if (MP_EQ(ax, gg))
 225       fputs("\n*** (Alternative result found.)\n", stderr);
 226     MP_DROP(ax);
 227     MP_DROP(by);
 228   }
 229
 230   if (!MP_EQ(g, gg)) {
 231     fputs("\n*** mp_gcd(gcd) failed", stderr);
 232     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 233     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 234     fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 16);
 235     fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 16);
 236     fputc('\n', stderr);
 237     ok = 0;
 238   }
 239   MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
 240   MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
 241   assert(mparena_count(MPARENA_GLOBAL) == 0);
 242   return (ok);
 243 }
 244
 245 static test_chunk tests[] = {
 246   { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 247   { 0, 0, { 0 } }
 248 };
 249
 250 int main(int argc, char *argv[])
 251 {
 252   sub_init();
 253   test_run(argc, argv, tests, SRCDIR "/tests/gf");
 254   return (0);
 255 }
 256
 257 #endif
 258
 259 /*----- That's all, folks -------------------------------------------------*/