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

   1 /* -*-c-*-
   2  *
   3  * $Id: gf-gcd.c,v 1.2 2004/03/21 22:52:06 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 1.2  2004/03/21 22:52:06  mdw
  34  * Merge and close elliptic curve branch.
  35  *
  36  * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
  37  * Elliptic curves on binary fields work.
  38  *
  39  */
  40
  41 /*----- Header files ------------------------------------------------------*/
  42
  43 #include "gf.h"
  44
  45 /*----- Main code ---------------------------------------------------------*/
  46
  47 /* --- @gf_gcd@ --- *
  48  *
  49  * Arguments:   @mp **gcd, **xx, **yy@ = where to write the results
  50  *              @mp *a, *b@ = sources (must be nonzero)
  51  *
  52  *
  53  * Returns:     ---
  54  *
  55  * Use:         Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
  56  *              @ax + by = gcd(a, b)@.  This is useful for computing modular
  57  *              inverses.
  58  */
  59
  60 void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
  61 {
  62   mp *x = MP_ONE, *X = MP_ZERO;
  63   mp *y = MP_ZERO, *Y = MP_ONE;
  64   mp *u, *v;
  65   mp *q = MP_NEW;
  66   unsigned f = 0;
  67
  68 #define f_swap 1u
  69 #define f_ext 2u
  70
  71   /* --- Sort out some initial flags --- */
  72
  73   if (xx || yy)
  74     f |= f_ext;
  75
  76   /* --- Ensure that @a@ is larger than @b@ --- *
  77    *
  78    * If they're the same length we don't care which order they're in, so this
  79    * unsigned comparison is fine.
  80    */
  81
  82   if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
  83     { mp *t = a; a = b; b = t; }
  84     f |= f_swap;
  85   }
  86
  87   /* --- Check for zeroness --- */
  88
  89   if (MP_EQ(b, MP_ZERO)) {
  90
  91     /* --- Store %$|a|$% as the GCD --- */
  92
  93     if (gcd) {
  94       if (*gcd) MP_DROP(*gcd);
  95       a = MP_COPY(a);
  96       *gcd = a;
  97     }
  98
  99     /* --- Store %$1$% and %$0$% in the appropriate bins --- */
 100
 101     if (f & f_ext) {
 102       if (f & f_swap) {
 103         mp **t = xx; xx = yy; yy = t;
 104       }
 105       if (xx) {
 106         if (*xx) MP_DROP(*xx);
 107         if (MP_EQ(a, MP_ZERO))
 108           *xx = MP_ZERO;
 109         else
 110           *xx = MP_ONE;
 111       }
 112       if (yy) {
 113         if (*yy) MP_DROP(*yy);
 114         *yy = MP_ZERO;
 115       }
 116     }
 117     return;
 118   }
 119
 120   /* --- Take a reference to the arguments --- */
 121
 122   a = MP_COPY(a);
 123   b = MP_COPY(b);
 124
 125   /* --- Make sure @a@ and @b@ are not both even --- */
 126
 127   MP_SPLIT(a); a->f &= ~MP_NEG;
 128   MP_SPLIT(b); b->f &= ~MP_NEG;
 129
 130   u = MP_COPY(a);
 131   v = MP_COPY(b);
 132
 133   while (MP_LEN(v)) {
 134     mp *t;
 135     gf_div(&q, &u, u, v);
 136     if (f & f_ext) {
 137       t = gf_mul(MP_NEW, X, q);
 138       t = gf_add(t, x, t);
 139       MP_DROP(x); x = X; X = t;
 140       t = gf_mul(MP_NEW, Y, q);
 141       t = gf_add(t, y, t);
 142       MP_DROP(y); y = Y; Y = t;
 143     }
 144     t = u; u = v; v = t;
 145   }
 146
 147   MP_DROP(q);
 148   if (!gcd)
 149     MP_DROP(u);
 150   else {
 151     if (*gcd) MP_DROP(*gcd);
 152     u->f &= ~MP_NEG;
 153     *gcd = u;
 154   }
 155
 156   /* --- Perform a little normalization --- */
 157
 158   if (f & f_ext) {
 159
 160     /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
 161
 162     if (f & f_swap) {
 163       mp *t = x; x = y; y = t;
 164       t = a; a = b; b = t;
 165     }
 166
 167     /* --- Store the results --- */
 168
 169     if (!xx)
 170       MP_DROP(x);
 171     else {
 172       if (*xx) MP_DROP(*xx);
 173       *xx = x;
 174     }
 175
 176     if (!yy)
 177       MP_DROP(y);
 178     else {
 179       if (*yy) MP_DROP(*yy);
 180       *yy = y;
 181     }
 182   }
 183
 184   MP_DROP(v);
 185   MP_DROP(X); MP_DROP(Y);
 186   MP_DROP(a); MP_DROP(b);
 187 }
 188
 189 /*----- Test rig ----------------------------------------------------------*/
 190
 191 #ifdef TEST_RIG
 192
 193 static int gcd(dstr *v)
 194 {
 195   int ok = 1;
 196   mp *a = *(mp **)v[0].buf;
 197   mp *b = *(mp **)v[1].buf;
 198   mp *g = *(mp **)v[2].buf;
 199   mp *x = *(mp **)v[3].buf;
 200   mp *y = *(mp **)v[4].buf;
 201
 202   mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
 203   gf_gcd(&gg, &xx, &yy, a, b);
 204   if (!MP_EQ(x, xx)) {
 205     fputs("\n*** mp_gcd(x) failed", stderr);
 206     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 207     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 208     fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 16);
 209     fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 16);
 210     fputc('\n', stderr);
 211     ok = 0;
 212   }
 213   if (!MP_EQ(y, yy)) {
 214     fputs("\n*** mp_gcd(y) failed", stderr);
 215     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 216     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 217     fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 16);
 218     fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 16);
 219     fputc('\n', stderr);
 220     ok = 0;
 221   }
 222
 223   if (!ok) {
 224     mp *ax = gf_mul(MP_NEW, a, xx);
 225     mp *by = gf_mul(MP_NEW, b, yy);
 226     ax = gf_add(ax, ax, by);
 227     if (MP_EQ(ax, gg))
 228       fputs("\n*** (Alternative result found.)\n", stderr);
 229     MP_DROP(ax);
 230     MP_DROP(by);
 231   }
 232
 233   if (!MP_EQ(g, gg)) {
 234     fputs("\n*** mp_gcd(gcd) failed", stderr);
 235     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 236     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 237     fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 16);
 238     fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 16);
 239     fputc('\n', stderr);
 240     ok = 0;
 241   }
 242   MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
 243   MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
 244   assert(mparena_count(MPARENA_GLOBAL) == 0);
 245   return (ok);
 246 }
 247
 248 static test_chunk tests[] = {
 249   { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 250   { 0, 0, { 0 } }
 251 };
 252
 253 int main(int argc, char *argv[])
 254 {
 255   sub_init();
 256   test_run(argc, argv, tests, SRCDIR "/tests/gf");
 257   return (0);
 258 }
 259
 260 #endif
 261
 262 /*----- That's all, folks -------------------------------------------------*/