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

   1 /* -*-c-*-
   2  *
   3  * $Id: ec.c,v 1.2 2001/05/07 17:29:44 mdw Exp $
   4  *
   5  * Elliptic curve definitions
   6  *
   7  * (c) 2001 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: ec.c,v $
  33  * Revision 1.2  2001/05/07 17:29:44  mdw
  34  * Treat projective coordinates as an internal representation.  Various
  35  * minor interface changes.
  36  *
  37  * Revision 1.1  2001/04/29 18:12:33  mdw
  38  * Prototype version.
  39  *
  40  */
  41
  42 /*----- Header files ------------------------------------------------------*/
  43
  44 #include "ec.h"
  45
  46 /*----- Trivial wrappers --------------------------------------------------*/
  47
  48 /* --- @ec_create@ --- *
  49  *
  50  * Arguments:   @ec *p@ = pointer to an elliptic-curve point
  51  *
  52  * Returns:     ---
  53  *
  54  * Use:         Initializes a new point.  The initial value is the additive
  55  *              identity (which is universal for all curves).
  56  */
  57
  58 void ec_create(ec *p) { EC_CREATE(p); }
  59
  60 /* --- @ec_destroy@ --- *
  61  *
  62  * Arguments:   @ec *p@ = pointer to an elliptic-curve point
  63  *
  64  * Returns:     ---
  65  *
  66  * Use:         Destroys a point, making it invalid.
  67  */
  68
  69 void ec_destroy(ec *p) { EC_DESTROY(p); }
  70
  71 /* --- @ec_atinf@ --- *
  72  *
  73  * Arguments:   @const ec *p@ = pointer to a point
  74  *
  75  * Returns:     Nonzero if %$p = O$% is the point at infinity, zero
  76  *              otherwise.
  77  */
  78
  79 int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
  80
  81 /* --- @ec_setinf@ --- *
  82  *
  83  * Arguments:   @ec *p@ = pointer to a point
  84  *
  85  * Returns:     ---
  86  *
  87  * Use:         Sets the given point to be the point %$O$% at infinity.
  88  */
  89
  90 void ec_setinf(ec *p) { EC_SETINF(p); }
  91
  92 /* --- @ec_copy@ --- *
  93  *
  94  * Arguments:   @ec *d@ = pointer to destination point
  95  *              @const ec *p@ = pointer to source point
  96  *
  97  * Returns:     ---
  98  *
  99  * Use:         Creates a copy of an elliptic curve point.
 100  */
 101
 102 void ec_copy(ec *d, const ec *p) { EC_COPY(d, p); }
 103
 104 /*----- Standard curve operations -----------------------------------------*/
 105
 106 /* --- @ec_idin@, @ec_idout@ --- *
 107  *
 108  * Arguments:   @ec_curve *c@ = pointer to an elliptic curve
 109  *              @ec *d@ = pointer to the destination
 110  *              @const ec *p@ = pointer to a source point
 111  *
 112  * Returns:     The destination @d@.
 113  *
 114  * Use:         An identity operation if your curve has no internal
 115  *              representation.  (The field internal representation is still
 116  *              used.)
 117  */
 118
 119 ec *ec_idin(ec_curve *c, ec *d, const ec *p)
 120 {
 121   if (EC_ATINF(p))
 122     EC_SETINF(d);
 123   else {
 124     field *f = c->f;
 125     d->x = F_IN(f, d->x, p->x);
 126     d->y = F_IN(f, d->y, p->y);
 127     mp_drop(d->z); d->z = 0;
 128   }
 129   return (d);
 130 }
 131
 132 ec *ec_idout(ec_curve *c, ec *d, const ec *p)
 133 {
 134   if (EC_ATINF(p))
 135     EC_SETINF(d);
 136   else {
 137     field *f = c->f;
 138     d->x = F_OUT(f, d->x, p->x);
 139     d->y = F_OUT(f, d->y, p->y);
 140     mp_drop(d->z); d->z = 0;
 141   }
 142   return (d);
 143 }
 144
 145 /* --- @ec_projin@, @ec_projout@ --- *
 146  *
 147  * Arguments:   @ec_curve *c@ = pointer to an elliptic curve
 148  *              @ec *d@ = pointer to the destination
 149  *              @const ec *p@ = pointer to a source point
 150  *
 151  * Returns:     The destination @d@.
 152  *
 153  * Use:         Conversion functions if your curve operations use a
 154  *              projective representation.
 155  */
 156
 157 ec *ec_projin(ec_curve *c, ec *d, const ec *p)
 158 {
 159   if (EC_ATINF(p))
 160     EC_SETINF(d);
 161   else {
 162     field *f = c->f;
 163     d->x = F_IN(f, d->x, p->x);
 164     d->y = F_IN(f, d->y, p->y);
 165     mp_drop(d->z); d->z = MP_COPY(f->one);
 166   }
 167   return (d);
 168 }
 169
 170 ec *ec_projout(ec_curve *c, ec *d, const ec *p)
 171 {
 172   if (EC_ATINF(p))
 173     EC_SETINF(d);
 174   else {
 175     mp *x, *y, *z;
 176     field *f = c->f;
 177     z = F_INV(f, MP_NEW, p->z);
 178     x = F_MUL(f, d->x, p->x, z);
 179     y = F_MUL(f, d->y, p->y, z);
 180     mp_drop(z);
 181     mp_drop(d->z);
 182     d->x = F_OUT(f, x, x);
 183     d->y = F_OUT(f, y, y);
 184     d->z = 0;
 185   }
 186   return (d);
 187 }
 188
 189 /*----- Real arithmetic ---------------------------------------------------*/
 190
 191 /* --- @ec_find@ --- *
 192  *
 193  * Arguments:   @ec_curve *c@ = pointer to an elliptic curve
 194  *              @ec *d@ = pointer to the destination point
 195  *              @mp *x@ = a possible x-coordinate
 196  *
 197  * Returns:     Zero if OK, nonzero if there isn't a point there.
 198  *
 199  * Use:         Finds a point on an elliptic curve with a given x-coordinate.
 200  */
 201
 202 ec *ec_find(ec_curve *c, ec *d, mp *x)
 203 {
 204   x = F_IN(c->f, MP_NEW, x);
 205   if ((d = EC_FIND(c, d, x)) != 0)
 206     EC_OUT(c, d, d);
 207   mp_drop(x);
 208   return (d);
 209 }
 210
 211 /* --- @ec_add@ --- *
 212  *
 213  * Arguments:   @ec_curve *c@ = pointer to an elliptic curve
 214  *              @ec *d@ = pointer to the destination point
 215  *              @const ec *p, *q@ = pointers to the operand points
 216  *
 217  * Returns:     ---
 218  *
 219  * Use:         Adds two points on an elliptic curve.
 220  */
 221
 222 ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
 223 {
 224   ec pp = EC_INIT, qq = EC_INIT;
 225   EC_IN(c, &pp, p);
 226   EC_IN(c, &qq, q);
 227   EC_ADD(c, d, &pp, &qq);
 228   EC_OUT(c, d, d);
 229   EC_DESTROY(&pp);
 230   EC_DESTROY(&qq);
 231   return (d);
 232 }
 233
 234 /* --- @ec_dbl@ --- *
 235  *
 236  * Arguments:   @ec_curve *c@ = pointer to an elliptic curve
 237  *              @ec *d@ = pointer to the destination point
 238  *              @const ec *p@ = pointer to the operand point
 239  *
 240  * Returns:     ---
 241  *
 242  * Use:         Doubles a point on an elliptic curve.
 243  */
 244
 245 ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
 246 {
 247   EC_IN(c, d, p);
 248   EC_DBL(c, d, d);
 249   return (EC_OUT(c, d, d));
 250 }
 251
 252 /* --- @ec_mul@ --- *
 253  *
 254  * Arguments:   @ec_curve *c@ = pointer to an elliptic curve
 255  *              @ec *d@ = pointer to the destination point
 256  *              @const ec *p@ = pointer to the generator point
 257  *              @mp *n@ = integer multiplier
 258  *
 259  * Returns:     ---
 260  *
 261  * Use:         Multiplies a point by a scalar, returning %$n p$%.
 262  */
 263
 264 ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
 265 {
 266   mpscan sc;
 267   ec g = EC_INIT;
 268   unsigned sq = 0;
 269
 270   EC_SETINF(d);
 271   if (EC_ATINF(p))
 272     return;
 273
 274   mp_rscan(&sc, n);
 275   if (!MP_RSTEP(&sc))
 276     goto exit;
 277   while (!MP_RBIT(&sc))
 278     MP_RSTEP(&sc);
 279
 280   EC_IN(c, &g, p);
 281   if ((n->f & MP_BURN) && !(g.x->f & MP_BURN))
 282     MP_DEST(g.x, 0, MP_BURN);
 283   if ((n->f & MP_BURN) && !(g.y->f & MP_BURN))
 284     MP_DEST(g.y, 0, MP_BURN);
 285
 286   for (;;) {
 287     EC_ADD(c, d, d, &g);
 288     sq = 0;
 289     for (;;) {
 290       if (!MP_RSTEP(&sc))
 291         goto done;
 292       if (MP_RBIT(&sc))
 293         break;
 294       sq++;
 295     }
 296     sq++;
 297     while (sq) {
 298       EC_DBL(c, d, d);
 299       sq--;
 300     }
 301   }
 302
 303 done:
 304   while (sq) {
 305     EC_DBL(c, d, d);
 306     sq--;
 307   }
 308
 309   EC_DESTROY(&g);
 310 exit:
 311   return (EC_OUT(c, d, d));
 312 }
 313
 314 /*----- That's all, folks -------------------------------------------------*/