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

   1 /* -*-c-*-
   2  *
   3  * $Id: f-prime.c,v 1.3.4.3 2004/03/21 22:39:46 mdw Exp $
   4  *
   5  * Prime fields with Montgomery arithmetic
   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: f-prime.c,v $
  33  * Revision 1.3.4.3  2004/03/21 22:39:46  mdw
  34  * Elliptic curves on binary fields work.
  35  *
  36  * Revision 1.3.4.2  2004/03/20 00:13:31  mdw
  37  * Projective coordinates for prime curves
  38  *
  39  * Revision 1.3.4.1  2003/06/10 13:43:53  mdw
  40  * Simple (non-projective) curves over prime fields now seem to work.
  41  *
  42  * Revision 1.3  2003/05/15 23:25:59  mdw
  43  * Make elliptic curve stuff build.
  44  *
  45  * Revision 1.2  2002/01/13 13:48:44  mdw
  46  * Further progress.
  47  *
  48  * Revision 1.1  2001/04/29 18:12:33  mdw
  49  * Prototype version.
  50  *
  51  */
  52
  53 /*----- Header files ------------------------------------------------------*/
  54
  55 #include <mLib/sub.h>
  56
  57 #include "field.h"
  58 #include "mpmont.h"
  59
  60 /*----- Data structures ---------------------------------------------------*/
  61
  62 typedef struct fctx {
  63   field f;
  64   mpmont mm;
  65 } fctx;
  66
  67 /*----- Main code ---------------------------------------------------------*/
  68
  69 /* --- Field operations --- */
  70
  71 static void fdestroy(field *ff)
  72 {
  73   fctx *f = (fctx *)ff;
  74   mpmont_destroy(&f->mm);
  75   DESTROY(f);
  76 }
  77
  78 static mp *fin(field *ff, mp *d, mp *x)
  79 {
  80   fctx *f = (fctx *)ff;
  81   mp_div(0, &d, x, f->mm.m);
  82   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
  83 }
  84
  85 static mp *fout(field *ff, mp *d, mp *x)
  86 {
  87   fctx *f = (fctx *)ff;
  88   return (mpmont_reduce(&f->mm, d, x));
  89 }
  90
  91 static int fzerop(field *ff, mp *x)
  92 {
  93   return (!MP_LEN(x));
  94 }
  95
  96 static mp *fneg(field *ff, mp *d, mp *x)
  97 {
  98   fctx *f = (fctx *)ff;
  99   return (mp_sub(d, f->mm.m, x));
 100 }
 101
 102 static mp *fadd(field *ff, mp *d, mp *x, mp *y)
 103 {
 104   fctx *f = (fctx *)ff;
 105   d = mp_add(d, x, y);
 106   if (d->f & MP_NEG)
 107     d = mp_add(d, d, f->mm.m);
 108   else if (MP_CMP(d, >, f->mm.m))
 109     d = mp_sub(d, d, f->mm.m);
 110   return (d);
 111 }
 112
 113 static mp *fsub(field *ff, mp *d, mp *x, mp *y)
 114 {
 115   fctx *f = (fctx *)ff;
 116   d = mp_sub(d, x, y);
 117   if (d->f & MP_NEG)
 118     d = mp_add(d, d, f->mm.m);
 119   else if (MP_CMP(d, >, f->mm.m))
 120     d = mp_sub(d, d, f->mm.m);
 121   return (d);
 122 }
 123
 124 static mp *fmul(field *ff, mp *d, mp *x, mp *y)
 125 {
 126   fctx *f = (fctx *)ff;
 127   return (mpmont_mul(&f->mm, d, x, y));
 128 }
 129
 130 static mp *fsqr(field *ff, mp *d, mp *x)
 131 {
 132   fctx *f = (fctx *)ff;
 133   d = mp_sqr(d, x);
 134   return (mpmont_reduce(&f->mm, d, d));
 135 }
 136
 137 static mp *finv(field *ff, mp *d, mp *x)
 138 {
 139   fctx *f = (fctx *)ff;
 140   d = mpmont_reduce(&f->mm, d, x);
 141   mp_gcd(0, 0, &d, f->mm.m, d);
 142   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 143 }
 144
 145 static mp *freduce(field *ff, mp *d, mp *x)
 146 {
 147   fctx *f = (fctx *)ff;
 148   mp_div(0, &d, x, f->mm.m);
 149   return (d);
 150 }
 151
 152 static mp *fsqrt(field *ff, mp *d, mp *x)
 153 {
 154   fctx *f = (fctx *)ff;
 155   d = mpmont_reduce(&f->mm, d, x);
 156   d = mp_modsqrt(d, d, f->mm.m);
 157   if (!d)
 158     return (d);
 159   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 160 }
 161
 162 static mp *fdbl(field *ff, mp *d, mp *x)
 163 {
 164   fctx *f = (fctx *)ff;
 165   d = mp_lsl(d, x, 1);
 166   if (MP_CMP(d, >, f->mm.m))
 167     d = mp_sub(d, d, f->mm.m);
 168   return (d);
 169 }
 170
 171 static mp *ftpl(field *ff, mp *d, mp *x)
 172 {
 173   fctx *f = (fctx *)ff;
 174   MP_DEST(d, MP_LEN(x) + 1, x->f);
 175   MPX_UMULN(d->v, d->vl, x->v, x->vl, 3);
 176   while (MP_CMP(d, >, f->mm.m))
 177     d = mp_sub(d, d, f->mm.m);
 178   return (d);
 179 }
 180
 181 static mp *fqdl(field *ff, mp *d, mp *x)
 182 {
 183   fctx *f = (fctx *)ff;
 184   d = mp_lsl(d, x, 2);
 185   while (MP_CMP(d, >, f->mm.m))
 186     d = mp_sub(d, d, f->mm.m);
 187   return (d);
 188 }
 189
 190 static mp *fhlv(field *ff, mp *d, mp *x)
 191 {
 192   fctx *f = (fctx *)ff;
 193   if (!MP_LEN(x)) {
 194     MP_COPY(x);
 195     MP_DROP(d);
 196     return (x);
 197   }
 198   if (x->v[0] & 1) {
 199     d = mp_add(d, x, f->mm.m);
 200     x = d;
 201   }
 202   return (mp_lsr(d, x, 1));
 203 }
 204
 205 /* --- Field operations table --- */
 206
 207 static field_ops fops = {
 208   fdestroy,
 209   fin, fout,
 210   fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
 211   0,
 212   fdbl, ftpl, fqdl, fhlv
 213 };
 214
 215 /* --- @field_prime@ --- *
 216  *
 217  * Arguments:   @mp *p@ = the characteristic of the field
 218  *
 219  * Returns:     A pointer to the field.
 220  *
 221  * Use:         Creates a field structure for a prime field of size %$p$%,
 222  *              using Montgomery reduction for arithmetic.
 223  */
 224
 225 field *field_prime(mp *p)
 226 {
 227   fctx *f = CREATE(fctx);
 228   f->f.ops = &fops;
 229   mpmont_create(&f->mm, p);
 230   f->f.zero = MP_ZERO;
 231   f->f.one = f->mm.r;
 232   return (&f->f);
 233 }
 234
 235 /*----- That's all, folks -------------------------------------------------*/