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

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