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

   1 /* -*-c-*-
   2  *
   3  * $Id: f-prime.c,v 1.4 2004/03/21 22:52:06 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 1.4  2004/03/21 22:52:06  mdw
  34  * Merge and close elliptic curve branch.
  35  *
  36  * Revision 1.3.4.3  2004/03/21 22:39:46  mdw
  37  * Elliptic curves on binary fields work.
  38  *
  39  * Revision 1.3.4.2  2004/03/20 00:13:31  mdw
  40  * Projective coordinates for prime curves
  41  *
  42  * Revision 1.3.4.1  2003/06/10 13:43:53  mdw
  43  * Simple (non-projective) curves over prime fields now seem to work.
  44  *
  45  * Revision 1.3  2003/05/15 23:25:59  mdw
  46  * Make elliptic curve stuff build.
  47  *
  48  * Revision 1.2  2002/01/13 13:48:44  mdw
  49  * Further progress.
  50  *
  51  * Revision 1.1  2001/04/29 18:12:33  mdw
  52  * Prototype version.
  53  *
  54  */
  55
  56 /*----- Header files ------------------------------------------------------*/
  57
  58 #include <mLib/sub.h>
  59
  60 #include "field.h"
  61 #include "mpmont.h"
  62
  63 /*----- Data structures ---------------------------------------------------*/
  64
  65 typedef struct fctx {
  66   field f;
  67   mpmont mm;
  68 } fctx;
  69
  70 /*----- Main code ---------------------------------------------------------*/
  71
  72 /* --- Field operations --- */
  73
  74 static void fdestroy(field *ff)
  75 {
  76   fctx *f = (fctx *)ff;
  77   mpmont_destroy(&f->mm);
  78   DESTROY(f);
  79 }
  80
  81 static mp *fin(field *ff, mp *d, mp *x)
  82 {
  83   fctx *f = (fctx *)ff;
  84   mp_div(0, &d, x, f->mm.m);
  85   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
  86 }
  87
  88 static mp *fout(field *ff, mp *d, mp *x)
  89 {
  90   fctx *f = (fctx *)ff;
  91   return (mpmont_reduce(&f->mm, d, x));
  92 }
  93
  94 static int fzerop(field *ff, mp *x)
  95 {
  96   return (!MP_LEN(x));
  97 }
  98
  99 static mp *fneg(field *ff, mp *d, mp *x)
 100 {
 101   fctx *f = (fctx *)ff;
 102   return (mp_sub(d, f->mm.m, x));
 103 }
 104
 105 static mp *fadd(field *ff, mp *d, mp *x, mp *y)
 106 {
 107   fctx *f = (fctx *)ff;
 108   d = mp_add(d, x, y);
 109   if (d->f & MP_NEG)
 110     d = mp_add(d, d, f->mm.m);
 111   else if (MP_CMP(d, >, f->mm.m))
 112     d = mp_sub(d, d, f->mm.m);
 113   return (d);
 114 }
 115
 116 static mp *fsub(field *ff, mp *d, mp *x, mp *y)
 117 {
 118   fctx *f = (fctx *)ff;
 119   d = mp_sub(d, x, y);
 120   if (d->f & MP_NEG)
 121     d = mp_add(d, d, f->mm.m);
 122   else if (MP_CMP(d, >, f->mm.m))
 123     d = mp_sub(d, d, f->mm.m);
 124   return (d);
 125 }
 126
 127 static mp *fmul(field *ff, mp *d, mp *x, mp *y)
 128 {
 129   fctx *f = (fctx *)ff;
 130   return (mpmont_mul(&f->mm, d, x, y));
 131 }
 132
 133 static mp *fsqr(field *ff, mp *d, mp *x)
 134 {
 135   fctx *f = (fctx *)ff;
 136   d = mp_sqr(d, x);
 137   return (mpmont_reduce(&f->mm, d, d));
 138 }
 139
 140 static mp *finv(field *ff, mp *d, mp *x)
 141 {
 142   fctx *f = (fctx *)ff;
 143   d = mpmont_reduce(&f->mm, d, x);
 144   mp_gcd(0, 0, &d, f->mm.m, d);
 145   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 146 }
 147
 148 static mp *freduce(field *ff, mp *d, mp *x)
 149 {
 150   fctx *f = (fctx *)ff;
 151   mp_div(0, &d, x, f->mm.m);
 152   return (d);
 153 }
 154
 155 static mp *fsqrt(field *ff, mp *d, mp *x)
 156 {
 157   fctx *f = (fctx *)ff;
 158   d = mpmont_reduce(&f->mm, d, x);
 159   d = mp_modsqrt(d, d, f->mm.m);
 160   if (!d)
 161     return (d);
 162   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 163 }
 164
 165 static mp *fdbl(field *ff, mp *d, mp *x)
 166 {
 167   fctx *f = (fctx *)ff;
 168   d = mp_lsl(d, x, 1);
 169   if (MP_CMP(d, >, f->mm.m))
 170     d = mp_sub(d, d, f->mm.m);
 171   return (d);
 172 }
 173
 174 static mp *ftpl(field *ff, mp *d, mp *x)
 175 {
 176   fctx *f = (fctx *)ff;
 177   MP_DEST(d, MP_LEN(x) + 1, x->f);
 178   MPX_UMULN(d->v, d->vl, x->v, x->vl, 3);
 179   while (MP_CMP(d, >, f->mm.m))
 180     d = mp_sub(d, d, f->mm.m);
 181   return (d);
 182 }
 183
 184 static mp *fqdl(field *ff, mp *d, mp *x)
 185 {
 186   fctx *f = (fctx *)ff;
 187   d = mp_lsl(d, x, 2);
 188   while (MP_CMP(d, >, f->mm.m))
 189     d = mp_sub(d, d, f->mm.m);
 190   return (d);
 191 }
 192
 193 static mp *fhlv(field *ff, mp *d, mp *x)
 194 {
 195   fctx *f = (fctx *)ff;
 196   if (!MP_LEN(x)) {
 197     MP_COPY(x);
 198     MP_DROP(d);
 199     return (x);
 200   }
 201   if (x->v[0] & 1) {
 202     d = mp_add(d, x, f->mm.m);
 203     x = d;
 204   }
 205   return (mp_lsr(d, x, 1));
 206 }
 207
 208 /* --- Field operations table --- */
 209
 210 static field_ops fops = {
 211   fdestroy,
 212   fin, fout,
 213   fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
 214   0,
 215   fdbl, ftpl, fqdl, fhlv
 216 };
 217
 218 /* --- @field_prime@ --- *
 219  *
 220  * Arguments:   @mp *p@ = the characteristic of the field
 221  *
 222  * Returns:     A pointer to the field.
 223  *
 224  * Use:         Creates a field structure for a prime field of size %$p$%,
 225  *              using Montgomery reduction for arithmetic.
 226  */
 227
 228 field *field_prime(mp *p)
 229 {
 230   fctx *f = CREATE(fctx);
 231   f->f.ops = &fops;
 232   mpmont_create(&f->mm, p);
 233   f->f.zero = MP_ZERO;
 234   f->f.one = f->mm.r;
 235   return (&f->f);
 236 }
 237
 238 /*----- That's all, folks -------------------------------------------------*/