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

   1 /* -*-c-*-
   2  *
   3  * $Id: f-prime.c,v 1.5 2004/03/23 12:08:26 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 1.5  2004/03/23 12:08:26  mdw
  34  * Random field-element selection.
  35  *
  36  * Revision 1.4  2004/03/21 22:52:06  mdw
  37  * Merge and close elliptic curve branch.
  38  *
  39  * Revision 1.3.4.3  2004/03/21 22:39:46  mdw
  40  * Elliptic curves on binary fields work.
  41  *
  42  * Revision 1.3.4.2  2004/03/20 00:13:31  mdw
  43  * Projective coordinates for prime curves
  44  *
  45  * Revision 1.3.4.1  2003/06/10 13:43:53  mdw
  46  * Simple (non-projective) curves over prime fields now seem to work.
  47  *
  48  * Revision 1.3  2003/05/15 23:25:59  mdw
  49  * Make elliptic curve stuff build.
  50  *
  51  * Revision 1.2  2002/01/13 13:48:44  mdw
  52  * Further progress.
  53  *
  54  * Revision 1.1  2001/04/29 18:12:33  mdw
  55  * Prototype version.
  56  *
  57  */
  58
  59 /*----- Header files ------------------------------------------------------*/
  60
  61 #include <mLib/sub.h>
  62
  63 #include "field.h"
  64 #include "mpmont.h"
  65 #include "mprand.h"
  66
  67 /*----- Data structures ---------------------------------------------------*/
  68
  69 typedef struct fctx {
  70   field f;
  71   mpmont mm;
  72 } fctx;
  73
  74 /*----- Main code ---------------------------------------------------------*/
  75
  76 /* --- Field operations --- */
  77
  78 static void fdestroy(field *ff)
  79 {
  80   fctx *f = (fctx *)ff;
  81   mpmont_destroy(&f->mm);
  82   DESTROY(f);
  83 }
  84
  85 static mp *frand(field *ff, mp *d, grand *r)
  86 {
  87   fctx *f = (fctx *)ff;
  88   return (mprand_range(d, f->mm.m, r, 0));
  89 }
  90
  91 static mp *fin(field *ff, mp *d, mp *x)
  92 {
  93   fctx *f = (fctx *)ff;
  94   mp_div(0, &d, x, f->mm.m);
  95   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
  96 }
  97
  98 static mp *fout(field *ff, mp *d, mp *x)
  99 {
 100   fctx *f = (fctx *)ff;
 101   return (mpmont_reduce(&f->mm, d, x));
 102 }
 103
 104 static int fzerop(field *ff, mp *x)
 105 {
 106   return (!MP_LEN(x));
 107 }
 108
 109 static mp *fneg(field *ff, mp *d, mp *x)
 110 {
 111   fctx *f = (fctx *)ff;
 112   return (mp_sub(d, f->mm.m, x));
 113 }
 114
 115 static mp *fadd(field *ff, mp *d, mp *x, mp *y)
 116 {
 117   fctx *f = (fctx *)ff;
 118   d = mp_add(d, x, y);
 119   if (d->f & MP_NEG)
 120     d = mp_add(d, d, f->mm.m);
 121   else if (MP_CMP(d, >, f->mm.m))
 122     d = mp_sub(d, d, f->mm.m);
 123   return (d);
 124 }
 125
 126 static mp *fsub(field *ff, mp *d, mp *x, mp *y)
 127 {
 128   fctx *f = (fctx *)ff;
 129   d = mp_sub(d, x, y);
 130   if (d->f & MP_NEG)
 131     d = mp_add(d, d, f->mm.m);
 132   else if (MP_CMP(d, >, f->mm.m))
 133     d = mp_sub(d, d, f->mm.m);
 134   return (d);
 135 }
 136
 137 static mp *fmul(field *ff, mp *d, mp *x, mp *y)
 138 {
 139   fctx *f = (fctx *)ff;
 140   return (mpmont_mul(&f->mm, d, x, y));
 141 }
 142
 143 static mp *fsqr(field *ff, mp *d, mp *x)
 144 {
 145   fctx *f = (fctx *)ff;
 146   d = mp_sqr(d, x);
 147   return (mpmont_reduce(&f->mm, d, d));
 148 }
 149
 150 static mp *finv(field *ff, mp *d, mp *x)
 151 {
 152   fctx *f = (fctx *)ff;
 153   d = mpmont_reduce(&f->mm, d, x);
 154   mp_gcd(0, 0, &d, f->mm.m, d);
 155   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 156 }
 157
 158 static mp *freduce(field *ff, mp *d, mp *x)
 159 {
 160   fctx *f = (fctx *)ff;
 161   mp_div(0, &d, x, f->mm.m);
 162   return (d);
 163 }
 164
 165 static mp *fsqrt(field *ff, mp *d, mp *x)
 166 {
 167   fctx *f = (fctx *)ff;
 168   d = mpmont_reduce(&f->mm, d, x);
 169   d = mp_modsqrt(d, d, f->mm.m);
 170   if (!d)
 171     return (d);
 172   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 173 }
 174
 175 static mp *fdbl(field *ff, mp *d, mp *x)
 176 {
 177   fctx *f = (fctx *)ff;
 178   d = mp_lsl(d, x, 1);
 179   if (MP_CMP(d, >, f->mm.m))
 180     d = mp_sub(d, d, f->mm.m);
 181   return (d);
 182 }
 183
 184 static mp *ftpl(field *ff, mp *d, mp *x)
 185 {
 186   fctx *f = (fctx *)ff;
 187   MP_DEST(d, MP_LEN(x) + 1, x->f);
 188   MPX_UMULN(d->v, d->vl, x->v, x->vl, 3);
 189   while (MP_CMP(d, >, f->mm.m))
 190     d = mp_sub(d, d, f->mm.m);
 191   return (d);
 192 }
 193
 194 static mp *fqdl(field *ff, mp *d, mp *x)
 195 {
 196   fctx *f = (fctx *)ff;
 197   d = mp_lsl(d, x, 2);
 198   while (MP_CMP(d, >, f->mm.m))
 199     d = mp_sub(d, d, f->mm.m);
 200   return (d);
 201 }
 202
 203 static mp *fhlv(field *ff, mp *d, mp *x)
 204 {
 205   fctx *f = (fctx *)ff;
 206   if (!MP_LEN(x)) {
 207     MP_COPY(x);
 208     MP_DROP(d);
 209     return (x);
 210   }
 211   if (x->v[0] & 1) {
 212     d = mp_add(d, x, f->mm.m);
 213     x = d;
 214   }
 215   return (mp_lsr(d, x, 1));
 216 }
 217
 218 /* --- Field operations table --- */
 219
 220 static field_ops fops = {
 221   fdestroy, frand,
 222   fin, fout,
 223   fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
 224   0,
 225   fdbl, ftpl, fqdl, fhlv
 226 };
 227
 228 /* --- @field_prime@ --- *
 229  *
 230  * Arguments:   @mp *p@ = the characteristic of the field
 231  *
 232  * Returns:     A pointer to the field.
 233  *
 234  * Use:         Creates a field structure for a prime field of size %$p$%,
 235  *              using Montgomery reduction for arithmetic.
 236  */
 237
 238 field *field_prime(mp *p)
 239 {
 240   fctx *f = CREATE(fctx);
 241   f->f.ops = &fops;
 242   mpmont_create(&f->mm, p);
 243   f->f.zero = MP_ZERO;
 244   f->f.one = f->mm.r;
 245   return (&f->f);
 246 }
 247
 248 /*----- That's all, folks -------------------------------------------------*/