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

   1 /* -*-c-*-
   2  *
   3  * $Id: f-prime.c,v 1.11 2004/04/03 03:32:05 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 1.11  2004/04/03 03:32:05  mdw
  34  * General robustification.
  35  *
  36  * Revision 1.10  2004/04/02 01:03:49  mdw
  37  * Miscellaneous constification.
  38  *
  39  * Revision 1.9  2004/04/01 21:28:41  mdw
  40  * Normal basis support (translates to poly basis internally).  Rewrite
  41  * EC and prime group table generators in awk, so that they can reuse data
  42  * for repeated constants.
  43  *
  44  * Revision 1.8  2004/04/01 12:50:09  mdw
  45  * Add cyclic group abstraction, with test code.  Separate off exponentation
  46  * functions for better static linking.  Fix a buttload of bugs on the way.
  47  * Generally ensure that negative exponents do inversion correctly.  Add
  48  * table of standard prime-field subgroups.  (Binary field subgroups are
  49  * currently unimplemented but easy to add if anyone ever finds a good one.)
  50  *
  51  * Revision 1.7  2004/03/27 17:54:11  mdw
  52  * Standard curves and curve checking.
  53  *
  54  * Revision 1.6  2004/03/23 15:19:32  mdw
  55  * Test elliptic curves more thoroughly.
  56  *
  57  * Revision 1.5  2004/03/23 12:08:26  mdw
  58  * Random field-element selection.
  59  *
  60  * Revision 1.4  2004/03/21 22:52:06  mdw
  61  * Merge and close elliptic curve branch.
  62  *
  63  * Revision 1.3.4.3  2004/03/21 22:39:46  mdw
  64  * Elliptic curves on binary fields work.
  65  *
  66  * Revision 1.3.4.2  2004/03/20 00:13:31  mdw
  67  * Projective coordinates for prime curves
  68  *
  69  * Revision 1.3.4.1  2003/06/10 13:43:53  mdw
  70  * Simple (non-projective) curves over prime fields now seem to work.
  71  *
  72  * Revision 1.3  2003/05/15 23:25:59  mdw
  73  * Make elliptic curve stuff build.
  74  *
  75  * Revision 1.2  2002/01/13 13:48:44  mdw
  76  * Further progress.
  77  *
  78  * Revision 1.1  2001/04/29 18:12:33  mdw
  79  * Prototype version.
  80  *
  81  */
  82
  83 /*----- Header files ------------------------------------------------------*/
  84
  85 #include <mLib/sub.h>
  86
  87 #include "field.h"
  88 #include "mpmont.h"
  89 #include "mprand.h"
  90
  91 /*----- Main code ---------------------------------------------------------*/
  92
  93 typedef struct fctx {
  94   field f;
  95   mpmont mm;
  96 } fctx;
  97
  98 /* --- Field operations --- */
  99
 100 static void fdestroy(field *ff)
 101   { fctx *f = (fctx *)ff; mpmont_destroy(&f->mm); DESTROY(f); }
 102
 103 static mp *frand(field *ff, mp *d, grand *r)
 104   { fctx *f = (fctx *)ff; return (mprand_range(d, f->mm.m, r, 0)); }
 105
 106 static mp *fin(field *ff, mp *d, mp *x) {
 107   fctx *f = (fctx *)ff;
 108   mp_div(0, &d, x, f->mm.m);
 109   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 110 }
 111
 112 static mp *fout(field *ff, mp *d, mp *x)
 113   { fctx *f = (fctx *)ff; return (mpmont_reduce(&f->mm, d, x)); }
 114
 115 static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); }
 116
 117 static mp *fneg(field *ff, mp *d, mp *x)
 118   { fctx *f = (fctx *)ff; return (mp_sub(d, f->mm.m, x)); }
 119
 120 static mp *fadd(field *ff, mp *d, mp *x, mp *y) {
 121   fctx *f = (fctx *)ff; d = mp_add(d, x, y);
 122   if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m);
 123   else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 124   return (d);
 125 }
 126
 127 static mp *fsub(field *ff, mp *d, mp *x, mp *y) {
 128   fctx *f = (fctx *)ff; d = mp_sub(d, x, y);
 129   if (d->f & MP_NEG) d = mp_add(d, d, f->mm.m);
 130   else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 131   return (d);
 132 }
 133
 134 static mp *fmul(field *ff, mp *d, mp *x, mp *y)
 135   { fctx *f = (fctx *)ff; return (mpmont_mul(&f->mm, d, x, y)); }
 136
 137 static mp *fsqr(field *ff, mp *d, mp *x) {
 138   fctx *f = (fctx *)ff; d = mp_sqr(d, x);
 139   return (mpmont_reduce(&f->mm, d, d));
 140 }
 141
 142 static mp *finv(field *ff, mp *d, mp *x) {
 143   fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x);
 144   mp_gcd(0, 0, &d, f->mm.m, d); return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 145 }
 146
 147 static mp *freduce(field *ff, mp *d, mp *x)
 148   { fctx *f = (fctx *)ff; mp_div(0, &d, x, f->mm.m); return (d); }
 149
 150 static mp *fsqrt(field *ff, mp *d, mp *x) {
 151   fctx *f = (fctx *)ff; d = mpmont_reduce(&f->mm, d, x);
 152   d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d);
 153   return (mpmont_mul(&f->mm, d, d, f->mm.r2));
 154 }
 155
 156 static mp *fdbl(field *ff, mp *d, mp *x) {
 157   fctx *f = (fctx *)ff; d = mp_lsl(d, x, 1);
 158   if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 159   return (d);
 160 }
 161
 162 static mp *ftpl(field *ff, mp *d, mp *x) {
 163   fctx *f = (fctx *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f);
 164   MPX_UMULN(d->v, d->vl, x->v, x->vl, 3);
 165   while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 166   return (d);
 167 }
 168
 169 static mp *fqdl(field *ff, mp *d, mp *x) {
 170   fctx *f = (fctx *)ff; d = mp_lsl(d, x, 2);
 171   while (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
 172   return (d);
 173 }
 174
 175 static mp *fhlv(field *ff, mp *d, mp *x) {
 176   fctx *f = (fctx *)ff;
 177   if (!MP_LEN(x)) { MP_COPY(x); MP_DROP(d); return (x); }
 178   if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; }
 179   return (mp_lsr(d, x, 1));
 180 }
 181
 182 /* --- Field operations table --- */
 183
 184 static const field_ops fops = {
 185   FTY_PRIME, "prime",
 186   fdestroy, frand, field_stdsamep,
 187   fin, fout,
 188   fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
 189   0,
 190   fdbl, ftpl, fqdl, fhlv
 191 };
 192
 193 /* --- @field_prime@ --- *
 194  *
 195  * Arguments:   @mp *p@ = the characteristic of the field
 196  *
 197  * Returns:     A pointer to the field or null.
 198  *
 199  * Use:         Creates a field structure for a prime field of size %$p$%,
 200  *              using Montgomery reduction for arithmetic.
 201  */
 202
 203 field *field_prime(mp *p)
 204 {
 205   fctx *f;
 206
 207   if (!MP_ISPOS(p) || !MP_ISODD(p))
 208     return (0);
 209   f = CREATE(fctx);
 210   f->f.ops = &fops;
 211   mpmont_create(&f->mm, p);
 212   f->f.zero = MP_ZERO;
 213   f->f.one = f->mm.r;
 214   f->f.m = f->mm.m;
 215   f->f.nbits = mp_bits(p);
 216   f->f.noctets = (f->f.nbits + 7) >> 3;
 217   return (&f->f);
 218 }
 219
 220 /*----- That's all, folks -------------------------------------------------*/