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

   1 /* -*-c-*-
   2  *
   3  * $Id: f-binpoly.c,v 1.8 2004/04/02 01:03:49 mdw Exp $
   4  *
   5  * Binary fields with polynomial basis representation
   6  *
   7  * (c) 2004 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-binpoly.c,v $
  33  * Revision 1.8  2004/04/02 01:03:49  mdw
  34  * Miscellaneous constification.
  35  *
  36  * Revision 1.7  2004/04/01 21:28:41  mdw
  37  * Normal basis support (translates to poly basis internally).  Rewrite
  38  * EC and prime group table generators in awk, so that they can reuse data
  39  * for repeated constants.
  40  *
  41  * Revision 1.6  2004/04/01 12:50:09  mdw
  42  * Add cyclic group abstraction, with test code.  Separate off exponentation
  43  * functions for better static linking.  Fix a buttload of bugs on the way.
  44  * Generally ensure that negative exponents do inversion correctly.  Add
  45  * table of standard prime-field subgroups.  (Binary field subgroups are
  46  * currently unimplemented but easy to add if anyone ever finds a good one.)
  47  *
  48  * Revision 1.5  2004/03/27 17:54:11  mdw
  49  * Standard curves and curve checking.
  50  *
  51  * Revision 1.4  2004/03/23 15:19:32  mdw
  52  * Test elliptic curves more thoroughly.
  53  *
  54  * Revision 1.3  2004/03/23 12:08:26  mdw
  55  * Random field-element selection.
  56  *
  57  * Revision 1.2  2004/03/21 22:52:06  mdw
  58  * Merge and close elliptic curve branch.
  59  *
  60  * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
  61  * Elliptic curves on binary fields work.
  62  *
  63  */
  64
  65 /*----- Header files ------------------------------------------------------*/
  66
  67 #include <mLib/sub.h>
  68
  69 #include "field.h"
  70 #include "gf.h"
  71 #include "gfreduce.h"
  72 #include "mprand.h"
  73 #include "gfn.h"
  74
  75 /*----- Polynomial basis --------------------------------------------------*/
  76
  77 typedef struct fctx {
  78   field f;
  79   gfreduce r;
  80 } fctx;
  81
  82 /* --- Field operations --- */
  83
  84 static void fdestroy(field *ff)
  85   { fctx *f = (fctx *)ff; gfreduce_destroy(&f->r); DESTROY(f); }
  86
  87 static mp *frand(field *f, mp *d, grand *r)
  88   { return (mprand(d, f->nbits, r, 0)); }
  89
  90 static int fzerop(field *ff, mp *x) { return (!MP_LEN(x)); }
  91
  92 static mp *fadd(field *ff, mp *d, mp *x, mp *y) { return (gf_add(d, x, y)); }
  93
  94 static mp *fmul(field *ff, mp *d, mp *x, mp *y) {
  95   fctx *f = (fctx *)ff; d = gf_mul(d, x, y);
  96   return (gfreduce_do(&f->r, d, d));
  97 }
  98
  99 static mp *fsqr(field *ff, mp *d, mp *x) {
 100   fctx *f = (fctx *)ff; d = gf_sqr(d, x);
 101   return (gfreduce_do(&f->r, d, d));
 102 }
 103
 104 static mp *finv(field *ff, mp *d, mp *x)
 105   { fctx *f = (fctx *)ff; gf_gcd(0, 0, &d, f->r.p, x); return (d); }
 106
 107 static mp *freduce(field *ff, mp *d, mp *x)
 108   { fctx *f = (fctx *)ff; return (gfreduce_do(&f->r, d, x)); }
 109
 110 static mp *fsqrt(field *ff, mp *d, mp *x)
 111   { fctx *f = (fctx *)ff; return (gfreduce_sqrt(&f->r, d, x)); }
 112
 113 static mp *fquadsolve(field *ff, mp *d, mp *x)
 114   { fctx *f = (fctx *)ff; return (gfreduce_quadsolve(&f->r, d, x)); }
 115
 116 /* --- Field operations table --- */
 117
 118 static const field_ops fops = {
 119   FTY_BINARY, "binpoly",
 120   fdestroy, frand, field_stdsamep,
 121   freduce, field_id,
 122   fzerop, field_id, fadd, fadd, fmul, fsqr, finv, freduce, fsqrt,
 123   fquadsolve,
 124   0, 0, 0, 0
 125 };
 126
 127 /* --- @field_binpoly@ --- *
 128  *
 129  * Arguments:   @mp *p@ = the reduction polynomial
 130  *
 131  * Returns:     A pointer to the field.
 132  *
 133  * Use:         Creates a field structure for a binary field mod @p@.
 134  */
 135
 136 field *field_binpoly(mp *p)
 137 {
 138   fctx *f = CREATE(fctx);
 139   f->f.ops = &fops;
 140   f->f.zero = MP_ZERO;
 141   f->f.one = MP_ONE;
 142   f->f.nbits = mp_bits(p) - 1;
 143   f->f.noctets = (f->f.nbits + 7) >> 3;
 144   gfreduce_create(&f->r, p);
 145   f->f.m = f->r.p;
 146   return (&f->f);
 147 }
 148
 149 /*----- Normal basis ------------------------------------------------------*/
 150
 151 typedef struct fnctx {
 152   fctx f;
 153   gfn ntop, pton;
 154 } fnctx;
 155
 156 /* --- Field operations --- */
 157
 158 static void fndestroy(field *ff) {
 159   fnctx *f = (fnctx *)ff; gfreduce_destroy(&f->f.r);
 160   gfn_destroy(&f->ntop); gfn_destroy(&f->pton);
 161   DESTROY(f);
 162 }
 163
 164 static int fnsamep(field *ff, field *gg) {
 165   fnctx *f = (fnctx *)ff, *g = (fnctx *)gg;
 166   return (MP_EQ(f->ntop.r[0], g->ntop.r[0]) && field_stdsamep(ff, gg));
 167 }
 168
 169 static mp *fnin(field *ff, mp *d, mp *x)
 170   { fnctx *f = (fnctx *)ff; return (gfn_transform(&f->ntop, d, x)); }
 171
 172 static mp *fnout(field *ff, mp *d, mp *x)
 173   { fnctx *f = (fnctx *)ff; return (gfn_transform(&f->pton, d, x)); }
 174
 175 /* --- Field operations table --- */
 176
 177 static const field_ops fnops = {
 178   FTY_BINARY, "binnorm",
 179   fndestroy, frand, fnsamep,
 180   fnin, fnout,
 181   fzerop, field_id, fadd, fadd, fmul, fsqr, finv, freduce, fsqrt,
 182   fquadsolve,
 183   0, 0, 0, 0
 184 };
 185
 186 /* --- @field_binnorm@ --- *
 187  *
 188  * Arguments:   @mp *p@ = the reduction polynomial
 189  *              @mp *beta@ = representation of normal point
 190  *
 191  * Returns:     A pointer to the field.
 192  *
 193  * Use:         Creates a field structure for a binary field mod @p@ which
 194  *              uses a normal basis representation externally.  Computations
 195  *              are still done on a polynomial-basis representation.
 196  */
 197
 198 field *field_binnorm(mp *p, mp *beta)
 199 {
 200   fnctx *f = CREATE(fnctx);
 201   f->f.f.ops = &fnops;
 202   f->f.f.zero = MP_ZERO;
 203   f->f.f.one = MP_ONE;
 204   f->f.f.nbits = mp_bits(p) - 1;
 205   f->f.f.noctets = (f->f.f.nbits + 7) >> 3;
 206   gfreduce_create(&f->f.r, p);
 207   f->f.f.m = f->f.r.p;
 208   gfn_create(p, beta, &f->ntop, &f->pton);
 209   return (&f->f.f);
 210 }
 211
 212 /*----- That's all, folks -------------------------------------------------*/