git.distorted.org.uk Git - u/mdw/catacomb/blob - field.h

   1 /* -*-c-*-
   2  *
   3  * $Id: field.h,v 1.9 2004/04/01 12:50:09 mdw Exp $
   4  *
   5  * Definitions for field arithmetic
   6  *
   7  * (c) 2000 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: field.h,v $
  33  * Revision 1.9  2004/04/01 12:50:09  mdw
  34  * Add cyclic group abstraction, with test code.  Separate off exponentation
  35  * functions for better static linking.  Fix a buttload of bugs on the way.
  36  * Generally ensure that negative exponents do inversion correctly.  Add
  37  * table of standard prime-field subgroups.  (Binary field subgroups are
  38  * currently unimplemented but easy to add if anyone ever finds a good one.)
  39  *
  40  * Revision 1.8  2004/03/27 17:54:11  mdw
  41  * Standard curves and curve checking.
  42  *
  43  * Revision 1.7  2004/03/27 00:04:46  mdw
  44  * Implement efficient reduction for pleasant-looking primes.
  45  *
  46  * Revision 1.6  2004/03/23 15:19:32  mdw
  47  * Test elliptic curves more thoroughly.
  48  *
  49  * Revision 1.5  2004/03/23 12:08:26  mdw
  50  * Random field-element selection.
  51  *
  52  * Revision 1.4  2004/03/21 22:52:06  mdw
  53  * Merge and close elliptic curve branch.
  54  *
  55  * Revision 1.3.4.2  2004/03/21 22:39:46  mdw
  56  * Elliptic curves on binary fields work.
  57  *
  58  * Revision 1.3.4.1  2004/03/20 00:13:31  mdw
  59  * Projective coordinates for prime curves
  60  *
  61  * Revision 1.3  2002/01/13 13:48:44  mdw
  62  * Further progress.
  63  *
  64  * Revision 1.2  2001/05/07 17:30:13  mdw
  65  * Add an internal-representation no-op function.
  66  *
  67  * Revision 1.1  2001/04/29 18:12:33  mdw
  68  * Prototype version.
  69  *
  70  */
  71
  72 #ifndef CATACOMB_FIELD_H
  73 #define CATACOMB_FIELD_H
  74
  75 #ifdef __cplusplus
  76   extern "C" {
  77 #endif
  78
  79 /*----- Header files ------------------------------------------------------*/
  80
  81 #ifndef CATACOMB_GRAND_H
  82 #  include "grand.h"
  83 #endif
  84
  85 #ifndef CATACOMB_MP_H
  86 #  include "mp.h"
  87 #endif
  88
  89 #ifndef CATACOMB_QDPARSE_H
  90 #  include "qdparse.h"
  91 #endif
  92
  93 /*----- Data structures ---------------------------------------------------*/
  94
  95 typedef struct field {
  96   const struct field_ops *ops;          /* Field operations */
  97   mp *zero, *one;                       /* Identities in the field */
  98   mp *m;                                /* Modulus (prime and binary) */
  99   unsigned long nbits;                  /* Length of field element in bits */
 100   size_t noctets;                       /* Length of element in octets */
 101 } field;
 102
 103 enum {
 104   FTY_PRIME,
 105   FTY_BINARY
 106 };
 107
 108 typedef struct field_ops {
 109
 110   /* --- General information --- */
 111
 112   unsigned ty;                          /* What kind of field this is */
 113   const char *name;                     /* Human-readable name string */
 114
 115   /* --- Universal operations --- */
 116
 117   void (*destroy)(field */*f*/);
 118   mp *(*rand)(field */*f*/, mp */*d*/, grand */*r*/);
 119   int (*samep)(field */*f*/, field */*g*/);
 120
 121   mp *(*in)(field */*f*/, mp */*d*/, mp */*x*/);
 122   mp *(*out)(field */*f*/, mp */*d*/, mp */*x*/);
 123
 124   int (*zerop)(field */*f*/, mp */*x*/);
 125   mp *(*neg)(field */*f*/, mp */*d*/, mp */*x*/);
 126   mp *(*add)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/);
 127   mp *(*sub)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/);
 128   mp *(*mul)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/);
 129   mp *(*sqr)(field */*f*/, mp */*d*/, mp */*x*/);
 130   mp *(*inv)(field */*f*/, mp */*d*/, mp */*x*/);
 131   mp *(*reduce)(field */*f*/, mp */*d*/, mp */*x*/);
 132   mp *(*sqrt)(field */*f*/, mp */*d*/, mp */*x*/);
 133
 134   /* --- Operations for binary fields only --- */
 135
 136   mp *(*quadsolve)(field */*f*/, mp */*d*/, mp */*x*/);
 137
 138   /* --- Operations for prime fields only --- */
 139
 140   mp *(*dbl)(field */*f*/, mp */*d*/, mp */*x*/);
 141   mp *(*tpl)(field */*f*/, mp */*d*/, mp */*x*/);
 142   mp *(*qdl)(field */*f*/, mp */*d*/, mp */*x*/);
 143   mp *(*hlv)(field */*f*/, mp */*d*/, mp */*x*/);
 144
 145 } field_ops;
 146
 147 #define F_TYPE(f)               (f)->ops->ty
 148 #define F_NAME(f)               (f)->ops->name
 149
 150 #define F_DESTROY(f)            (f)->ops->destroy((f))
 151 #define F_RAND(f, d, r)         (f)->ops->rand((f), (d), (r))
 152 #define F_SAMEP(f, g)           (f)->ops->samep((f), (g))
 153
 154 #define F_IN(f, d, x)           (f)->ops->in((f), (d), (x))
 155 #define F_OUT(f, d, x)          (f)->ops->out((f), (d), (x))
 156
 157 #define F_ZEROP(f, x)           (f)->ops->zerop((f), (x))
 158 #define F_NEG(f, d, x)          (f)->ops->neg((f), (d), (x))
 159 #define F_ADD(f, d, x, y)       (f)->ops->add((f), (d), (x), (y))
 160 #define F_SUB(f, d, x, y)       (f)->ops->sub((f), (d), (x), (y))
 161 #define F_MUL(f, d, x, y)       (f)->ops->mul((f), (d), (x), (y))
 162 #define F_SQR(f, d, x)          (f)->ops->sqr((f), (d), (x))
 163 #define F_INV(f, d, x)          (f)->ops->inv((f), (d), (x))
 164 #define F_REDUCE(f, d, x)       (f)->ops->reduce((f), (d), (x))
 165 #define F_SQRT(f, d, x)         (f)->ops->sqrt((f), (d), (x))
 166
 167 #define F_QUADSOLVE(f, d, x)    (f)->ops->quadsolve((f), (d), (x))
 168
 169 #define F_DBL(f, d, x)          (f)->ops->dbl((f), (d), (x))
 170 #define F_TPL(f, d, x)          (f)->ops->tpl((f), (d), (x))
 171 #define F_QDL(f, d, x)          (f)->ops->qdl((f), (d), (x))
 172 #define F_HLV(f, d, x)          (f)->ops->hlv((f), (d), (x))
 173
 174 /*----- Helpful field operations ------------------------------------------*/
 175
 176 /* --- @field_id@ --- *
 177  *
 178  * Arguments:   @field *f@ = pointer to a field
 179  *              @mp *d@ = a destination element
 180  *              @mp *x@ = a source element
 181  *
 182  * Returns:     The result element.
 183  *
 184  * Use:         An identity operation which can be used if your field has no
 185  *              internal representation.
 186  */
 187
 188 extern mp *field_id(field */*f*/, mp */*d*/, mp */*x*/);
 189
 190 /* --- @field_samep@ --- *
 191  *
 192  * Arguments:   @field *f, *g@ = two fields
 193  *
 194  * Returns:     Nonzero if the fields are identical (not just isomorphic).
 195  *
 196  * Use:         Checks for sameness of fields.  This function does the full
 197  *              check, not just the field-type-specific check done by the
 198  *              @sampep@ field operation.
 199  */
 200
 201 extern int field_samep(field */*f*/, field */*g*/);
 202
 203 /* --- @field_stdsamep@ --- *
 204  *
 205  * Arguments:   @field *f, *g@ = two fields
 206  *
 207  * Returns:     Nonzero if the fields are identical (not just isomorphic).
 208  *
 209  * Use:         Standard sameness check, based on equality of the @m@
 210  *              member.
 211  */
 212
 213 extern int field_stdsamep(field */*f*/, field */*g*/);
 214
 215 /*----- Creating fields ---------------------------------------------------*/
 216
 217 /* --- @field_prime@ --- *
 218  *
 219  * Arguments:   @mp *p@ = the characteristic of the field
 220  *
 221  * Returns:     A pointer to the field.
 222  *
 223  * Use:         Creates a field structure for a prime field of size %$p$%,
 224  *              using Montgomery reduction for arithmetic.
 225  */
 226
 227 extern field *field_prime(mp */*p*/);
 228
 229 /* --- @field_niceprime@ --- *
 230  *
 231  * Arguments:   @mp *p@ = the characteristic of the field
 232  *
 233  * Returns:     A pointer to the field.
 234  *
 235  * Use:         Creates a field structure for a prime field of size %$p$%,
 236  *              using efficient reduction for nice primes.
 237  */
 238
 239 extern field *field_niceprime(mp */*p*/);
 240
 241 /* --- @field_binpoly@ --- *
 242  *
 243  * Arguments:   @mp *p@ = an irreducible polynomial over %$\gf{2}$%
 244  *
 245  * Returns:     A pointer to the field.
 246  *
 247  * Use:         Creates a field structure for a binary field using naive
 248  *              arithmetic.
 249  */
 250
 251 extern field *field_binpoly(mp */*p*/);
 252
 253 /* --- @field_parse@ --- *
 254  *
 255  * Arguments:   @qd_parse *qd@ = parser context
 256  *
 257  * Returns:     Field pointer if OK, or null.
 258  *
 259  * Use:         Parses a field description, which has the form
 260  *
 261  *                * `prime', `niceprime' or `binpoly'
 262  *                * an optional `:'
 263  *                * the field modulus
 264  */
 265
 266 extern field *field_parse(qd_parse */*qd*/);
 267
 268 /*----- That's all, folks -------------------------------------------------*/
 269
 270 #ifdef __cplusplus
 271   }
 272 #endif
 273
 274 #endif