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

   1 /* -*-c-*-
   2  *
   3  * Definitions for field arithmetic
   4  *
   5  * (c) 2000 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 #ifndef CATACOMB_FIELD_H
  29 #define CATACOMB_FIELD_H
  30
  31 #ifdef __cplusplus
  32   extern "C" {
  33 #endif
  34
  35 /*----- Header files ------------------------------------------------------*/
  36
  37 #ifndef CATACOMB_GRAND_H
  38 #  include "grand.h"
  39 #endif
  40
  41 #ifndef CATACOMB_MP_H
  42 #  include "mp.h"
  43 #endif
  44
  45 #ifndef CATACOMB_QDPARSE_H
  46 #  include "qdparse.h"
  47 #endif
  48
  49 /*----- Data structures ---------------------------------------------------*/
  50
  51 typedef struct field {
  52   const struct field_ops *ops;          /* Field operations */
  53   mp *zero, *one;                       /* Identities in the field */
  54   mp *m;                                /* Modulus (prime and binary) */
  55   unsigned long nbits;                  /* Length of field element in bits */
  56   size_t noctets;                       /* Length of element in octets */
  57   mp *q;                                /* Number of elements in field */
  58 } field;
  59
  60 enum {
  61   FTY_PRIME,
  62   FTY_BINARY
  63 };
  64
  65 typedef struct field_ops {
  66
  67   /* --- General information --- */
  68
  69   unsigned ty;                          /* What kind of field this is */
  70   const char *name;                     /* Human-readable name string */
  71
  72   /* --- Universal operations --- */
  73
  74   void (*destroy)(field */*f*/);
  75   mp *(*rand)(field */*f*/, mp */*d*/, grand */*r*/);
  76   int (*samep)(field */*f*/, field */*g*/);
  77
  78   mp *(*in)(field */*f*/, mp */*d*/, mp */*x*/);
  79   mp *(*out)(field */*f*/, mp */*d*/, mp */*x*/);
  80
  81   int (*zerop)(field */*f*/, mp */*x*/);
  82   mp *(*neg)(field */*f*/, mp */*d*/, mp */*x*/);
  83   mp *(*add)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/);
  84   mp *(*sub)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/);
  85   mp *(*mul)(field */*f*/, mp */*d*/, mp */*x*/, mp */*y*/);
  86   mp *(*sqr)(field */*f*/, mp */*d*/, mp */*x*/);
  87   mp *(*inv)(field */*f*/, mp */*d*/, mp */*x*/);
  88   mp *(*reduce)(field */*f*/, mp */*d*/, mp */*x*/);
  89   mp *(*sqrt)(field */*f*/, mp */*d*/, mp */*x*/);
  90
  91   /* --- Operations for binary fields only --- */
  92
  93   mp *(*quadsolve)(field */*f*/, mp */*d*/, mp */*x*/);
  94
  95   /* --- Operations for prime fields only --- */
  96
  97   mp *(*dbl)(field */*f*/, mp */*d*/, mp */*x*/);
  98   mp *(*tpl)(field */*f*/, mp */*d*/, mp */*x*/);
  99   mp *(*qdl)(field */*f*/, mp */*d*/, mp */*x*/);
 100   mp *(*hlv)(field */*f*/, mp */*d*/, mp */*x*/);
 101
 102 } field_ops;
 103
 104 #define F_TYPE(f)               (f)->ops->ty
 105 #define F_NAME(f)               (f)->ops->name
 106
 107 #define F_DESTROY(f)            (f)->ops->destroy((f))
 108 #define F_RAND(f, d, r)         (f)->ops->rand((f), (d), (r))
 109 #define F_SAMEP(f, g)           (f)->ops->samep((f), (g))
 110
 111 #define F_IN(f, d, x)           (f)->ops->in((f), (d), (x))
 112 #define F_OUT(f, d, x)          (f)->ops->out((f), (d), (x))
 113
 114 #define F_ZEROP(f, x)           (f)->ops->zerop((f), (x))
 115 #define F_NEG(f, d, x)          (f)->ops->neg((f), (d), (x))
 116 #define F_ADD(f, d, x, y)       (f)->ops->add((f), (d), (x), (y))
 117 #define F_SUB(f, d, x, y)       (f)->ops->sub((f), (d), (x), (y))
 118 #define F_MUL(f, d, x, y)       (f)->ops->mul((f), (d), (x), (y))
 119 #define F_SQR(f, d, x)          (f)->ops->sqr((f), (d), (x))
 120 #define F_INV(f, d, x)          (f)->ops->inv((f), (d), (x))
 121 #define F_REDUCE(f, d, x)       (f)->ops->reduce((f), (d), (x))
 122 #define F_SQRT(f, d, x)         (f)->ops->sqrt((f), (d), (x))
 123
 124 #define F_QUADSOLVE(f, d, x)    (f)->ops->quadsolve((f), (d), (x))
 125
 126 #define F_DBL(f, d, x)          (f)->ops->dbl((f), (d), (x))
 127 #define F_TPL(f, d, x)          (f)->ops->tpl((f), (d), (x))
 128 #define F_QDL(f, d, x)          (f)->ops->qdl((f), (d), (x))
 129 #define F_HLV(f, d, x)          (f)->ops->hlv((f), (d), (x))
 130
 131 /*----- Helpful field operations ------------------------------------------*/
 132
 133 /* --- @field_id@ --- *
 134  *
 135  * Arguments:   @field *f@ = pointer to a field
 136  *              @mp *d@ = a destination element
 137  *              @mp *x@ = a source element
 138  *
 139  * Returns:     The result element.
 140  *
 141  * Use:         An identity operation which can be used if your field has no
 142  *              internal representation.
 143  */
 144
 145 extern mp *field_id(field */*f*/, mp */*d*/, mp */*x*/);
 146
 147 /* --- @field_samep@ --- *
 148  *
 149  * Arguments:   @field *f, *g@ = two fields
 150  *
 151  * Returns:     Nonzero if the fields are identical (not just isomorphic).
 152  *
 153  * Use:         Checks for sameness of fields.  This function does the full
 154  *              check, not just the field-type-specific check done by the
 155  *              @sampep@ field operation.
 156  */
 157
 158 extern int field_samep(field */*f*/, field */*g*/);
 159
 160 /* --- @field_stdsamep@ --- *
 161  *
 162  * Arguments:   @field *f, *g@ = two fields
 163  *
 164  * Returns:     Nonzero if the fields are identical (not just isomorphic).
 165  *
 166  * Use:         Standard sameness check, based on equality of the @m@
 167  *              member.
 168  */
 169
 170 extern int field_stdsamep(field */*f*/, field */*g*/);
 171
 172 /*----- Arithmetic --------------------------------------------------------*/
 173
 174 /* --- @field_exp@ --- *
 175  *
 176  * Arguments:   @field *f@ = pointer to field
 177  *              @mp *d@ = fake destination
 178  *              @mp *a@ = base
 179  *              @mp *e@ = exponent
 180  *
 181  * Returns:     Result, %$a^e$%.
 182  *
 183  * Use:         Exponentiation in a finite field.  Note that all quantities
 184  *              are in internal format.  This is a generic implementation
 185  *              suitable for use with all fields and is not intended to be
 186  *              optimal.
 187  */
 188
 189 extern mp *field_exp(field */*f*/, mp */*d*/, mp */*a*/, mp */*e*/);
 190
 191 /*----- Creating fields ---------------------------------------------------*/
 192
 193 /* --- @field_prime@ --- *
 194  *
 195  * Arguments:   @mp *p@ = the characteristic of the field
 196  *
 197  * Returns:     A pointer to the field.
 198  *
 199  * Use:         Creates a field structure for a prime field of size %$p$%,
 200  *              using Montgomery reduction for arithmetic.
 201  */
 202
 203 extern field *field_prime(mp */*p*/);
 204
 205 /* --- @field_niceprime@ --- *
 206  *
 207  * Arguments:   @mp *p@ = the characteristic of the field
 208  *
 209  * Returns:     A pointer to the field, or null.
 210  *
 211  * Use:         Creates a field structure for a prime field of size %$p$%,
 212  *              using efficient reduction for nice primes.
 213  */
 214
 215 extern field *field_niceprime(mp */*p*/);
 216
 217 /* --- @field_binpoly@ --- *
 218  *
 219  * Arguments:   @mp *p@ = an irreducible polynomial over %$\gf{2}$%
 220  *
 221  * Returns:     A pointer to the field.
 222  *
 223  * Use:         Creates a field structure for a binary field using naive
 224  *              arithmetic.
 225  */
 226
 227 extern field *field_binpoly(mp */*p*/);
 228
 229 /* --- @field_binnorm@ --- *
 230  *
 231  * Arguments:   @mp *p@ = the reduction polynomial
 232  *              @mp *beta@ = representation of normal point
 233  *
 234  * Returns:     A pointer to the field.
 235  *
 236  * Use:         Creates a field structure for a binary field mod @p@ which
 237  *              uses a normal basis representation externally.  Computations
 238  *              are still done on a polynomial-basis representation.
 239  */
 240
 241 extern field *field_binnorm(mp */*p*/, mp */*beta*/);
 242
 243 /* --- @field_parse@ --- *
 244  *
 245  * Arguments:   @qd_parse *qd@ = parser context
 246  *
 247  * Returns:     Field pointer if OK, or null.
 248  *
 249  * Use:         Parses a field description, which has the form
 250  *
 251  *                * `prime', `niceprime', `binpoly', or `binnorm'
 252  *                * an optional `:'
 253  *                * the field modulus
 254  *                * for `binnorm', an optional `,' and the beta value
 255  */
 256
 257 extern field *field_parse(qd_parse */*qd*/);
 258
 259 /*----- That's all, folks -------------------------------------------------*/
 260
 261 #ifdef __cplusplus
 262   }
 263 #endif
 264
 265 #endif