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   1 /* -*-c-*-
   2  *
   3  * $Id: group.h,v 1.1 2004/04/01 12:50:09 mdw Exp $
   4  *
   5  * General cyclic group abstraction
   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: group.h,v $
  33  * Revision 1.1  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  */
  41
  42 #ifndef CATACOMB_GROUP_H
  43 #define CATACOMB_GROUP_H
  44
  45 #ifdef __cplusplus
  46   extern "C" {
  47 #endif
  48
  49 /*----- Header files ------------------------------------------------------*/
  50
  51 #include <mLib/dstr.h>
  52
  53 #ifndef CATACOMB_BUF_H
  54 #  include "buf.h"
  55 #endif
  56
  57 #ifndef CATACOMB_DH_H
  58 #  include "ec.h"
  59 #endif
  60
  61 #ifndef CATACOMB_GRAND_H
  62 #  include "grand.h"
  63 #endif
  64
  65 #ifndef CATACOMB_MP_H
  66 #  include "mp.h"
  67 #endif
  68
  69 #ifndef CATACOMB_QDPARSE_H
  70 #  include "qdparse.h"
  71 #endif
  72
  73 /*----- Data structures ---------------------------------------------------*/
  74
  75 #ifndef ge
  76   typedef struct ge ge;                 /* Group element (abstract type) */
  77 #endif
  78
  79 typedef struct group {
  80   const struct group_ops *ops;          /* Operations table */
  81   size_t nbits;                         /* Size of an element in bits */
  82   size_t noctets;                       /* Size of an element in octets */
  83   ge *i;                                /* Identity element */
  84   ge *g;                                /* Generator element */
  85   mp *r;                                /* Order of the generator */
  86   mp *h;                                /* Cofactor */
  87 } group;
  88
  89 typedef struct group_expfactor {
  90   ge *base;                             /* The base */
  91   mp *exp;                              /* The exponent */
  92 } group_expfactor;
  93
  94 typedef struct group_ops {
  95   unsigned ty;                          /* Type of this group */
  96
  97   /* --- Memory management --- */
  98
  99   void (*destroygroup)(group */*g*/);
 100   ge *(*create)(group */*g*/);
 101   void (*copy)(group */*g*/, ge */*d*/, ge */*x*/);
 102   void (*burn)(group */*g*/, ge */*x*/);
 103   void (*destroy)(group */*g*/, ge */*e*/);
 104
 105   /* --- Comparisons --- */
 106
 107   int (*samep)(group */*g*/, group */*h*/);
 108   int (*eq)(group */*g*/, ge */*x*/, ge */*y*/);
 109   int (*identp)(group */*g*/, ge */*x*/);
 110
 111   /* --- Other stuff --- */
 112
 113   const char *(*check)(group */*g*/, grand */*gr*/);
 114
 115   /* --- Arithmetic --- */
 116
 117   void (*mul)(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/);
 118   void (*sqr)(group */*g*/, ge */*d*/, ge */*x*/);
 119   void (*inv)(group */*g*/, ge */*d*/, ge */*x*/);
 120   void (*div)(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/);
 121   void (*exp)(group */*g*/, ge */*d*/, ge */*x*/, mp */*n*/);
 122   void (*mexp)(group */*g*/, ge */*d*/,
 123                const group_expfactor */*f*/, size_t /*n*/);
 124
 125   /* --- Debugging --- */
 126
 127   int (*read)(group */*g*/, ge */*d*/,
 128               const mptext_ops */*ops*/, void */*p*/);
 129   int (*write)(group */*g*/, ge */*x*/,
 130                const mptext_ops */*ops*/, void */*p*/);
 131
 132   /* --- Conversions --- */
 133
 134   mp *(*toint)(group */*g*/, mp */*d*/, ge */*x*/);
 135   int (*fromint)(group */*g*/, ge */*d*/, mp */*x*/);
 136   int (*toec)(group */*g*/, ec */*d*/, ge */*x*/);
 137   int (*fromec)(group */*g*/, ge */*d*/, ec */*p*/);
 138   int (*tobuf)(group */*h*/, buf */*b*/, ge */*x*/);
 139   int (*frombuf)(group */*h*/, buf */*b*/, ge */*d*/);
 140
 141 } group_ops;
 142
 143 enum {
 144   GTY_PRIME,                            /* Prime field subgroup */
 145   GTY_BINARY,                           /* Binary feld subgroup */
 146   GTY_EC                                /* Elliptic curve group */
 147 };
 148
 149 #define G_DESTROYGROUP(g)       (g)->ops->destroygroup((g))
 150 #define G_CREATE(g)             (g)->ops->create((g))
 151 #define G_COPY(g, d, x)         (g)->ops->copy((g), (d), (x))
 152 #define G_BURN(g, x)            (g)->ops->burn((g), (x))
 153 #define G_DESTROY(g, x)         (g)->ops->destroy((g), (x))
 154
 155 #define G_SAMEP(g, h)           (g)->ops->samep((g), (h))
 156 #define G_EQ(g, x, y)           (g)->ops->eq((g), (x), (y))
 157 #define G_IDENTP(g, x)          (g)->ops->identp((g), (x))
 158
 159 #define G_CHECK(g, gr)          (g)->ops->check((g), (gr))
 160
 161 #define G_MUL(g, d, x, y)       (g)->ops->mul((g), (d), (x), (y))
 162 #define G_SQR(g, d, x)          (g)->ops->sqr((g), (d), (x))
 163 #define G_INV(g, d, x)          (g)->ops->inv((g), (d), (x))
 164 #define G_DIV(g, d, x, y)       (g)->ops->div((g), (d), (x), (y))
 165 #define G_EXP(g, d, x, n)       (g)->ops->exp((g), (d), (x), (n))
 166 #define G_MEXP(g, d, f, n)      (g)->ops->mexp((g), (d), (f), (n))
 167
 168 #define G_READ(g, d, o, p)      (g)->ops->read((g), (d), (o), (p))
 169 #define G_WRITE(g, x, o, p)     (g)->ops->write((g), (x), (o), (p))
 170
 171 #define G_TOINT(g, d, x)        (g)->ops->toint((g), (d), (x))
 172 #define G_FROMINT(g, d, x)      (g)->ops->fromint((g), (d), (x))
 173 #define G_TOEC(g, d, x)         (g)->ops->toec((g), (d), (x))
 174 #define G_FROMEC(g, d, p)       (g)->ops->fromec((g), (d), (p))
 175 #define G_TOBUF(g, b, x)        (g)->ops->tobuf((g), (b), (x))
 176 #define G_FROMBUF(g, b, d)      (g)->ops->frombuf((g), (b), (d))
 177
 178 /*----- Handy functions ---------------------------------------------------*/
 179
 180 /* --- @group_check@ --- *
 181  *
 182  * Arguments:   @group *g@ = an abstract group
 183  *              @ge *x@ = a group element
 184  *
 185  * Returns:     Zero on success, nonzero for failure.
 186  *
 187  * Use:         Checks that @x@ is a valid group element.  This may take a
 188  *              while, since it checks that %$x^h \ne 1$%.
 189  */
 190
 191 extern int group_check(group */*g*/, ge */*x*/);
 192
 193 /* --- @group_samep@ --- *
 194  *
 195  * Arguments:   @group *g, *h@ = two abstract groups
 196  *
 197  * Returns:     Nonzero if the groups are in fact identical (not just
 198  *              isomorphic).
 199  *
 200  * Use:         Checks to see whether two groups are actually the same.  This
 201  *              function does the full check: the group operatrion @samep@
 202  *              just does the group-specific details.
 203  */
 204
 205 extern int group_samep(group */*g*/, group */*h*/);
 206
 207 /*----- Textual I/O on group elements -------------------------------------*/
 208
 209 extern int group_readstring(group */*g*/, ge */*d*/,
 210                             const char */*p*/, char **/*end*/);
 211 extern int group_writestring(group */*g*/, ge */*d*/,
 212                              char */*p*/, size_t /*sz*/);
 213
 214 extern int group_readfile(group */*g*/, ge */*d*/, FILE */*fp*/);
 215 extern int group_writefile(group */*g*/, ge */*x*/, FILE */*fp*/);
 216
 217 extern int group_readdstr(group */*g*/, ge */*d*/,
 218                           dstr */*dd*/, size_t */*off*/);
 219 extern int group_writedstr(group */*g*/, ge */*x*/, dstr */*d*/);
 220
 221 /*----- Standard implementations ------------------------------------------*/
 222
 223 /* --- @group_stdidentp@ --- *
 224  *
 225  * Arguments:   @group *g@ = abstract group
 226  *              @ge *x@ = group element
 227  *
 228  * Returns:     Nonzero if %$x$% is the group identity.
 229  */
 230
 231 extern int group_stdidentp(group */*g*/, ge */*x*/);
 232
 233 /* --- @group_stdcheck@ --- *
 234  *
 235  * Arguments:   @group *g@ = abstract group
 236  *              @grand *gr@ = random number source.
 237  *
 238  * Returns:     Null on success, or a pointer to an error message.
 239  */
 240
 241 extern const char *group_stdcheck(group */*g*/, grand */*gr*/);
 242
 243 /* --- @group_stdsqr@ --- *
 244  *
 245  * Arguments:   @group *g@ = abstract group
 246  *              @ge *d@ = destination pointer
 247  *              @ge *x@ = group element
 248  *
 249  * Returns:     ---
 250  *
 251  * Use:         Computes %$d = x^2$% as %$d = x x$%.
 252  */
 253
 254 extern void group_stdsqr(group */*g*/, ge */*d*/, ge */*x*/);
 255
 256 /* --- @group_stddiv@ --- *
 257  *
 258  * Arguments:   @group *g@ = abstract group
 259  *              @ge *d@ = destination pointer
 260  *              @ge *x@ = dividend
 261  *              @ge *y@ = divisor
 262  *
 263  * Returns:     ---
 264  *
 265  * Use:         Computes %$d = x/y$% as %$d = x y^{-1}$%.
 266  */
 267
 268 extern void group_stddiv(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/);
 269
 270 /* --- @group_stdexp@ --- *
 271  *
 272  * Arguments:   @group *g@ = abstract group
 273  *              @ge *d@ = destination pointer
 274  *              @ge *x@ = base element
 275  *              @mp *n@ = exponent
 276  *
 277  * Returns:     ---
 278  *
 279  * Use:         Computes %$d = x^n$% efficiently.
 280  */
 281
 282 extern void group_stdexp(group */*g*/, ge */*d*/, ge */*x*/, mp */*n*/);
 283
 284 /* --- @group_stdmexp@ --- *
 285  *
 286  * Arguments:   @group *g@ = abstract group
 287  *              @ge *d@ = destination pointer
 288  *              @const group_expfactor *f@ = vector of factors
 289  *              @size_t n@ = number of factors
 290  *
 291  * Returns:     ---
 292  *
 293  * Use:         Computes %$d = g_0^{x_0} g_1^{x_1} \ldots$% efficiently.
 294  */
 295
 296 extern void group_stdmexp(group */*g*/, ge */*d*/,
 297                           const group_expfactor */*f*/, size_t /*n*/);
 298
 299 /* --- @group_stdtoec@ --- *
 300  *
 301  * Arguments:   @group *g@ = abstract group
 302  *              @ec *d@ = destination point
 303  *              @ge *x@ = group element
 304  *
 305  * Returns:     @-1@, indicating failure.
 306  *
 307  * Use:         Fails to convert a group element to an elliptic curve point.
 308  */
 309
 310 extern int group_stdtoec(group */*g*/, ec */*d*/, ge */*x*/);
 311
 312 /* --- @group_stdfromec@ --- *
 313  *
 314  * Arguments:   @group *g@ = abstract group
 315  *              @ge *d@ = destination pointer
 316  *              @ec *p@ = elliptic curve point
 317  *
 318  * Returns:     Zero for success, @-1@ on failure.
 319  *
 320  * Use:         Converts %$p$% to a group element by converting its %$x$%-
 321  *              coordinate.
 322  */
 323
 324 extern int group_stdfromec(group */*g*/, ge */*d*/, ec */*p*/);
 325
 326 /*----- Prime field subgroups ---------------------------------------------*/
 327
 328 typedef struct gprime_param {
 329   mp *p, *q;                            /* Prime numbers %$p$% and %$q$% */
 330   mp *g;                                /* Generates order-%$q$% subgroup */
 331 } gprime_param;
 332
 333 /* --- @group_prime@ --- *
 334  *
 335  * Arguments:   @const gprime_param *gp@ = group parameters
 336  *
 337  * Returns:     A pointer to the group.
 338  *
 339  * Use:         Constructs an abstract group interface for a subgroup of a
 340  *              prime field.  Group elements are @mp *@ pointers.
 341  */
 342
 343 group *group_prime(const gprime_param */*gp*/);
 344
 345 /*----- Elliptic curve groups ---------------------------------------------*/
 346
 347 /* --- @group_ec@ --- *
 348  *
 349  * Arguments:   @const ec_info *ei@ = elliptic curve parameters
 350  *
 351  * Returns:     A pointer to the group.
 352  *
 353  * Use:         Constructs an abstract group interface for an elliptic curve
 354  *              group.  Group elements are @ec@ structures.  The contents of
 355  *              the @ec_info@ structure becomes the property of the @group@
 356  *              object; you can (and should) free the structure itself, but
 357  *              calling @ec_freeinfo@ on it is not allowed.
 358  */
 359
 360 group *group_ec(const ec_info */*ei*/);
 361
 362 /*----- General group initialization --------------------------------------*/
 363
 364 /* --- @group_parse@ --- *
 365  *
 366  * Arguments:   @qd_parse *qd@ = quick-and-dirty parser
 367  *
 368  * Returns:     Group pointer, or null for failure.
 369  *
 370  * Use:         Parses a group description and returns the group.  This has
 371  *              the form `TYPE { SPEC }' where TYPE is `prime' or `ec', and
 372  *              SPEC is the appropriate kind of group specification of the
 373  *              given type.
 374  */
 375
 376 extern group *group_parse(qd_parse */*qd*/);
 377
 378 /* --- @group_fromstring@ --- *
 379  *
 380  * Arguments:   @const char *p@ = pointer to string to read
 381  *              @group **gg@ = where to put the group pointer
 382  *
 383  * Returns:     Null if OK, or an error string.
 384  *
 385  * Use:         Parses a group spec from a string, and returns the group.
 386  */
 387
 388 extern const char *group_fromstring(const char */*p*/, group **/*gg*/);
 389
 390 /*----- That's all, folks -------------------------------------------------*/
 391
 392 #ifdef __cplusplus
 393   }
 394 #endif
 395
 396 #endif