[u/mdw/catacomb] / math / group.h

/* -*-c-*-
 *
 * General cyclic group abstraction
 *
 * (c) 2004 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------*
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 *
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

#ifndef CATACOMB_GROUP_H
#define CATACOMB_GROUP_H

#ifdef __cplusplus
  extern "C" {
#endif

/*----- Header files ------------------------------------------------------*/

#include <mLib/dstr.h>

#ifndef CATACOMB_BUF_H
#  include "buf.h"
#endif

#ifndef CATACOMB_DH_H
#  include "ec.h"
#endif

#ifndef CATACOMB_GRAND_H
#  include "grand.h"
#endif

#ifndef CATACOMB_MP_H
#  include "mp.h"
#endif

#ifndef CATACOMB_QDPARSE_H
#  include "qdparse.h"
#endif

/*----- Data structures ---------------------------------------------------*/

#ifndef ge
  typedef struct ge ge;			/* Group element (abstract type) */
#endif

typedef struct group_ {
  const struct group_ops *ops;		/* Operations table */
  size_t nbits;				/* Size of an element in bits */
  size_t noctets;			/* Size of raw element in octets */
  ge *i;				/* Identity element */
  ge *g;				/* Generator element */
  mp *r;				/* Order of the generator */
  mp *h;				/* Cofactor */
} group;

typedef struct group_expfactor {
  ge *base;				/* The base */
  mp *exp;				/* The exponent */
} group_expfactor;

typedef struct group_ops {

  /* --- General information --- */

  unsigned ty;				/* Type of this group */
  const char *name;			/* Textual name string */

  /* --- Memory management --- */

  void (*destroygroup)(group */*g*/);
  ge *(*create)(group */*g*/);
  void (*copy)(group */*g*/, ge */*d*/, ge */*x*/);
  void (*burn)(group */*g*/, ge */*x*/);
  void (*destroy)(group */*g*/, ge */*e*/);

  /* --- Comparisons --- */

  int (*samep)(group */*g*/, group */*h*/);
  int (*eq)(group */*g*/, ge */*x*/, ge */*y*/);
  int (*identp)(group */*g*/, ge */*x*/);

  /* --- Other stuff --- */

  const char *(*check)(group */*g*/, grand */*gr*/);

  /* --- Arithmetic --- */

  void (*mul)(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/);
  void (*sqr)(group */*g*/, ge */*d*/, ge */*x*/);
  void (*inv)(group */*g*/, ge */*d*/, ge */*x*/);
  void (*div)(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/);
  void (*exp)(group */*g*/, ge */*d*/, ge */*x*/, mp */*n*/);
  void (*mexp)(group */*g*/, ge */*d*/,
	       const group_expfactor */*f*/, size_t /*n*/);

  /* --- Debugging --- */

  int (*read)(group */*g*/, ge */*d*/,
	      const mptext_ops */*ops*/, void */*p*/);
  int (*write)(group */*g*/, ge */*x*/,
	       const mptext_ops */*ops*/, void */*p*/);

  /* --- Conversions --- */

  mp *(*toint)(group */*g*/, mp */*d*/, ge */*x*/);
  int (*fromint)(group */*g*/, ge */*d*/, mp */*x*/);
  int (*toec)(group */*g*/, ec */*d*/, ge */*x*/);
  int (*fromec)(group */*g*/, ge */*d*/, const ec */*p*/);
  int (*tobuf)(group */*h*/, buf */*b*/, ge */*x*/);
  int (*frombuf)(group */*h*/, buf */*b*/, ge */*d*/);
  int (*toraw)(group */*h*/, buf */*b*/, ge */*x*/);
  int (*fromraw)(group */*h*/, buf */*b*/, ge */*d*/);

} group_ops;

enum {
  GTY_PRIME,				/* Prime field subgroup */
  GTY_BINARY,				/* Binary feld subgroup */
  GTY_EC				/* Elliptic curve group */
};

#define G_NAME(g)		(g)->ops->name
#define G_TYPE(g)		(g)->ops->ty

#define G_DESTROYGROUP(g)	(g)->ops->destroygroup((g))
#define G_CREATE(g)		(g)->ops->create((g))
#define G_COPY(g, d, x)		(g)->ops->copy((g), (d), (x))
#define G_BURN(g, x)		(g)->ops->burn((g), (x))
#define G_DESTROY(g, x)		(g)->ops->destroy((g), (x))

#define G_SAMEP(g, h)		(g)->ops->samep((g), (h))
#define G_EQ(g, x, y)		(g)->ops->eq((g), (x), (y))
#define G_IDENTP(g, x)		(g)->ops->identp((g), (x))

#define G_CHECK(g, gr)		(g)->ops->check((g), (gr))

#define G_MUL(g, d, x, y)	(g)->ops->mul((g), (d), (x), (y))
#define G_SQR(g, d, x)		(g)->ops->sqr((g), (d), (x))
#define G_INV(g, d, x)		(g)->ops->inv((g), (d), (x))
#define G_DIV(g, d, x, y)	(g)->ops->div((g), (d), (x), (y))
#define G_EXP(g, d, x, n)	(g)->ops->exp((g), (d), (x), (n))
#define G_MEXP(g, d, f, n)	(g)->ops->mexp((g), (d), (f), (n))

#define G_READ(g, d, o, p)	(g)->ops->read((g), (d), (o), (p))
#define G_WRITE(g, x, o, p)	(g)->ops->write((g), (x), (o), (p))

#define G_TOINT(g, d, x)	(g)->ops->toint((g), (d), (x))
#define G_FROMINT(g, d, x)	(g)->ops->fromint((g), (d), (x))
#define G_TOEC(g, d, x)		(g)->ops->toec((g), (d), (x))
#define G_FROMEC(g, d, p)	(g)->ops->fromec((g), (d), (p))
#define G_TOBUF(g, b, x)	(g)->ops->tobuf((g), (b), (x))
#define G_FROMBUF(g, b, d)	(g)->ops->frombuf((g), (b), (d))
#define G_TORAW(g, b, x)	(g)->ops->toraw((g), (b), (x))
#define G_FROMRAW(g, b, d)	(g)->ops->fromraw((g), (b), (d))

/*----- Handy functions ---------------------------------------------------*/

/* --- @group_check@ --- *
 *
 * Arguments:	@group *g@ = an abstract group
 *		@ge *x@ = a group element
 *
 * Returns:	Zero on success, nonzero for failure.
 *
 * Use:		Checks that @x@ is a valid group element.  This may take a
 *		while, since it checks that %$x^h \ne 1$%.
 */

extern int group_check(group */*g*/, ge */*x*/);

/* --- @group_samep@ --- *
 *
 * Arguments:	@group *g, *h@ = two abstract groups
 *
 * Returns:	Nonzero if the groups are in fact identical (not just
 *		isomorphic).
 *
 * Use:		Checks to see whether two groups are actually the same.  This
 *		function does the full check: the group operatrion @samep@
 *		just does the group-specific details.
 */

extern int group_samep(group */*g*/, group */*h*/);

/*----- Textual I/O on group elements -------------------------------------*/

extern int group_readstring(group */*g*/, ge */*d*/,
			    const char */*p*/, char **/*end*/);
extern int group_writestring(group */*g*/, ge */*d*/,
			     char */*p*/, size_t /*sz*/);

extern int group_readfile(group */*g*/, ge */*d*/, FILE */*fp*/);
extern int group_writefile(group */*g*/, ge */*x*/, FILE */*fp*/);

extern int group_readdstr(group */*g*/, ge */*d*/,
			  dstr */*dd*/, size_t */*off*/);
extern int group_writedstr(group */*g*/, ge */*x*/, dstr */*d*/);

/*----- Standard implementations ------------------------------------------*/

/* --- @group_stdidentp@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ge *x@ = group element
 *
 * Returns:	Nonzero if %$x$% is the group identity.
 */

extern int group_stdidentp(group */*g*/, ge */*x*/);

/* --- @group_stdcheck@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@grand *gr@ = random number source.
 *
 * Returns:	Null on success, or a pointer to an error message.
 */

extern const char *group_stdcheck(group */*g*/, grand */*gr*/);

/* --- @group_stdsqr@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ge *d@ = destination pointer
 *		@ge *x@ = group element
 *
 * Returns:	---
 *
 * Use:		Computes %$d = x^2$% as %$d = x x$%.
 */

extern void group_stdsqr(group */*g*/, ge */*d*/, ge */*x*/);

/* --- @group_stddiv@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ge *d@ = destination pointer
 *		@ge *x@ = dividend
 *		@ge *y@ = divisor
 *
 * Returns:	---
 *
 * Use:		Computes %$d = x/y$% as %$d = x y^{-1}$%.
 */

extern void group_stddiv(group */*g*/, ge */*d*/, ge */*x*/, ge */*y*/);

/* --- @group_stdexp@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ge *d@ = destination pointer
 *		@ge *x@ = base element
 *		@mp *n@ = exponent
 *
 * Returns:	---
 *
 * Use:		Computes %$d = x^n$% efficiently.
 */

extern void group_stdexp(group */*g*/, ge */*d*/, ge */*x*/, mp */*n*/);

/* --- @group_stdmexp@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ge *d@ = destination pointer
 *		@const group_expfactor *f@ = vector of factors
 *		@size_t n@ = number of factors
 *
 * Returns:	---
 *
 * Use:		Computes %$d = g_0^{x_0} g_1^{x_1} \ldots$% efficiently.
 */

extern void group_stdmexp(group */*g*/, ge */*d*/,
			  const group_expfactor */*f*/, size_t /*n*/);

/* --- @group_stdtoec@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ec *d@ = destination point
 *		@ge *x@ = group element
 *
 * Returns:	@-1@, indicating failure.
 *
 * Use:		Fails to convert a group element to an elliptic curve point.
 */

extern int group_stdtoec(group */*g*/, ec */*d*/, ge */*x*/);

/* --- @group_stdfromec@ --- *
 *
 * Arguments:	@group *g@ = abstract group
 *		@ge *d@ = destination pointer
 *		@const ec *p@ = elliptic curve point
 *
 * Returns:	Zero for success, @-1@ on failure.
 *
 * Use:		Converts %$p$% to a group element by converting its %$x$%-
 *		coordinate.
 */

extern int group_stdfromec(group */*g*/, ge */*d*/, const ec */*p*/);

/*----- Prime field subgroups ---------------------------------------------*/

typedef struct gprime_param {
  mp *p, *q;				/* Prime numbers %$p$% and %$q$% */
  mp *g;				/* Generates order-%$q$% subgroup */
} gprime_param;

/* --- @group_prime@ --- *
 *
 * Arguments:	@const gprime_param *gp@ = group parameters
 *
 * Returns:	A pointer to the group, or null.
 *
 * Use:		Constructs an abstract group interface for a subgroup of a
 *		prime field.  Group elements are @mp *@ pointers.
 */

group *group_prime(const gprime_param */*gp*/);

/*----- Binary field subgroups --------------------------------------------*/

typedef gprime_param gbin_param;

/* --- @group_binary@ --- *
 *
 * Arguments:	@const gbin_param *gb@ = group parameters
 *
 * Returns:	A pointer to the group, or null.
 *
 * Use:		Constructs an abstract group interface for a subgroup of a
 *		prime field.  Group elements are @mp *@ pointers.
 */

group *group_binary(const gbin_param */*gp*/);

/*----- Elliptic curve groups ---------------------------------------------*/

/* --- @group_ec@ --- *
 *
 * Arguments:	@const ec_info *ei@ = elliptic curve parameters
 *
 * Returns:	A pointer to the group, or null.
 *
 * Use:		Constructs an abstract group interface for an elliptic curve
 *		group.  Group elements are @ec@ structures.  The contents of
 *		the @ec_info@ structure becomes the property of the @group@
 *		object; you can (and should) free the structure itself, but
 *		calling @ec_freeinfo@ on it is not allowed.
 */

group *group_ec(const ec_info */*ei*/);

/*----- General group initialization --------------------------------------*/

/* --- @group_parse@ --- *
 *
 * Arguments:	@qd_parse *qd@ = quick-and-dirty parser
 *
 * Returns:	Group pointer, or null for failure.
 *
 * Use:		Parses a group description and returns the group.  This has
 *		the form `TYPE { SPEC }' where TYPE is `prime' or `ec', and
 *		SPEC is the appropriate kind of group specification of the
 *		given type.
 */

extern group *group_parse(qd_parse */*qd*/);

/* --- @group_fromstring@ --- *
 *
 * Arguments:	@const char *p@ = pointer to string to read
 *		@group **gg@ = where to put the group pointer
 *
 * Returns:	Null if OK, or an error string.
 *
 * Use:		Parses a group spec from a string, and returns the group.
 */

extern const char *group_fromstring(const char */*p*/, group **/*gg*/);

/*----- That's all, folks -------------------------------------------------*/

#ifdef __cplusplus
  }
#endif

#endif
Commit	Line	Data
34e4f738	1	/* --c--
34e4f738	2	*
34e4f738	3	* General cyclic group abstraction
	4	*
	5	* (c) 2004 Straylight/Edgeware
	6	*/
	7
45c0fd36	8	/----- Licensing notice --------------------------------------------------
34e4f738	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.
45c0fd36	16	*
34e4f738	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.
45c0fd36	21	*
34e4f738	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
34e4f738	28	#ifndef CATACOMB_GROUP_H
	29	#define CATACOMB_GROUP_H
	30
	31	#ifdef __cplusplus
	32	extern "C" {
	33	#endif
	34
	35	/----- Header files ------------------------------------------------------/
	36
	37	#include <mLib/dstr.h>
	38
	39	#ifndef CATACOMB_BUF_H
	40	# include "buf.h"
	41	#endif
	42
	43	#ifndef CATACOMB_DH_H
	44	# include "ec.h"
	45	#endif
	46
	47	#ifndef CATACOMB_GRAND_H
	48	# include "grand.h"
	49	#endif
	50
	51	#ifndef CATACOMB_MP_H
	52	# include "mp.h"
	53	#endif
	54
	55	#ifndef CATACOMB_QDPARSE_H
	56	# include "qdparse.h"
	57	#endif
	58
	59	/----- Data structures ---------------------------------------------------/
	60
	61	#ifndef ge
	62	typedef struct ge ge; /* Group element (abstract type) */
	63	#endif
	64
a5b0f8ff	65	typedef struct group_ {
34e4f738	66	const struct group_ops ops; / Operations table */
34e4f738	67	size_t nbits; /* Size of an element in bits */
0f3faccd	68	size_t noctets; /* Size of raw element in octets */
34e4f738	69	ge i; / Identity element */
	70	ge g; / Generator element */
	71	mp r; / Order of the generator */
	72	mp h; / Cofactor */
	73	} group;
	74
	75	typedef struct group_expfactor {
	76	ge base; / The base */
	77	mp exp; / The exponent */
	78	} group_expfactor;
	79
	80	typedef struct group_ops {
f94b972d	81
	82	/* --- General information --- */
	83
34e4f738	84	unsigned ty; /* Type of this group */
f94b972d	85	const char name; / Textual name string */
34e4f738	86
	87	/* --- Memory management --- */
	88
	89	void (destroygroup)(group /g/);
	90	ge (create)(group /g*/);
	91	void (copy)(group /g/, ge /d/, ge /x/);
	92	void (burn)(group /g/, ge /x*/);
	93	void (destroy)(group /g/, ge /e*/);
	94
	95	/* --- Comparisons --- */
	96
	97	int (samep)(group /g/, group /h*/);
	98	int (eq)(group /g/, ge /x/, ge /y/);
	99	int (identp)(group /g/, ge /x*/);
	100
	101	/* --- Other stuff --- */
	102
	103	const char (check)(group /g/, grand /gr/);
	104
	105	/* --- Arithmetic --- */
	106
	107	void (mul)(group /g/, ge /d/, ge /x/, ge /y*/);
	108	void (sqr)(group /g/, ge /d/, ge /x/);
	109	void (inv)(group /g/, ge /d/, ge /x/);
	110	void (div)(group /g/, ge /d/, ge /x/, ge /y*/);
	111	void (exp)(group /g/, ge /d/, ge /x/, mp /n*/);
	112	void (mexp)(group /g/, ge /d*/,
	113	const group_expfactor /f/, size_t /n*/);
	114
	115	/* --- Debugging --- */
	116
	117	int (read)(group /g/, ge /d*/,
	118	const mptext_ops /ops/, void /p/);
	119	int (write)(group /g/, ge /x*/,
	120	const mptext_ops /ops/, void /p/);
	121
	122	/* --- Conversions --- */
	123
	124	mp (toint)(group /g/, mp /d/, ge /x*/);
	125	int (fromint)(group /g/, ge /d/, mp /x/);
	126	int (toec)(group /g/, ec /d/, ge /x/);
5c3f75ec	127	int (fromec)(group /g/, ge /d/, const ec /p/);
34e4f738	128	int (tobuf)(group /h/, buf /b/, ge /x/);
34e4f738	129	int (frombuf)(group /h/, buf /b/, ge /d/);
0f3faccd	130	int (toraw)(group /h/, buf /b/, ge /x/);
0f3faccd	131	int (fromraw)(group /h/, buf /b/, ge /d/);
34e4f738	132
	133	} group_ops;
	134
	135	enum {
	136	GTY_PRIME, /* Prime field subgroup */
	137	GTY_BINARY, /* Binary feld subgroup */
	138	GTY_EC /* Elliptic curve group */
	139	};
	140
f94b972d	141	#define G_NAME(g) (g)->ops->name
	142	#define G_TYPE(g) (g)->ops->ty
	143
34e4f738	144	#define G_DESTROYGROUP(g) (g)->ops->destroygroup((g))
	145	#define G_CREATE(g) (g)->ops->create((g))
	146	#define G_COPY(g, d, x) (g)->ops->copy((g), (d), (x))
	147	#define G_BURN(g, x) (g)->ops->burn((g), (x))
	148	#define G_DESTROY(g, x) (g)->ops->destroy((g), (x))
	149
	150	#define G_SAMEP(g, h) (g)->ops->samep((g), (h))
	151	#define G_EQ(g, x, y) (g)->ops->eq((g), (x), (y))
	152	#define G_IDENTP(g, x) (g)->ops->identp((g), (x))
	153
	154	#define G_CHECK(g, gr) (g)->ops->check((g), (gr))
	155
	156	#define G_MUL(g, d, x, y) (g)->ops->mul((g), (d), (x), (y))
	157	#define G_SQR(g, d, x) (g)->ops->sqr((g), (d), (x))
	158	#define G_INV(g, d, x) (g)->ops->inv((g), (d), (x))
	159	#define G_DIV(g, d, x, y) (g)->ops->div((g), (d), (x), (y))
	160	#define G_EXP(g, d, x, n) (g)->ops->exp((g), (d), (x), (n))
	161	#define G_MEXP(g, d, f, n) (g)->ops->mexp((g), (d), (f), (n))
	162
	163	#define G_READ(g, d, o, p) (g)->ops->read((g), (d), (o), (p))
	164	#define G_WRITE(g, x, o, p) (g)->ops->write((g), (x), (o), (p))
	165
	166	#define G_TOINT(g, d, x) (g)->ops->toint((g), (d), (x))
	167	#define G_FROMINT(g, d, x) (g)->ops->fromint((g), (d), (x))
	168	#define G_TOEC(g, d, x) (g)->ops->toec((g), (d), (x))
	169	#define G_FROMEC(g, d, p) (g)->ops->fromec((g), (d), (p))
	170	#define G_TOBUF(g, b, x) (g)->ops->tobuf((g), (b), (x))
	171	#define G_FROMBUF(g, b, d) (g)->ops->frombuf((g), (b), (d))
0f3faccd	172	#define G_TORAW(g, b, x) (g)->ops->toraw((g), (b), (x))
0f3faccd	173	#define G_FROMRAW(g, b, d) (g)->ops->fromraw((g), (b), (d))
34e4f738	174
	175	/----- Handy functions ---------------------------------------------------/
	176
	177	/* --- @group_check@ --- *
	178	*
	179	* Arguments: @group *g@ = an abstract group
	180	* @ge *x@ = a group element
	181	*
	182	* Returns: Zero on success, nonzero for failure.
	183	*
	184	* Use: Checks that @x@ is a valid group element. This may take a
	185	* while, since it checks that %$x^h \ne 1$%.
	186	*/
	187
	188	extern int group_check(group /g/, ge /x/);
	189
	190	/* --- @group_samep@ --- *
	191	*
	192	* Arguments: @group g, h@ = two abstract groups
	193	*
	194	* Returns: Nonzero if the groups are in fact identical (not just
	195	* isomorphic).
	196	*
	197	* Use: Checks to see whether two groups are actually the same. This
	198	* function does the full check: the group operatrion @samep@
	199	* just does the group-specific details.
	200	*/
	201
	202	extern int group_samep(group /g/, group /h/);
	203
	204	/----- Textual I/O on group elements -------------------------------------/
	205
	206	extern int group_readstring(group /g/, ge /d/,
	207	const char /p/, char /end*/);
	208	extern int group_writestring(group /g/, ge /d/,
	209	char /p/, size_t /sz*/);
	210
	211	extern int group_readfile(group /g/, ge /d/, FILE /fp*/);
	212	extern int group_writefile(group /g/, ge /x/, FILE /fp*/);
	213
	214	extern int group_readdstr(group /g/, ge /d/,
	215	dstr /dd/, size_t /off/);
	216	extern int group_writedstr(group /g/, ge /x/, dstr /d*/);
	217
	218	/----- Standard implementations ------------------------------------------/
	219
	220	/* --- @group_stdidentp@ --- *
	221	*
	222	* Arguments: @group *g@ = abstract group
	223	* @ge *x@ = group element
	224	*
	225	* Returns: Nonzero if %$x$% is the group identity.
	226	*/
	227
	228	extern int group_stdidentp(group /g/, ge /x/);
	229
	230	/* --- @group_stdcheck@ --- *
	231	*
	232	* Arguments: @group *g@ = abstract group
	233	* @grand *gr@ = random number source.
	234	*
	235	* Returns: Null on success, or a pointer to an error message.
	236	*/
	237
238	extern const char group_stdcheck(group /g/, grand /gr*/);
239
240	/* --- @group_stdsqr@ --- *
241	*
242	* Arguments: @group *g@ = abstract group
243	* @ge *d@ = destination pointer
244	* @ge *x@ = group element
245	*
246	* Returns: ---
247	*
248	* Use: Computes %$d = x^2$% as %$d = x x$%.
249	*/
250
251	extern void group_stdsqr(group /g/, ge /d/, ge /x*/);
252
253	/* --- @group_stddiv@ --- *
254	*
255	* Arguments: @group *g@ = abstract group
256	* @ge *d@ = destination pointer
257	* @ge *x@ = dividend
258	* @ge *y@ = divisor
259	*
260	* Returns: ---
261	*
262	* Use: Computes %$d = x/y$% as %$d = x y^{-1}$%.
263	*/
264
265	extern void group_stddiv(group /g/, ge /d/, ge /x/, ge /y/);
266
267	/* --- @group_stdexp@ --- *
268	*
269	* Arguments: @group *g@ = abstract group
270	* @ge *d@ = destination pointer
271	* @ge *x@ = base element
272	* @mp *n@ = exponent
273	*
274	* Returns: ---
275	*
276	* Use: Computes %$d = x^n$% efficiently.
277	*/
278
279	extern void group_stdexp(group /g/, ge /d/, ge /x/, mp /n/);
280
281	/* --- @group_stdmexp@ --- *
282	*
283	* Arguments: @group *g@ = abstract group
284	* @ge *d@ = destination pointer
285	* @const group_expfactor *f@ = vector of factors
286	* @size_t n@ = number of factors
287	*
288	* Returns: ---
289	*
290	* Use: Computes %$d = g_0^{x_0} g_1^{x_1} \ldots$% efficiently.
291	*/
292
293	extern void group_stdmexp(group /g/, ge /d/,
294	const group_expfactor /f/, size_t /n*/);
295
296	/* --- @group_stdtoec@ --- *
297	*
298	* Arguments: @group *g@ = abstract group
299	* @ec *d@ = destination point
300	* @ge *x@ = group element
301	*
302	* Returns: @-1@, indicating failure.
303	*
304	* Use: Fails to convert a group element to an elliptic curve point.
305	*/
306
307	extern int group_stdtoec(group /g/, ec /d/, ge /x*/);
308
309	/* --- @group_stdfromec@ --- *
310	*
311	* Arguments: @group *g@ = abstract group
312	* @ge *d@ = destination pointer
5c3f75ec	313	* @const ec *p@ = elliptic curve point
34e4f738	314	*
	315	* Returns: Zero for success, @-1@ on failure.
	316	*
	317	* Use: Converts %$p$% to a group element by converting its %$x$%-
	318	* coordinate.
	319	*/
	320
5c3f75ec	321	extern int group_stdfromec(group /g/, ge /d/, const ec /p*/);
34e4f738	322
	323	/----- Prime field subgroups ---------------------------------------------/
	324
	325	typedef struct gprime_param {
	326	mp p, q; /* Prime numbers %$p$% and %$q$% */
	327	mp g; / Generates order-%$q$% subgroup */
	328	} gprime_param;
	329
	330	/* --- @group_prime@ --- *
	331	*
	332	* Arguments: @const gprime_param *gp@ = group parameters
	333	*
02d7884d	334	* Returns: A pointer to the group, or null.
34e4f738	335	*
	336	* Use: Constructs an abstract group interface for a subgroup of a
	337	* prime field. Group elements are @mp *@ pointers.
	338	*/
	339
	340	group group_prime(const gprime_param /gp/);
	341
3688eb75	342	/----- Binary field subgroups --------------------------------------------/
	343
	344	typedef gprime_param gbin_param;
	345
	346	/* --- @group_binary@ --- *
	347	*
	348	* Arguments: @const gbin_param *gb@ = group parameters
	349	*
	350	* Returns: A pointer to the group, or null.
	351	*
	352	* Use: Constructs an abstract group interface for a subgroup of a
	353	* prime field. Group elements are @mp *@ pointers.
	354	*/
	355
	356	group group_binary(const gbin_param /gp/);
	357
34e4f738	358	/----- Elliptic curve groups ---------------------------------------------/
	359
	360	/* --- @group_ec@ --- *
	361	*
	362	* Arguments: @const ec_info *ei@ = elliptic curve parameters
	363	*
02d7884d	364	* Returns: A pointer to the group, or null.
34e4f738	365	*
	366	* Use: Constructs an abstract group interface for an elliptic curve
	367	* group. Group elements are @ec@ structures. The contents of
	368	* the @ec_info@ structure becomes the property of the @group@
	369	* object; you can (and should) free the structure itself, but
	370	* calling @ec_freeinfo@ on it is not allowed.
	371	*/
	372
	373	group group_ec(const ec_info /ei/);
	374
	375	/----- General group initialization --------------------------------------/
	376
	377	/* --- @group_parse@ --- *
	378	*
	379	* Arguments: @qd_parse *qd@ = quick-and-dirty parser
	380	*
	381	* Returns: Group pointer, or null for failure.
	382	*
	383	* Use: Parses a group description and returns the group. This has
	384	* the form `TYPE { SPEC }' where TYPE is `prime' or `ec', and
	385	* SPEC is the appropriate kind of group specification of the
	386	* given type.
	387	*/
	388
	389	extern group group_parse(qd_parse /qd/);
	390
	391	/* --- @group_fromstring@ --- *
	392	*
	393	* Arguments: @const char *p@ = pointer to string to read
	394	* @group **gg@ = where to put the group pointer
	395	*
	396	* Returns: Null if OK, or an error string.
	397	*
	398	* Use: Parses a group spec from a string, and returns the group.
	399	*/
	400
	401	extern const char group_fromstring(const char /p/, group */gg*/);
	402
	403	/----- That's all, folks -------------------------------------------------/
	404
	405	#ifdef __cplusplus
	406	}
	407	#endif
	408
	409	#endif