[u/mdw/catacomb] / bbs.h

/* -*-c-*-
 *
 * $Id: bbs.h,v 1.4 2000/06/17 10:45:48 mdw Exp $
 *
 * The Blum-Blum-Shub random bit generator
 *
 * (c) 1999 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.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: bbs.h,v $
 * Revision 1.4  2000/06/17 10:45:48  mdw
 * Minor changes for key fetching.  Typesetting fixes.
 *
 * Revision 1.3  2000/02/12 18:21:02  mdw
 * Overhaul of key management (again).
 *
 * Revision 1.2  1999/12/22 15:52:08  mdw
 * Rename `bbs_params' to `bbs_param' for consistency.
 *
 * Revision 1.1  1999/12/10 23:14:59  mdw
 * Blum-Blum-Shub generator, and Blum-Goldwasser encryption.
 *
 */

/*----- Notes on the BBS generator ----------------------------------------*
 *
 * The Blum-Blum-Shub generator takes the least significant bits from the
 * sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of
 * two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%.
 * For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$%
 * should be coprime.  It is safe to use the least significant
 * %$\log \log n$% bits of each step in the sequence -- an adversary must
 * factor the modulus before being able to work forwards or backwards.  The
 * output of the generator cannot be distinguished from a (uniform,
 * independent) random sequence of bits using any polynomial-time test.  This
 * is by far the strongest pseudorandom number generator provided in
 * Catacomb, and by far the slowest too.  For normal use, the standard
 * Catacomb @rand@ generator should be more than adequate.
 */

#ifndef CATACOMB_BBS_H
#define CATACOMB_BBS_H

#ifdef __cplusplus
  extern "C" {
#endif

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

#include <mLib/bits.h>

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

#ifndef CATACOMB_KEY_H
#  include "key.h"
#endif

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

#ifndef CATACOMB_MPBARRETT_H
#  include "mpbarrett.h"
#endif

#ifndef CATACOMB_PGEN_H
#  include "pgen.h"
#endif

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

/* --- Basic generator state --- */

typedef struct bbs {
  mpbarrett mb;				/* Barrett reduction context */
  mp *x;				/* Current quadratic residue */
  unsigned k;				/* Number of bits from each step */
  unsigned b;				/* Number of bits in reservoir */
  mpw r;				/* Reservoir of output bits */
} bbs;

/* --- Parameters --- */

typedef struct bbs_pub {
  mp *n;
} bbs_pub;

typedef struct bbs_param {
  mp *p, *q;				/* Prime factors (3 mod 4) */
  mp *n;				/* Product @pq@ -- a Blum integer */
} bbs_param, bbs_priv;

/*----- Key fetching ------------------------------------------------------*/

extern const key_fetchdef bbs_pubfetch[];
#define BBS_PUBFETCHSZ 3

extern const key_fetchdef bbs_privfetch[];
#define BBS_PRIVFETCHSZ 7

/*----- The basic generator -----------------------------------------------*/

/* --- @bbs_create@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state to initialize
 *		@mp *m@ = modulus (must be a Blum integer)
 *		@mp *x@ = initial seed for generator
 *
 * Returns:	---
 *
 * Use:		Initializes a BBS generator.  The generator is stepped once
 *		after initialization, as for @bbs_seed@.
 */

extern void bbs_create(bbs */*b*/, mp */*m*/, mp */*x*/);

/* --- @bbs_destroy@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state
 *
 * Returns:	---
 *
 * Use:		Destroys a generator state when it's no longer wanted.
 */

extern void bbs_destroy(bbs */*b*/);

/* --- @bbs_step@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state
 *
 * Returns:	---
 *
 * Use:		Steps the generator once.  This isn't too useful in client
 *		code.
 */

extern void bbs_step(bbs */*b*/);

/* --- @bbs_set@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state
 *		@mp *x@ = new residue to set
 *
 * Returns:	---
 *
 * Use:		Sets a new quadratic residue.  The generator is stepped once.
 */

extern void bbs_set(bbs */*b*/, mp */*x*/);

/* --- @bbs_seed@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state
 *		@mp *x@ = new seed to set
 *
 * Returns	---
 *
 * Use:		Sets a new seed.  The generator is stepped until the residue
 *		has clearly wrapped around.
 */

extern void bbs_seed(bbs */*b*/, mp */*x*/);

/* --- @bbs_bits@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state
 *		@unsigned bits@ = number of bits wanted
 *
 * Returns:	Bits extracted from the BBS generator.
 *
 * Use:		Extracts a requested number of bits from the BBS generator.
 */

extern uint32 bbs_bits(bbs */*b*/, unsigned /*bits*/);

/* --- @bbs_wrap@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to BBS generator state
 *
 * Returns:	---
 *
 * Use:		Steps the generator if any of the reservoir bits are used.
 *		This can be used to `wrap up' after a Blum-Goldwasser
 *		encryption, for example, producing the final value to be sent
 *		along with the ciphertext.
 *
 *		If a generator is seeded, %$b$% bits are extracted, and then
 *		@bbs_wrap@ is called, the generator will have been stepped
 *		%$\lceil b/k \rceil$% times.
 */

extern void bbs_wrap(bbs */*b*/);

/*----- Large forwards and backwards jumps --------------------------------*/

/* --- @bbs_ff@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to a BBS generator state
 *		@bbs_param *bp@ = pointer to BBS modulus factors
 *		@unsigned long n@ = number of steps to make
 *
 * Returns:	---
 *
 * Use:		`Fast-forwards' a Blum-Blum-Shub generator by @n@ steps.
 *		Requires the factorization of the Blum modulus to do this
 *		efficiently.
 */

extern void bbs_ff(bbs */*b*/, bbs_param */*bp*/, unsigned long /*n*/);

/* --- @bbs_rew@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to a BBS generator state
 *		@bbs_param *bp@ = pointer to BBS modulus factors
 *		@unsigned long n@ = number of steps to make
 *
 * Returns:	---
 *
 * Use:		`Rewinds' a Blum-Blum-Shub generator by @n@ steps.
 *		Requires the factorization of the Blum modulus to do this
 *		at all.
 */

extern void bbs_rew(bbs */*b*/, bbs_param */*bp*/, unsigned long /*n*/);

/*----- Parameter generation ----------------------------------------------*/

/* --- @bbs_gen@ --- *
 *
 * Arguments:	@bbs_param *bp@ = pointer to parameter block
 *		@unsigned nbits@ = number of bits in the modulus
 *		@grand *r@ = pointer to random number source
 *		@unsigned n@ = number of attempts to make
 *		@pgen_proc *event@ = event handler function
 *		@void *ectx@ = argument for event handler
 *
 * Returns:	If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@.
 *
 * Use:		Finds two prime numbers %$p'$% and %$q'$% such that both are
 *		congruent to %$3 \bmod 4$%, and  $(p - 1)/2$% and
 *		%$(q - 1)/2$% have no common factors.  The product %$n = pq$%
 *		is eminently suitable for use as a modulus in a Blum-Blum-
 *		Shub pseudorandom bit generator.
 */

extern int bbs_gen(bbs_param */*bp*/, unsigned /*nbits*/, grand */*r*/,
		   unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/);

/*----- Generic random number generator interface -------------------------*/

/* --- @bbs_rand@ --- *
 *
 * Arguments:   @mp *m@ = modulus
 *		@mp *x@ = initial seed
 *
 * Returns:     Pointer to a generic generator.
 *
 * Use:         Constructs a generic generator interface over a
 *		Blum-Blum-Shub generator.
 */

extern grand *bbs_rand(mp */*m*/, mp */*x*/);

/* --- Blum-Blum-Shub-specific misc op codes --- */

enum {
  BBS_SET = GRAND_SPECIFIC		/* @mp *x@ */
};

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

#ifdef __cplusplus
  }
#endif

#endif
Commit	Line	Data
2c52abe6	1	/* --c--
2c52abe6	2	*
05cac080	3	* $Id: bbs.h,v 1.4 2000/06/17 10:45:48 mdw Exp $
2c52abe6	4	*
	5	* The Blum-Blum-Shub random bit generator
	6	*
	7	* (c) 1999 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: bbs.h,v $
05cac080	33	* Revision 1.4 2000/06/17 10:45:48 mdw
	34	* Minor changes for key fetching. Typesetting fixes.
	35	*
052b36d0	36	* Revision 1.3 2000/02/12 18:21:02 mdw
	37	* Overhaul of key management (again).
	38	*
4f743df5	39	* Revision 1.2 1999/12/22 15:52:08 mdw
	40	* Rename `bbs_params' to `bbs_param' for consistency.
	41	*
2c52abe6	42	* Revision 1.1 1999/12/10 23:14:59 mdw
	43	* Blum-Blum-Shub generator, and Blum-Goldwasser encryption.
	44	*
	45	*/
	46
	47	/----- Notes on the BBS generator ----------------------------------------
	48	*
	49	* The Blum-Blum-Shub generator takes the least significant bits from the
	50	* sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of
	51	* two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%.
	52	* For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$%
05cac080	53	* should be coprime. It is safe to use the least significant
	54	* %$\log \log n$% bits of each step in the sequence -- an adversary must
	55	* factor the modulus before being able to work forwards or backwards. The
	56	* output of the generator cannot be distinguished from a (uniform,
	57	* independent) random sequence of bits using any polynomial-time test. This
	58	* is by far the strongest pseudorandom number generator provided in
	59	* Catacomb, and by far the slowest too. For normal use, the standard
	60	* Catacomb @rand@ generator should be more than adequate.
2c52abe6	61	*/
	62
	63	#ifndef CATACOMB_BBS_H
	64	#define CATACOMB_BBS_H
	65
	66	#ifdef __cplusplus
	67	extern "C" {
	68	#endif
	69
	70	/----- Header files ------------------------------------------------------/
	71
	72	#include <mLib/bits.h>
	73
	74	#ifndef CATACOMB_GRAND_H
	75	# include "grand.h"
	76	#endif
	77
05cac080	78	#ifndef CATACOMB_KEY_H
	79	# include "key.h"
	80	#endif
	81
2c52abe6	82	#ifndef CATACOMB_MP_H
	83	# include "mp.h"
	84	#endif
	85
	86	#ifndef CATACOMB_MPBARRETT_H
	87	# include "mpbarrett.h"
	88	#endif
	89
4f743df5	90	#ifndef CATACOMB_PGEN_H
	91	# include "pgen.h"
	92	#endif
	93
2c52abe6	94	/----- Data structures ---------------------------------------------------/
	95
	96	/* --- Basic generator state --- */
	97
	98	typedef struct bbs {
	99	mpbarrett mb; /* Barrett reduction context */
	100	mp x; / Current quadratic residue */
	101	unsigned k; /* Number of bits from each step */
	102	unsigned b; /* Number of bits in reservoir */
	103	mpw r; /* Reservoir of output bits */
	104	} bbs;
	105
	106	/* --- Parameters --- */
	107
05cac080	108	typedef struct bbs_pub {
	109	mp *n;
	110	} bbs_pub;
	111
4f743df5	112	typedef struct bbs_param {
2c52abe6	113	mp p, q; /* Prime factors (3 mod 4) */
2c52abe6	114	mp n; / Product @pq@ -- a Blum integer */
05cac080	115	} bbs_param, bbs_priv;
	116
	117	/----- Key fetching ------------------------------------------------------/
	118
	119	extern const key_fetchdef bbs_pubfetch[];
	120	#define BBS_PUBFETCHSZ 3
	121
	122	extern const key_fetchdef bbs_privfetch[];
	123	#define BBS_PRIVFETCHSZ 7
2c52abe6	124
	125	/----- The basic generator -----------------------------------------------/
	126
	127	/* --- @bbs_create@ --- *
	128	*
	129	* Arguments: @bbs *b@ = pointer to BBS generator state to initialize
	130	* @mp *m@ = modulus (must be a Blum integer)
	131	* @mp *x@ = initial seed for generator
	132	*
	133	* Returns: ---
	134	*
	135	* Use: Initializes a BBS generator. The generator is stepped once
	136	* after initialization, as for @bbs_seed@.
	137	*/
	138
	139	extern void bbs_create(bbs /b/, mp /m/, mp /x*/);
	140
	141	/* --- @bbs_destroy@ --- *
	142	*
	143	* Arguments: @bbs *b@ = pointer to BBS generator state
	144	*
	145	* Returns: ---
	146	*
	147	* Use: Destroys a generator state when it's no longer wanted.
	148	*/
	149
	150	extern void bbs_destroy(bbs /b*/);
	151
	152	/* --- @bbs_step@ --- *
	153	*
	154	* Arguments: @bbs *b@ = pointer to BBS generator state
	155	*
	156	* Returns: ---
	157	*
	158	* Use: Steps the generator once. This isn't too useful in client
	159	* code.
	160	*/
	161
	162	extern void bbs_step(bbs /b*/);
	163
	164	/* --- @bbs_set@ --- *
	165	*
	166	* Arguments: @bbs *b@ = pointer to BBS generator state
	167	* @mp *x@ = new residue to set
	168	*
	169	* Returns: ---
	170	*
	171	* Use: Sets a new quadratic residue. The generator is stepped once.
	172	*/
	173
	174	extern void bbs_set(bbs /b/, mp /x/);
	175
	176	/* --- @bbs_seed@ --- *
	177	*
	178	* Arguments: @bbs *b@ = pointer to BBS generator state
	179	* @mp *x@ = new seed to set
	180	*
	181	* Returns ---
	182	*
	183	* Use: Sets a new seed. The generator is stepped until the residue
	184	* has clearly wrapped around.
	185	*/
	186
	187	extern void bbs_seed(bbs /b/, mp /x/);
188
189	/* --- @bbs_bits@ --- *
190	*
191	* Arguments: @bbs *b@ = pointer to BBS generator state
192	* @unsigned bits@ = number of bits wanted
193	*
194	* Returns: Bits extracted from the BBS generator.
195	*
196	* Use: Extracts a requested number of bits from the BBS generator.
197	*/
198
199	extern uint32 bbs_bits(bbs /b/, unsigned /bits*/);
200
201	/* --- @bbs_wrap@ --- *
202	*
203	* Arguments: @bbs *b@ = pointer to BBS generator state
204	*
205	* Returns: ---
206	*
207	* Use: Steps the generator if any of the reservoir bits are used.
208	* This can be used to `wrap up' after a Blum-Goldwasser
209	* encryption, for example, producing the final value to be sent
210	* along with the ciphertext.
211	*
212	* If a generator is seeded, %$b$% bits are extracted, and then
213	* @bbs_wrap@ is called, the generator will have been stepped
05cac080	214	* %$\lceil b/k \rceil$% times.
2c52abe6	215	*/
	216
	217	extern void bbs_wrap(bbs /b*/);
	218
	219	/----- Large forwards and backwards jumps --------------------------------/
	220
	221	/* --- @bbs_ff@ --- *
	222	*
	223	* Arguments: @bbs *b@ = pointer to a BBS generator state
4f743df5	224	* @bbs_param *bp@ = pointer to BBS modulus factors
2c52abe6	225	* @unsigned long n@ = number of steps to make
	226	*
	227	* Returns: ---
	228	*
	229	* Use: `Fast-forwards' a Blum-Blum-Shub generator by @n@ steps.
	230	* Requires the factorization of the Blum modulus to do this
	231	* efficiently.
	232	*/
	233
4f743df5	234	extern void bbs_ff(bbs /b/, bbs_param /bp/, unsigned long /n/);
2c52abe6	235
	236	/* --- @bbs_rew@ --- *
	237	*
	238	* Arguments: @bbs *b@ = pointer to a BBS generator state
4f743df5	239	* @bbs_param *bp@ = pointer to BBS modulus factors
2c52abe6	240	* @unsigned long n@ = number of steps to make
	241	*
	242	* Returns: ---
	243	*
	244	* Use: `Rewinds' a Blum-Blum-Shub generator by @n@ steps.
	245	* Requires the factorization of the Blum modulus to do this
	246	* at all.
	247	*/
	248
4f743df5	249	extern void bbs_rew(bbs /b/, bbs_param /bp/, unsigned long /n/);
2c52abe6	250
	251	/----- Parameter generation ----------------------------------------------/
	252
	253	/* --- @bbs_gen@ --- *
	254	*
4f743df5	255	* Arguments: @bbs_param *bp@ = pointer to parameter block
052b36d0	256	* @unsigned nbits@ = number of bits in the modulus
	257	* @grand *r@ = pointer to random number source
	258	* @unsigned n@ = number of attempts to make
4f743df5	259	* @pgen_proc *event@ = event handler function
4f743df5	260	* @void *ectx@ = argument for event handler
2c52abe6	261	*
4f743df5	262	* Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@.
2c52abe6	263	*
	264	* Use: Finds two prime numbers %$p'$% and %$q'$% such that both are
	265	* congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and
	266	* %$(q - 1)/2$% have no common factors. The product %$n = pq$%
	267	* is eminently suitable for use as a modulus in a Blum-Blum-
	268	* Shub pseudorandom bit generator.
	269	*/
	270
052b36d0	271	extern int bbs_gen(bbs_param /bp/, unsigned /nbits/, grand /r/,
052b36d0	272	unsigned /n/, pgen_proc /event/, void /ectx/);
2c52abe6	273
	274	/----- Generic random number generator interface -------------------------/
	275
	276	/* --- @bbs_rand@ --- *
	277	*
	278	* Arguments: @mp *m@ = modulus
	279	* @mp *x@ = initial seed
	280	*
	281	* Returns: Pointer to a generic generator.
	282	*
	283	* Use: Constructs a generic generator interface over a
	284	* Blum-Blum-Shub generator.
	285	*/
	286
	287	extern grand bbs_rand(mp /m/, mp /x*/);
	288
	289	/* --- Blum-Blum-Shub-specific misc op codes --- */
	290
	291	enum {
	292	BBS_SET = GRAND_SPECIFIC /* @mp x@ /
	293	};
	294
	295	/----- That's all, folks -------------------------------------------------/
	296
	297	#ifdef __cplusplus
	298	}
	299	#endif
	300
	301	#endif