[u/mdw/catacomb] / pub / bbs.h

/* -*-c-*-
 *
 * 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.
 */

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

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

extern const key_fetchdef bbs_pubfetch[];
#define BBS_PUBFETCHSZ 3

extern const key_fetchdef bbs_privfetch[];
#define BBS_PRIVFETCHSZ 7

/* --- @bbs_pubfree@, @bbs_privfree@ --- *
 *
 * Arguments:	@bbs_pub *bp@, @bbs_priv *bp@ = pointer to key block
 *
 * Returns:	---
 *
 * Use:		Frees a BBS key block.
 */

extern void bbs_pubfree(bbs_pub */*bp*/);
extern void bbs_privfree(bbs_priv */*bp*/);

/*----- 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,rew}{,n}@ --- *
 *
 * Arguments:	@bbs *b@ = pointer to a BBS generator state
 *		@const bbs_priv *bp@ = pointer to BBS modulus factors
 *		@mp *n@, @unsigned long n@ = number of steps to make
 *
 * Returns:	---
 *
 * Use:		`Fast-forwards' or rewinds a Blum-Blum-Shub generator by @n@
 *		steps.  The @...n@ versions take an @unsigned long@ argument;
 *		the non-@...n@ versions a multiprecision integer.  If @n@ is
 *		negative then the generator is stepped in the reverse
 *		direction.
 */

extern void bbs_ff(bbs */*b*/, const bbs_priv */*bp*/, mp */*n*/);
extern void bbs_ffn(bbs */*b*/, const bbs_priv */*bp*/, unsigned long /*n*/);
extern void bbs_rew(bbs */*b*/, const bbs_priv */*bp*/, mp */*n*/);
extern void bbs_rewn(bbs */*b*/, const bbs_priv */*bp*/, unsigned long /*n*/);

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

/* --- @bbs_gen@ --- *
 *
 * Arguments:	@bbs_priv *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_priv */*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('B'),	/* @mp *x@ */
  BBS_STEP,				/* @void@ */
  BBS_STEPSZ,				/* @void@ */
  BBS_BITS,				/* @unsigned bits, uint32 *w@ */
  BBS_WRAP,				/* @void@ */
  BBS_FF,				/* @bbs_priv *p, mp *n@ */
  BBS_FFN,				/* @bbs_priv *p, unsigned long n@ */
  BBS_REW,				/* @bbs_priv *p, mp *n@ */
  BBS_REWN,				/* @bbs_priv *p, unsigned long n@ */
  BBS_MOD,				/* @mp **n@ */
  BBS_STATE				/* @mp **x@ */
};

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

#ifdef __cplusplus
  }
#endif

#endif
Commit	Line	Data
2c52abe6	1	/* --c--
2c52abe6	2	*
2c52abe6	3	* The Blum-Blum-Shub random bit generator
	4	*
	5	* (c) 1999 Straylight/Edgeware
	6	*/
	7
45c0fd36	8	/----- Licensing notice --------------------------------------------------
2c52abe6	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	*
2c52abe6	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	*
2c52abe6	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
2c52abe6	28	/----- Notes on the BBS generator ----------------------------------------
	29	*
	30	* The Blum-Blum-Shub generator takes the least significant bits from the
	31	* sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of
	32	* two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%.
	33	* For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$%
05cac080	34	* should be coprime. It is safe to use the least significant
	35	* %$\log \log n$% bits of each step in the sequence -- an adversary must
	36	* factor the modulus before being able to work forwards or backwards. The
	37	* output of the generator cannot be distinguished from a (uniform,
	38	* independent) random sequence of bits using any polynomial-time test. This
	39	* is by far the strongest pseudorandom number generator provided in
	40	* Catacomb, and by far the slowest too. For normal use, the standard
	41	* Catacomb @rand@ generator should be more than adequate.
2c52abe6	42	*/
	43
	44	#ifndef CATACOMB_BBS_H
	45	#define CATACOMB_BBS_H
	46
	47	#ifdef __cplusplus
	48	extern "C" {
	49	#endif
	50
	51	/----- Header files ------------------------------------------------------/
	52
	53	#include <mLib/bits.h>
	54
	55	#ifndef CATACOMB_GRAND_H
	56	# include "grand.h"
	57	#endif
	58
05cac080	59	#ifndef CATACOMB_KEY_H
	60	# include "key.h"
	61	#endif
	62
2c52abe6	63	#ifndef CATACOMB_MP_H
	64	# include "mp.h"
	65	#endif
	66
	67	#ifndef CATACOMB_MPBARRETT_H
	68	# include "mpbarrett.h"
	69	#endif
	70
4f743df5	71	#ifndef CATACOMB_PGEN_H
	72	# include "pgen.h"
	73	#endif
	74
2c52abe6	75	/----- Data structures ---------------------------------------------------/
	76
	77	/* --- Basic generator state --- */
	78
	79	typedef struct bbs {
	80	mpbarrett mb; /* Barrett reduction context */
	81	mp x; / Current quadratic residue */
	82	unsigned k; /* Number of bits from each step */
	83	unsigned b; /* Number of bits in reservoir */
	84	mpw r; /* Reservoir of output bits */
	85	} bbs;
	86
	87	/* --- Parameters --- */
	88
05cac080	89	typedef struct bbs_pub {
	90	mp *n;
	91	} bbs_pub;
	92
9083376e	93	typedef struct bbs_priv {
2c52abe6	94	mp p, q; /* Prime factors (3 mod 4) */
2c52abe6	95	mp n; / Product @pq@ -- a Blum integer */
9083376e	96	} bbs_priv;
05cac080	97
	98	/----- Key fetching ------------------------------------------------------/
	99
	100	extern const key_fetchdef bbs_pubfetch[];
	101	#define BBS_PUBFETCHSZ 3
	102
	103	extern const key_fetchdef bbs_privfetch[];
	104	#define BBS_PRIVFETCHSZ 7
2c52abe6	105
9083376e	106	/* --- @bbs_pubfree@, @bbs_privfree@ --- *
	107	*
	108	* Arguments: @bbs_pub bp@, @bbs_priv bp@ = pointer to key block
	109	*
	110	* Returns: ---
	111	*
	112	* Use: Frees a BBS key block.
	113	*/
	114
	115	extern void bbs_pubfree(bbs_pub /bp*/);
	116	extern void bbs_privfree(bbs_priv /bp*/);
	117
2c52abe6	118	/----- The basic generator -----------------------------------------------/
	119
	120	/* --- @bbs_create@ --- *
	121	*
	122	* Arguments: @bbs *b@ = pointer to BBS generator state to initialize
	123	* @mp *m@ = modulus (must be a Blum integer)
	124	* @mp *x@ = initial seed for generator
	125	*
	126	* Returns: ---
	127	*
	128	* Use: Initializes a BBS generator. The generator is stepped once
	129	* after initialization, as for @bbs_seed@.
	130	*/
	131
	132	extern void bbs_create(bbs /b/, mp /m/, mp /x*/);
	133
	134	/* --- @bbs_destroy@ --- *
	135	*
	136	* Arguments: @bbs *b@ = pointer to BBS generator state
	137	*
	138	* Returns: ---
	139	*
	140	* Use: Destroys a generator state when it's no longer wanted.
	141	*/
	142
	143	extern void bbs_destroy(bbs /b*/);
	144
	145	/* --- @bbs_step@ --- *
	146	*
	147	* Arguments: @bbs *b@ = pointer to BBS generator state
	148	*
	149	* Returns: ---
	150	*
	151	* Use: Steps the generator once. This isn't too useful in client
	152	* code.
	153	*/
	154
	155	extern void bbs_step(bbs /b*/);
	156
	157	/* --- @bbs_set@ --- *
	158	*
	159	* Arguments: @bbs *b@ = pointer to BBS generator state
	160	* @mp *x@ = new residue to set
	161	*
	162	* Returns: ---
	163	*
	164	* Use: Sets a new quadratic residue. The generator is stepped once.
	165	*/
	166
	167	extern void bbs_set(bbs /b/, mp /x/);
	168
	169	/* --- @bbs_seed@ --- *
	170	*
	171	* Arguments: @bbs *b@ = pointer to BBS generator state
	172	* @mp *x@ = new seed to set
	173	*
	174	* Returns ---
	175	*
	176	* Use: Sets a new seed. The generator is stepped until the residue
	177	* has clearly wrapped around.
	178	*/
	179
	180	extern void bbs_seed(bbs /b/, mp /x/);
	181
182	/* --- @bbs_bits@ --- *
183	*
184	* Arguments: @bbs *b@ = pointer to BBS generator state
185	* @unsigned bits@ = number of bits wanted
186	*
187	* Returns: Bits extracted from the BBS generator.
188	*
189	* Use: Extracts a requested number of bits from the BBS generator.
190	*/
191
192	extern uint32 bbs_bits(bbs /b/, unsigned /bits*/);
193
194	/* --- @bbs_wrap@ --- *
195	*
196	* Arguments: @bbs *b@ = pointer to BBS generator state
197	*
198	* Returns: ---
199	*
200	* Use: Steps the generator if any of the reservoir bits are used.
201	* This can be used to `wrap up' after a Blum-Goldwasser
202	* encryption, for example, producing the final value to be sent
203	* along with the ciphertext.
204	*
205	* If a generator is seeded, %$b$% bits are extracted, and then
206	* @bbs_wrap@ is called, the generator will have been stepped
05cac080	207	* %$\lceil b/k \rceil$% times.
2c52abe6	208	*/
	209
	210	extern void bbs_wrap(bbs /b*/);
	211
	212	/----- Large forwards and backwards jumps --------------------------------/
	213
2cc3d1d0	214	/* --- @bbs_{ff,rew}{,n}@ --- *
2c52abe6	215	*
2c52abe6	216	* Arguments: @bbs *b@ = pointer to a BBS generator state
2cc3d1d0	217	* @const bbs_priv *bp@ = pointer to BBS modulus factors
2cc3d1d0	218	* @mp *n@, @unsigned long n@ = number of steps to make
2c52abe6	219	*
	220	* Returns: ---
	221	*
2cc3d1d0	222	* Use: `Fast-forwards' or rewinds a Blum-Blum-Shub generator by @n@
	223	* steps. The @...n@ versions take an @unsigned long@ argument;
	224	* the non-@...n@ versions a multiprecision integer. If @n@ is
	225	* negative then the generator is stepped in the reverse
45c0fd36	226	* direction.
2c52abe6	227	*/
2c52abe6	228
2cc3d1d0	229	extern void bbs_ff(bbs /b/, const bbs_priv /bp/, mp /n*/);
	230	extern void bbs_ffn(bbs /b/, const bbs_priv /bp/, unsigned long /n/);
	231	extern void bbs_rew(bbs /b/, const bbs_priv /bp/, mp /n*/);
	232	extern void bbs_rewn(bbs /b/, const bbs_priv /bp/, unsigned long /n/);
2c52abe6	233
	234	/----- Parameter generation ----------------------------------------------/
	235
	236	/* --- @bbs_gen@ --- *
	237	*
9083376e	238	* Arguments: @bbs_priv *bp@ = pointer to parameter block
052b36d0	239	* @unsigned nbits@ = number of bits in the modulus
	240	* @grand *r@ = pointer to random number source
	241	* @unsigned n@ = number of attempts to make
4f743df5	242	* @pgen_proc *event@ = event handler function
4f743df5	243	* @void *ectx@ = argument for event handler
2c52abe6	244	*
4f743df5	245	* Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@.
2c52abe6	246	*
2c52abe6	247	* Use: Finds two prime numbers %$p'$% and %$q'$% such that both are
45c0fd36	248	* congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and
2c52abe6	249	* %$(q - 1)/2$% have no common factors. The product %$n = pq$%
	250	* is eminently suitable for use as a modulus in a Blum-Blum-
	251	* Shub pseudorandom bit generator.
	252	*/
	253
9083376e	254	extern int bbs_gen(bbs_priv /bp/, unsigned /nbits/, grand /r/,
052b36d0	255	unsigned /n/, pgen_proc /event/, void /ectx/);
2c52abe6	256
	257	/----- Generic random number generator interface -------------------------/
	258
	259	/* --- @bbs_rand@ --- *
	260	*
45c0fd36	261	* Arguments: @mp *m@ = modulus
2c52abe6	262	* @mp *x@ = initial seed
2c52abe6	263	*
45c0fd36	264	* Returns: Pointer to a generic generator.
2c52abe6	265	*
45c0fd36	266	* Use: Constructs a generic generator interface over a
2c52abe6	267	* Blum-Blum-Shub generator.
	268	*/
	269
	270	extern grand bbs_rand(mp /m/, mp /x*/);
	271
	272	/* --- Blum-Blum-Shub-specific misc op codes --- */
	273
	274	enum {
2cc3d1d0	275	BBS_SET = GRAND_SPECIFIC('B'), /* @mp x@ /
	276	BBS_STEP, /* @void@ */
	277	BBS_STEPSZ, /* @void@ */
	278	BBS_BITS, /* @unsigned bits, uint32 w@ /
	279	BBS_WRAP, /* @void@ */
	280	BBS_FF, /* @bbs_priv p, mp n@ */
	281	BBS_FFN, /* @bbs_priv p, unsigned long n@ /
	282	BBS_REW, /* @bbs_priv p, mp n@ */
	283	BBS_REWN, /* @bbs_priv p, unsigned long n@ /
	284	BBS_MOD, /* @mp *n@ /
	285	BBS_STATE /* @mp *x@ /
2c52abe6	286	};
	287
	288	/----- That's all, folks -------------------------------------------------/
	289
	290	#ifdef __cplusplus
	291	}
	292	#endif
	293
	294	#endif