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