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   1 /* -*-c-*-
   2  *
   3  * $Id: bbs.h,v 1.5 2000/07/01 11:20:24 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 1.5  2000/07/01 11:20:24  mdw
  34  * New functions for freeing public and private keys.  Remove bad type name
  35  * `bbs_param'.
  36  *
  37  * Revision 1.4  2000/06/17 10:45:48  mdw
  38  * Minor changes for key fetching.  Typesetting fixes.
  39  *
  40  * Revision 1.3  2000/02/12 18:21:02  mdw
  41  * Overhaul of key management (again).
  42  *
  43  * Revision 1.2  1999/12/22 15:52:08  mdw
  44  * Rename `bbs_params' to `bbs_param' for consistency.
  45  *
  46  * Revision 1.1  1999/12/10 23:14:59  mdw
  47  * Blum-Blum-Shub generator, and Blum-Goldwasser encryption.
  48  *
  49  */
  50
  51 /*----- Notes on the BBS generator ----------------------------------------*
  52  *
  53  * The Blum-Blum-Shub generator takes the least significant bits from the
  54  * sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of
  55  * two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%.
  56  * For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$%
  57  * should be coprime.  It is safe to use the least significant
  58  * %$\log \log n$% bits of each step in the sequence -- an adversary must
  59  * factor the modulus before being able to work forwards or backwards.  The
  60  * output of the generator cannot be distinguished from a (uniform,
  61  * independent) random sequence of bits using any polynomial-time test.  This
  62  * is by far the strongest pseudorandom number generator provided in
  63  * Catacomb, and by far the slowest too.  For normal use, the standard
  64  * Catacomb @rand@ generator should be more than adequate.
  65  */
  66
  67 #ifndef CATACOMB_BBS_H
  68 #define CATACOMB_BBS_H
  69
  70 #ifdef __cplusplus
  71   extern "C" {
  72 #endif
  73
  74 /*----- Header files ------------------------------------------------------*/
  75
  76 #include <mLib/bits.h>
  77
  78 #ifndef CATACOMB_GRAND_H
  79 #  include "grand.h"
  80 #endif
  81
  82 #ifndef CATACOMB_KEY_H
  83 #  include "key.h"
  84 #endif
  85
  86 #ifndef CATACOMB_MP_H
  87 #  include "mp.h"
  88 #endif
  89
  90 #ifndef CATACOMB_MPBARRETT_H
  91 #  include "mpbarrett.h"
  92 #endif
  93
  94 #ifndef CATACOMB_PGEN_H
  95 #  include "pgen.h"
  96 #endif
  97
  98 /*----- Data structures ---------------------------------------------------*/
  99
 100 /* --- Basic generator state --- */
 101
 102 typedef struct bbs {
 103   mpbarrett mb;                         /* Barrett reduction context */
 104   mp *x;                                /* Current quadratic residue */
 105   unsigned k;                           /* Number of bits from each step */
 106   unsigned b;                           /* Number of bits in reservoir */
 107   mpw r;                                /* Reservoir of output bits */
 108 } bbs;
 109
 110 /* --- Parameters --- */
 111
 112 typedef struct bbs_pub {
 113   mp *n;
 114 } bbs_pub;
 115
 116 typedef struct bbs_priv {
 117   mp *p, *q;                            /* Prime factors (3 mod 4) */
 118   mp *n;                                /* Product @pq@ -- a Blum integer */
 119 } bbs_priv;
 120
 121 /*----- Key fetching ------------------------------------------------------*/
 122
 123 extern const key_fetchdef bbs_pubfetch[];
 124 #define BBS_PUBFETCHSZ 3
 125
 126 extern const key_fetchdef bbs_privfetch[];
 127 #define BBS_PRIVFETCHSZ 7
 128
 129 /* --- @bbs_pubfree@, @bbs_privfree@ --- *
 130  *
 131  * Arguments:   @bbs_pub *bp@, @bbs_priv *bp@ = pointer to key block
 132  *
 133  * Returns:     ---
 134  *
 135  * Use:         Frees a BBS key block.
 136  */
 137
 138 extern void bbs_pubfree(bbs_pub */*bp*/);
 139 extern void bbs_privfree(bbs_priv */*bp*/);
 140
 141 /*----- The basic generator -----------------------------------------------*/
 142
 143 /* --- @bbs_create@ --- *
 144  *
 145  * Arguments:   @bbs *b@ = pointer to BBS generator state to initialize
 146  *              @mp *m@ = modulus (must be a Blum integer)
 147  *              @mp *x@ = initial seed for generator
 148  *
 149  * Returns:     ---
 150  *
 151  * Use:         Initializes a BBS generator.  The generator is stepped once
 152  *              after initialization, as for @bbs_seed@.
 153  */
 154
 155 extern void bbs_create(bbs */*b*/, mp */*m*/, mp */*x*/);
 156
 157 /* --- @bbs_destroy@ --- *
 158  *
 159  * Arguments:   @bbs *b@ = pointer to BBS generator state
 160  *
 161  * Returns:     ---
 162  *
 163  * Use:         Destroys a generator state when it's no longer wanted.
 164  */
 165
 166 extern void bbs_destroy(bbs */*b*/);
 167
 168 /* --- @bbs_step@ --- *
 169  *
 170  * Arguments:   @bbs *b@ = pointer to BBS generator state
 171  *
 172  * Returns:     ---
 173  *
 174  * Use:         Steps the generator once.  This isn't too useful in client
 175  *              code.
 176  */
 177
 178 extern void bbs_step(bbs */*b*/);
 179
 180 /* --- @bbs_set@ --- *
 181  *
 182  * Arguments:   @bbs *b@ = pointer to BBS generator state
 183  *              @mp *x@ = new residue to set
 184  *
 185  * Returns:     ---
 186  *
 187  * Use:         Sets a new quadratic residue.  The generator is stepped once.
 188  */
 189
 190 extern void bbs_set(bbs */*b*/, mp */*x*/);
 191
 192 /* --- @bbs_seed@ --- *
 193  *
 194  * Arguments:   @bbs *b@ = pointer to BBS generator state
 195  *              @mp *x@ = new seed to set
 196  *
 197  * Returns      ---
 198  *
 199  * Use:         Sets a new seed.  The generator is stepped until the residue
 200  *              has clearly wrapped around.
 201  */
 202
 203 extern void bbs_seed(bbs */*b*/, mp */*x*/);
 204
 205 /* --- @bbs_bits@ --- *
 206  *
 207  * Arguments:   @bbs *b@ = pointer to BBS generator state
 208  *              @unsigned bits@ = number of bits wanted
 209  *
 210  * Returns:     Bits extracted from the BBS generator.
 211  *
 212  * Use:         Extracts a requested number of bits from the BBS generator.
 213  */
 214
 215 extern uint32 bbs_bits(bbs */*b*/, unsigned /*bits*/);
 216
 217 /* --- @bbs_wrap@ --- *
 218  *
 219  * Arguments:   @bbs *b@ = pointer to BBS generator state
 220  *
 221  * Returns:     ---
 222  *
 223  * Use:         Steps the generator if any of the reservoir bits are used.
 224  *              This can be used to `wrap up' after a Blum-Goldwasser
 225  *              encryption, for example, producing the final value to be sent
 226  *              along with the ciphertext.
 227  *
 228  *              If a generator is seeded, %$b$% bits are extracted, and then
 229  *              @bbs_wrap@ is called, the generator will have been stepped
 230  *              %$\lceil b/k \rceil$% times.
 231  */
 232
 233 extern void bbs_wrap(bbs */*b*/);
 234
 235 /*----- Large forwards and backwards jumps --------------------------------*/
 236
 237 /* --- @bbs_ff@ --- *
 238  *
 239  * Arguments:   @bbs *b@ = pointer to a BBS generator state
 240  *              @bbs_priv *bp@ = pointer to BBS modulus factors
 241  *              @unsigned long n@ = number of steps to make
 242  *
 243  * Returns:     ---
 244  *
 245  * Use:         `Fast-forwards' a Blum-Blum-Shub generator by @n@ steps.
 246  *              Requires the factorization of the Blum modulus to do this
 247  *              efficiently.
 248  */
 249
 250 extern void bbs_ff(bbs */*b*/, bbs_priv */*bp*/, unsigned long /*n*/);
 251
 252 /* --- @bbs_rew@ --- *
 253  *
 254  * Arguments:   @bbs *b@ = pointer to a BBS generator state
 255  *              @bbs_priv *bp@ = pointer to BBS modulus factors
 256  *              @unsigned long n@ = number of steps to make
 257  *
 258  * Returns:     ---
 259  *
 260  * Use:         `Rewinds' a Blum-Blum-Shub generator by @n@ steps.
 261  *              Requires the factorization of the Blum modulus to do this
 262  *              at all.
 263  */
 264
 265 extern void bbs_rew(bbs */*b*/, bbs_priv */*bp*/, unsigned long /*n*/);
 266
 267 /*----- Parameter generation ----------------------------------------------*/
 268
 269 /* --- @bbs_gen@ --- *
 270  *
 271  * Arguments:   @bbs_priv *bp@ = pointer to parameter block
 272  *              @unsigned nbits@ = number of bits in the modulus
 273  *              @grand *r@ = pointer to random number source
 274  *              @unsigned n@ = number of attempts to make
 275  *              @pgen_proc *event@ = event handler function
 276  *              @void *ectx@ = argument for event handler
 277  *
 278  * Returns:     If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@.
 279  *
 280  * Use:         Finds two prime numbers %$p'$% and %$q'$% such that both are
 281  *              congruent to %$3 \bmod 4$%, and  $(p - 1)/2$% and
 282  *              %$(q - 1)/2$% have no common factors.  The product %$n = pq$%
 283  *              is eminently suitable for use as a modulus in a Blum-Blum-
 284  *              Shub pseudorandom bit generator.
 285  */
 286
 287 extern int bbs_gen(bbs_priv */*bp*/, unsigned /*nbits*/, grand */*r*/,
 288                    unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/);
 289
 290 /*----- Generic random number generator interface -------------------------*/
 291
 292 /* --- @bbs_rand@ --- *
 293  *
 294  * Arguments:   @mp *m@ = modulus
 295  *              @mp *x@ = initial seed
 296  *
 297  * Returns:     Pointer to a generic generator.
 298  *
 299  * Use:         Constructs a generic generator interface over a
 300  *              Blum-Blum-Shub generator.
 301  */
 302
 303 extern grand *bbs_rand(mp */*m*/, mp */*x*/);
 304
 305 /* --- Blum-Blum-Shub-specific misc op codes --- */
 306
 307 enum {
 308   BBS_SET = GRAND_SPECIFIC              /* @mp *x@ */
 309 };
 310
 311 /*----- That's all, folks -------------------------------------------------*/
 312
 313 #ifdef __cplusplus
 314   }
 315 #endif
 316
 317 #endif