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   1 /* -*-c-*-
   2  *
   3  * The Blum-Blum-Shub random bit generator
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   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.
  16  *
  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.
  21  *
  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
  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 %$(q - 1)/1$%
  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.
  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
  59 #ifndef CATACOMB_KEY_H
  60 #  include "key.h"
  61 #endif
  62
  63 #ifndef CATACOMB_MP_H
  64 #  include "mp.h"
  65 #endif
  66
  67 #ifndef CATACOMB_MPBARRETT_H
  68 #  include "mpbarrett.h"
  69 #endif
  70
  71 #ifndef CATACOMB_PGEN_H
  72 #  include "pgen.h"
  73 #endif
  74
  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
  89 typedef struct bbs_pub {
  90   mp *n;
  91 } bbs_pub;
  92
  93 typedef struct bbs_priv {
  94   mp *p, *q;                            /* Prime factors (3 mod 4) */
  95   mp *n;                                /* Product @pq@ -- a Blum integer */
  96 } bbs_priv;
  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
 105
 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
 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
 207  *              %$\lceil b/k \rceil$% times.
 208  */
 209
 210 extern void bbs_wrap(bbs */*b*/);
 211
 212 /*----- Large forwards and backwards jumps --------------------------------*/
 213
 214 /* --- @bbs_{ff,rew}{,n}@ --- *
 215  *
 216  * Arguments:   @bbs *b@ = pointer to a BBS generator state
 217  *              @const bbs_priv *bp@ = pointer to BBS modulus factors
 218  *              @mp *n@, @unsigned long n@ = number of steps to make
 219  *
 220  * Returns:     ---
 221  *
 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
 226  *              direction.
 227  */
 228
 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*/);
 233
 234 /*----- Parameter generation ----------------------------------------------*/
 235
 236 /* --- @bbs_gen@ --- *
 237  *
 238  * Arguments:   @bbs_priv *bp@ = pointer to parameter block
 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
 242  *              @pgen_proc *event@ = event handler function
 243  *              @void *ectx@ = argument for event handler
 244  *
 245  * Returns:     If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@.
 246  *
 247  * Use:         Finds two prime numbers %$p'$% and %$q'$% such that both are
 248  *              congruent to %$3 \bmod 4$%, and  $(p - 1)/2$% and
 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
 254 extern int bbs_gen(bbs_priv */*bp*/, unsigned /*nbits*/, grand */*r*/,
 255                    unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/);
 256
 257 /*----- Generic random number generator interface -------------------------*/
 258
 259 /* --- @bbs_rand@ --- *
 260  *
 261  * Arguments:   @mp *m@ = modulus
 262  *              @mp *x@ = initial seed
 263  *
 264  * Returns:     Pointer to a generic generator.
 265  *
 266  * Use:         Constructs a generic generator interface over a
 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 {
 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@ */
 286 };
 287
 288 /*----- That's all, folks -------------------------------------------------*/
 289
 290 #ifdef __cplusplus
 291   }
 292 #endif
 293
 294 #endif