| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id$ |
| 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 | /*----- Notes on the BBS generator ----------------------------------------* |
| 31 | * |
| 32 | * The Blum-Blum-Shub generator takes the least significant bits from the |
| 33 | * sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of |
| 34 | * two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%. |
| 35 | * For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$% |
| 36 | * should be coprime. It is safe to use the least significant |
| 37 | * %$\log \log n$% bits of each step in the sequence -- an adversary must |
| 38 | * factor the modulus before being able to work forwards or backwards. The |
| 39 | * output of the generator cannot be distinguished from a (uniform, |
| 40 | * independent) random sequence of bits using any polynomial-time test. This |
| 41 | * is by far the strongest pseudorandom number generator provided in |
| 42 | * Catacomb, and by far the slowest too. For normal use, the standard |
| 43 | * Catacomb @rand@ generator should be more than adequate. |
| 44 | */ |
| 45 | |
| 46 | #ifndef CATACOMB_BBS_H |
| 47 | #define CATACOMB_BBS_H |
| 48 | |
| 49 | #ifdef __cplusplus |
| 50 | extern "C" { |
| 51 | #endif |
| 52 | |
| 53 | /*----- Header files ------------------------------------------------------*/ |
| 54 | |
| 55 | #include <mLib/bits.h> |
| 56 | |
| 57 | #ifndef CATACOMB_GRAND_H |
| 58 | # include "grand.h" |
| 59 | #endif |
| 60 | |
| 61 | #ifndef CATACOMB_KEY_H |
| 62 | # include "key.h" |
| 63 | #endif |
| 64 | |
| 65 | #ifndef CATACOMB_MP_H |
| 66 | # include "mp.h" |
| 67 | #endif |
| 68 | |
| 69 | #ifndef CATACOMB_MPBARRETT_H |
| 70 | # include "mpbarrett.h" |
| 71 | #endif |
| 72 | |
| 73 | #ifndef CATACOMB_PGEN_H |
| 74 | # include "pgen.h" |
| 75 | #endif |
| 76 | |
| 77 | /*----- Data structures ---------------------------------------------------*/ |
| 78 | |
| 79 | /* --- Basic generator state --- */ |
| 80 | |
| 81 | typedef struct bbs { |
| 82 | mpbarrett mb; /* Barrett reduction context */ |
| 83 | mp *x; /* Current quadratic residue */ |
| 84 | unsigned k; /* Number of bits from each step */ |
| 85 | unsigned b; /* Number of bits in reservoir */ |
| 86 | mpw r; /* Reservoir of output bits */ |
| 87 | } bbs; |
| 88 | |
| 89 | /* --- Parameters --- */ |
| 90 | |
| 91 | typedef struct bbs_pub { |
| 92 | mp *n; |
| 93 | } bbs_pub; |
| 94 | |
| 95 | typedef struct bbs_priv { |
| 96 | mp *p, *q; /* Prime factors (3 mod 4) */ |
| 97 | mp *n; /* Product @pq@ -- a Blum integer */ |
| 98 | } bbs_priv; |
| 99 | |
| 100 | /*----- Key fetching ------------------------------------------------------*/ |
| 101 | |
| 102 | extern const key_fetchdef bbs_pubfetch[]; |
| 103 | #define BBS_PUBFETCHSZ 3 |
| 104 | |
| 105 | extern const key_fetchdef bbs_privfetch[]; |
| 106 | #define BBS_PRIVFETCHSZ 7 |
| 107 | |
| 108 | /* --- @bbs_pubfree@, @bbs_privfree@ --- * |
| 109 | * |
| 110 | * Arguments: @bbs_pub *bp@, @bbs_priv *bp@ = pointer to key block |
| 111 | * |
| 112 | * Returns: --- |
| 113 | * |
| 114 | * Use: Frees a BBS key block. |
| 115 | */ |
| 116 | |
| 117 | extern void bbs_pubfree(bbs_pub */*bp*/); |
| 118 | extern void bbs_privfree(bbs_priv */*bp*/); |
| 119 | |
| 120 | /*----- The basic generator -----------------------------------------------*/ |
| 121 | |
| 122 | /* --- @bbs_create@ --- * |
| 123 | * |
| 124 | * Arguments: @bbs *b@ = pointer to BBS generator state to initialize |
| 125 | * @mp *m@ = modulus (must be a Blum integer) |
| 126 | * @mp *x@ = initial seed for generator |
| 127 | * |
| 128 | * Returns: --- |
| 129 | * |
| 130 | * Use: Initializes a BBS generator. The generator is stepped once |
| 131 | * after initialization, as for @bbs_seed@. |
| 132 | */ |
| 133 | |
| 134 | extern void bbs_create(bbs */*b*/, mp */*m*/, mp */*x*/); |
| 135 | |
| 136 | /* --- @bbs_destroy@ --- * |
| 137 | * |
| 138 | * Arguments: @bbs *b@ = pointer to BBS generator state |
| 139 | * |
| 140 | * Returns: --- |
| 141 | * |
| 142 | * Use: Destroys a generator state when it's no longer wanted. |
| 143 | */ |
| 144 | |
| 145 | extern void bbs_destroy(bbs */*b*/); |
| 146 | |
| 147 | /* --- @bbs_step@ --- * |
| 148 | * |
| 149 | * Arguments: @bbs *b@ = pointer to BBS generator state |
| 150 | * |
| 151 | * Returns: --- |
| 152 | * |
| 153 | * Use: Steps the generator once. This isn't too useful in client |
| 154 | * code. |
| 155 | */ |
| 156 | |
| 157 | extern void bbs_step(bbs */*b*/); |
| 158 | |
| 159 | /* --- @bbs_set@ --- * |
| 160 | * |
| 161 | * Arguments: @bbs *b@ = pointer to BBS generator state |
| 162 | * @mp *x@ = new residue to set |
| 163 | * |
| 164 | * Returns: --- |
| 165 | * |
| 166 | * Use: Sets a new quadratic residue. The generator is stepped once. |
| 167 | */ |
| 168 | |
| 169 | extern void bbs_set(bbs */*b*/, mp */*x*/); |
| 170 | |
| 171 | /* --- @bbs_seed@ --- * |
| 172 | * |
| 173 | * Arguments: @bbs *b@ = pointer to BBS generator state |
| 174 | * @mp *x@ = new seed to set |
| 175 | * |
| 176 | * Returns --- |
| 177 | * |
| 178 | * Use: Sets a new seed. The generator is stepped until the residue |
| 179 | * has clearly wrapped around. |
| 180 | */ |
| 181 | |
| 182 | extern void bbs_seed(bbs */*b*/, mp */*x*/); |
| 183 | |
| 184 | /* --- @bbs_bits@ --- * |
| 185 | * |
| 186 | * Arguments: @bbs *b@ = pointer to BBS generator state |
| 187 | * @unsigned bits@ = number of bits wanted |
| 188 | * |
| 189 | * Returns: Bits extracted from the BBS generator. |
| 190 | * |
| 191 | * Use: Extracts a requested number of bits from the BBS generator. |
| 192 | */ |
| 193 | |
| 194 | extern uint32 bbs_bits(bbs */*b*/, unsigned /*bits*/); |
| 195 | |
| 196 | /* --- @bbs_wrap@ --- * |
| 197 | * |
| 198 | * Arguments: @bbs *b@ = pointer to BBS generator state |
| 199 | * |
| 200 | * Returns: --- |
| 201 | * |
| 202 | * Use: Steps the generator if any of the reservoir bits are used. |
| 203 | * This can be used to `wrap up' after a Blum-Goldwasser |
| 204 | * encryption, for example, producing the final value to be sent |
| 205 | * along with the ciphertext. |
| 206 | * |
| 207 | * If a generator is seeded, %$b$% bits are extracted, and then |
| 208 | * @bbs_wrap@ is called, the generator will have been stepped |
| 209 | * %$\lceil b/k \rceil$% times. |
| 210 | */ |
| 211 | |
| 212 | extern void bbs_wrap(bbs */*b*/); |
| 213 | |
| 214 | /*----- Large forwards and backwards jumps --------------------------------*/ |
| 215 | |
| 216 | /* --- @bbs_{ff,rew}{,n}@ --- * |
| 217 | * |
| 218 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
| 219 | * @const bbs_priv *bp@ = pointer to BBS modulus factors |
| 220 | * @mp *n@, @unsigned long n@ = number of steps to make |
| 221 | * |
| 222 | * Returns: --- |
| 223 | * |
| 224 | * Use: `Fast-forwards' or rewinds a Blum-Blum-Shub generator by @n@ |
| 225 | * steps. The @...n@ versions take an @unsigned long@ argument; |
| 226 | * the non-@...n@ versions a multiprecision integer. If @n@ is |
| 227 | * negative then the generator is stepped in the reverse |
| 228 | * direction. |
| 229 | */ |
| 230 | |
| 231 | extern void bbs_ff(bbs */*b*/, const bbs_priv */*bp*/, mp */*n*/); |
| 232 | extern void bbs_ffn(bbs */*b*/, const bbs_priv */*bp*/, unsigned long /*n*/); |
| 233 | extern void bbs_rew(bbs */*b*/, const bbs_priv */*bp*/, mp */*n*/); |
| 234 | extern void bbs_rewn(bbs */*b*/, const bbs_priv */*bp*/, unsigned long /*n*/); |
| 235 | |
| 236 | /*----- Parameter generation ----------------------------------------------*/ |
| 237 | |
| 238 | /* --- @bbs_gen@ --- * |
| 239 | * |
| 240 | * Arguments: @bbs_priv *bp@ = pointer to parameter block |
| 241 | * @unsigned nbits@ = number of bits in the modulus |
| 242 | * @grand *r@ = pointer to random number source |
| 243 | * @unsigned n@ = number of attempts to make |
| 244 | * @pgen_proc *event@ = event handler function |
| 245 | * @void *ectx@ = argument for event handler |
| 246 | * |
| 247 | * Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@. |
| 248 | * |
| 249 | * Use: Finds two prime numbers %$p'$% and %$q'$% such that both are |
| 250 | * congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and |
| 251 | * %$(q - 1)/2$% have no common factors. The product %$n = pq$% |
| 252 | * is eminently suitable for use as a modulus in a Blum-Blum- |
| 253 | * Shub pseudorandom bit generator. |
| 254 | */ |
| 255 | |
| 256 | extern int bbs_gen(bbs_priv */*bp*/, unsigned /*nbits*/, grand */*r*/, |
| 257 | unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/); |
| 258 | |
| 259 | /*----- Generic random number generator interface -------------------------*/ |
| 260 | |
| 261 | /* --- @bbs_rand@ --- * |
| 262 | * |
| 263 | * Arguments: @mp *m@ = modulus |
| 264 | * @mp *x@ = initial seed |
| 265 | * |
| 266 | * Returns: Pointer to a generic generator. |
| 267 | * |
| 268 | * Use: Constructs a generic generator interface over a |
| 269 | * Blum-Blum-Shub generator. |
| 270 | */ |
| 271 | |
| 272 | extern grand *bbs_rand(mp */*m*/, mp */*x*/); |
| 273 | |
| 274 | /* --- Blum-Blum-Shub-specific misc op codes --- */ |
| 275 | |
| 276 | enum { |
| 277 | BBS_SET = GRAND_SPECIFIC('B'), /* @mp *x@ */ |
| 278 | BBS_STEP, /* @void@ */ |
| 279 | BBS_STEPSZ, /* @void@ */ |
| 280 | BBS_BITS, /* @unsigned bits, uint32 *w@ */ |
| 281 | BBS_WRAP, /* @void@ */ |
| 282 | BBS_FF, /* @bbs_priv *p, mp *n@ */ |
| 283 | BBS_FFN, /* @bbs_priv *p, unsigned long n@ */ |
| 284 | BBS_REW, /* @bbs_priv *p, mp *n@ */ |
| 285 | BBS_REWN, /* @bbs_priv *p, unsigned long n@ */ |
| 286 | BBS_MOD, /* @mp **n@ */ |
| 287 | BBS_STATE /* @mp **x@ */ |
| 288 | }; |
| 289 | |
| 290 | /*----- That's all, folks -------------------------------------------------*/ |
| 291 | |
| 292 | #ifdef __cplusplus |
| 293 | } |
| 294 | #endif |
| 295 | |
| 296 | #endif |