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1 | /* -*-c-*- |
2 | * |
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3 | * $Id$ |
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4 | * |
5 | * The Blum-Blum-Shub random bit generator |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
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10 | /*----- Licensing notice --------------------------------------------------* |
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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. |
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18 | * |
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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. |
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23 | * |
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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 | |
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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 %$(q - 1)/1$% |
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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. |
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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 | |
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61 | #ifndef CATACOMB_KEY_H |
62 | # include "key.h" |
63 | #endif |
64 | |
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65 | #ifndef CATACOMB_MP_H |
66 | # include "mp.h" |
67 | #endif |
68 | |
69 | #ifndef CATACOMB_MPBARRETT_H |
70 | # include "mpbarrett.h" |
71 | #endif |
72 | |
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73 | #ifndef CATACOMB_PGEN_H |
74 | # include "pgen.h" |
75 | #endif |
76 | |
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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 | |
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91 | typedef struct bbs_pub { |
92 | mp *n; |
93 | } bbs_pub; |
94 | |
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95 | typedef struct bbs_priv { |
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96 | mp *p, *q; /* Prime factors (3 mod 4) */ |
97 | mp *n; /* Product @pq@ -- a Blum integer */ |
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98 | } bbs_priv; |
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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 |
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107 | |
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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 | |
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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 |
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209 | * %$\lceil b/k \rceil$% times. |
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210 | */ |
211 | |
212 | extern void bbs_wrap(bbs */*b*/); |
213 | |
214 | /*----- Large forwards and backwards jumps --------------------------------*/ |
215 | |
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216 | /* --- @bbs_{ff,rew}{,n}@ --- * |
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217 | * |
218 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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219 | * @const bbs_priv *bp@ = pointer to BBS modulus factors |
220 | * @mp *n@, @unsigned long n@ = number of steps to make |
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221 | * |
222 | * Returns: --- |
223 | * |
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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 |
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228 | * direction. |
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229 | */ |
230 | |
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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*/); |
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235 | |
236 | /*----- Parameter generation ----------------------------------------------*/ |
237 | |
238 | /* --- @bbs_gen@ --- * |
239 | * |
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240 | * Arguments: @bbs_priv *bp@ = pointer to parameter block |
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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 |
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244 | * @pgen_proc *event@ = event handler function |
245 | * @void *ectx@ = argument for event handler |
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246 | * |
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247 | * Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@. |
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248 | * |
249 | * Use: Finds two prime numbers %$p'$% and %$q'$% such that both are |
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250 | * congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and |
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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 | |
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256 | extern int bbs_gen(bbs_priv */*bp*/, unsigned /*nbits*/, grand */*r*/, |
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257 | unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/); |
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258 | |
259 | /*----- Generic random number generator interface -------------------------*/ |
260 | |
261 | /* --- @bbs_rand@ --- * |
262 | * |
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263 | * Arguments: @mp *m@ = modulus |
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264 | * @mp *x@ = initial seed |
265 | * |
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266 | * Returns: Pointer to a generic generator. |
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267 | * |
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268 | * Use: Constructs a generic generator interface over a |
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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 { |
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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@ */ |
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288 | }; |
289 | |
290 | /*----- That's all, folks -------------------------------------------------*/ |
291 | |
292 | #ifdef __cplusplus |
293 | } |
294 | #endif |
295 | |
296 | #endif |