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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: bbs.h,v 1.2 1999/12/22 15:52:08 mdw Exp $ |
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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 $ |
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33 | * Revision 1.2 1999/12/22 15:52:08 mdw |
34 | * Rename `bbs_params' to `bbs_param' for consistency. |
35 | * |
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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 | |
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80 | #ifndef CATACOMB_PGEN_H |
81 | # include "pgen.h" |
82 | #endif |
83 | |
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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 | |
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98 | typedef struct bbs_param { |
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99 | mp *p, *q; /* Prime factors (3 mod 4) */ |
100 | mp *n; /* Product @pq@ -- a Blum integer */ |
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101 | } bbs_param; |
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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 |
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202 | * @bbs_param *bp@ = pointer to BBS modulus factors |
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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 | |
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212 | extern void bbs_ff(bbs */*b*/, bbs_param */*bp*/, unsigned long /*n*/); |
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213 | |
214 | /* --- @bbs_rew@ --- * |
215 | * |
216 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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217 | * @bbs_param *bp@ = pointer to BBS modulus factors |
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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 | |
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227 | extern void bbs_rew(bbs */*b*/, bbs_param */*bp*/, unsigned long /*n*/); |
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228 | |
229 | /*----- Parameter generation ----------------------------------------------*/ |
230 | |
231 | /* --- @bbs_gen@ --- * |
232 | * |
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233 | * Arguments: @bbs_param *bp@ = pointer to parameter block |
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234 | * @mp *p, *q@ = initial numbers to search from |
235 | * @size_t n@ = number of attempts to make |
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236 | * @pgen_proc *event@ = event handler function |
237 | * @void *ectx@ = argument for event handler |
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238 | * |
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239 | * Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@. |
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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 | |
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248 | extern int bbs_gen(bbs_param */*bp*/, mp */*p*/, mp */*q*/, size_t /*n*/, |
249 | pgen_proc */*event*/, void */*ectx*/); |
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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 |