2c52abe6 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: bbs.h,v 1.1 1999/12/10 23:14:59 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 1.1 1999/12/10 23:14:59 mdw |
34 | * Blum-Blum-Shub generator, and Blum-Goldwasser encryption. |
35 | * |
36 | */ |
37 | |
38 | /*----- Notes on the BBS generator ----------------------------------------* |
39 | * |
40 | * The Blum-Blum-Shub generator takes the least significant bits from the |
41 | * sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of |
42 | * two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%. |
43 | * For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$% |
44 | * should be coprime. It is safe to use the least significant %$\log \log |
45 | * n$% bits of each step in the sequence -- an adversary must factor the |
46 | * modulus before being able to work forwards or backwards. The output of |
47 | * the generator cannot be distinguished from a (uniform, independent) random |
48 | * sequence of bits using any polynomial-time test. This is by far the |
49 | * strongest pseudorandom number generator provided in Catacomb, and by far |
50 | * the slowest too. For normal use, the standard Catacomb @rand@ generator |
51 | * should be more than adequate. |
52 | */ |
53 | |
54 | #ifndef CATACOMB_BBS_H |
55 | #define CATACOMB_BBS_H |
56 | |
57 | #ifdef __cplusplus |
58 | extern "C" { |
59 | #endif |
60 | |
61 | /*----- Header files ------------------------------------------------------*/ |
62 | |
63 | #include <mLib/bits.h> |
64 | |
65 | #ifndef CATACOMB_GRAND_H |
66 | # include "grand.h" |
67 | #endif |
68 | |
69 | #ifndef CATACOMB_MP_H |
70 | # include "mp.h" |
71 | #endif |
72 | |
73 | #ifndef CATACOMB_MPBARRETT_H |
74 | # include "mpbarrett.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_params { |
92 | mp *p, *q; /* Prime factors (3 mod 4) */ |
93 | mp *n; /* Product @pq@ -- a Blum integer */ |
94 | } bbs_params; |
95 | |
96 | /*----- Event codes from @bbs_gen@ ----------------------------------------*/ |
97 | |
98 | enum { |
99 | BBSEV_OK, |
100 | |
101 | BBSEV_FINDP, |
102 | BBSEV_TRYP, |
103 | BBSEV_PASSP, |
104 | BBSEV_FAILP, |
105 | BBSEV_GOODP, |
106 | |
107 | BBSEV_FINDQ, |
108 | BBSEV_TRYQ, |
109 | BBSEV_PASSQ, |
110 | BBSEV_FAILQ, |
111 | BBSEV_GOODQ |
112 | }; |
113 | |
114 | /*----- The basic generator -----------------------------------------------*/ |
115 | |
116 | /* --- @bbs_create@ --- * |
117 | * |
118 | * Arguments: @bbs *b@ = pointer to BBS generator state to initialize |
119 | * @mp *m@ = modulus (must be a Blum integer) |
120 | * @mp *x@ = initial seed for generator |
121 | * |
122 | * Returns: --- |
123 | * |
124 | * Use: Initializes a BBS generator. The generator is stepped once |
125 | * after initialization, as for @bbs_seed@. |
126 | */ |
127 | |
128 | extern void bbs_create(bbs */*b*/, mp */*m*/, mp */*x*/); |
129 | |
130 | /* --- @bbs_destroy@ --- * |
131 | * |
132 | * Arguments: @bbs *b@ = pointer to BBS generator state |
133 | * |
134 | * Returns: --- |
135 | * |
136 | * Use: Destroys a generator state when it's no longer wanted. |
137 | */ |
138 | |
139 | extern void bbs_destroy(bbs */*b*/); |
140 | |
141 | /* --- @bbs_step@ --- * |
142 | * |
143 | * Arguments: @bbs *b@ = pointer to BBS generator state |
144 | * |
145 | * Returns: --- |
146 | * |
147 | * Use: Steps the generator once. This isn't too useful in client |
148 | * code. |
149 | */ |
150 | |
151 | extern void bbs_step(bbs */*b*/); |
152 | |
153 | /* --- @bbs_set@ --- * |
154 | * |
155 | * Arguments: @bbs *b@ = pointer to BBS generator state |
156 | * @mp *x@ = new residue to set |
157 | * |
158 | * Returns: --- |
159 | * |
160 | * Use: Sets a new quadratic residue. The generator is stepped once. |
161 | */ |
162 | |
163 | extern void bbs_set(bbs */*b*/, mp */*x*/); |
164 | |
165 | /* --- @bbs_seed@ --- * |
166 | * |
167 | * Arguments: @bbs *b@ = pointer to BBS generator state |
168 | * @mp *x@ = new seed to set |
169 | * |
170 | * Returns --- |
171 | * |
172 | * Use: Sets a new seed. The generator is stepped until the residue |
173 | * has clearly wrapped around. |
174 | */ |
175 | |
176 | extern void bbs_seed(bbs */*b*/, mp */*x*/); |
177 | |
178 | /* --- @bbs_bits@ --- * |
179 | * |
180 | * Arguments: @bbs *b@ = pointer to BBS generator state |
181 | * @unsigned bits@ = number of bits wanted |
182 | * |
183 | * Returns: Bits extracted from the BBS generator. |
184 | * |
185 | * Use: Extracts a requested number of bits from the BBS generator. |
186 | */ |
187 | |
188 | extern uint32 bbs_bits(bbs */*b*/, unsigned /*bits*/); |
189 | |
190 | /* --- @bbs_wrap@ --- * |
191 | * |
192 | * Arguments: @bbs *b@ = pointer to BBS generator state |
193 | * |
194 | * Returns: --- |
195 | * |
196 | * Use: Steps the generator if any of the reservoir bits are used. |
197 | * This can be used to `wrap up' after a Blum-Goldwasser |
198 | * encryption, for example, producing the final value to be sent |
199 | * along with the ciphertext. |
200 | * |
201 | * If a generator is seeded, %$b$% bits are extracted, and then |
202 | * @bbs_wrap@ is called, the generator will have been stepped |
203 | * %$\lceil b/k \rceil% times. |
204 | */ |
205 | |
206 | extern void bbs_wrap(bbs */*b*/); |
207 | |
208 | /*----- Large forwards and backwards jumps --------------------------------*/ |
209 | |
210 | /* --- @bbs_ff@ --- * |
211 | * |
212 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
213 | * @bbs_params *bp@ = pointer to BBS modulus factors |
214 | * @unsigned long n@ = number of steps to make |
215 | * |
216 | * Returns: --- |
217 | * |
218 | * Use: `Fast-forwards' a Blum-Blum-Shub generator by @n@ steps. |
219 | * Requires the factorization of the Blum modulus to do this |
220 | * efficiently. |
221 | */ |
222 | |
223 | extern void bbs_ff(bbs */*b*/, bbs_params */*bp*/, unsigned long /*n*/); |
224 | |
225 | /* --- @bbs_rew@ --- * |
226 | * |
227 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
228 | * @bbs_params *bp@ = pointer to BBS modulus factors |
229 | * @unsigned long n@ = number of steps to make |
230 | * |
231 | * Returns: --- |
232 | * |
233 | * Use: `Rewinds' a Blum-Blum-Shub generator by @n@ steps. |
234 | * Requires the factorization of the Blum modulus to do this |
235 | * at all. |
236 | */ |
237 | |
238 | extern void bbs_rew(bbs */*b*/, bbs_params */*bp*/, unsigned long /*n*/); |
239 | |
240 | /*----- Parameter generation ----------------------------------------------*/ |
241 | |
242 | /* --- @bbs_gen@ --- * |
243 | * |
244 | * Arguments: @bbs_params *bp@ = pointer to parameter block |
245 | * @mp *p, *q@ = initial numbers to search from |
246 | * @size_t n@ = number of attempts to make |
247 | * @void (*proc)(int ev, mp *m, void *p)@ = event handler |
248 | * @void *arg@ = argument for event handler |
249 | * |
250 | * Returns: Zero if all went well, otherwise an event code which explains |
251 | * the problem. |
252 | * |
253 | * Use: Finds two prime numbers %$p'$% and %$q'$% such that both are |
254 | * congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and |
255 | * %$(q - 1)/2$% have no common factors. The product %$n = pq$% |
256 | * is eminently suitable for use as a modulus in a Blum-Blum- |
257 | * Shub pseudorandom bit generator. |
258 | */ |
259 | |
260 | extern int bbs_gen(bbs_params */*bp*/, mp */*p*/, mp */*q*/, size_t /*n*/, |
261 | int (*/*proc*/)(int /*ev*/, mp */*m*/, void */*p*/), |
262 | void */*arg*/); |
263 | |
264 | /*----- Generic random number generator interface -------------------------*/ |
265 | |
266 | /* --- @bbs_rand@ --- * |
267 | * |
268 | * Arguments: @mp *m@ = modulus |
269 | * @mp *x@ = initial seed |
270 | * |
271 | * Returns: Pointer to a generic generator. |
272 | * |
273 | * Use: Constructs a generic generator interface over a |
274 | * Blum-Blum-Shub generator. |
275 | */ |
276 | |
277 | extern grand *bbs_rand(mp */*m*/, mp */*x*/); |
278 | |
279 | /* --- Blum-Blum-Shub-specific misc op codes --- */ |
280 | |
281 | enum { |
282 | BBS_SET = GRAND_SPECIFIC /* @mp *x@ */ |
283 | }; |
284 | |
285 | /*----- That's all, folks -------------------------------------------------*/ |
286 | |
287 | #ifdef __cplusplus |
288 | } |
289 | #endif |
290 | |
291 | #endif |