2c52abe6 |
1 | /* -*-c-*- |
2 | * |
05cac080 |
3 | * $Id: bbs.h,v 1.4 2000/06/17 10:45:48 mdw Exp $ |
2c52abe6 |
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 $ |
05cac080 |
33 | * Revision 1.4 2000/06/17 10:45:48 mdw |
34 | * Minor changes for key fetching. Typesetting fixes. |
35 | * |
052b36d0 |
36 | * Revision 1.3 2000/02/12 18:21:02 mdw |
37 | * Overhaul of key management (again). |
38 | * |
4f743df5 |
39 | * Revision 1.2 1999/12/22 15:52:08 mdw |
40 | * Rename `bbs_params' to `bbs_param' for consistency. |
41 | * |
2c52abe6 |
42 | * Revision 1.1 1999/12/10 23:14:59 mdw |
43 | * Blum-Blum-Shub generator, and Blum-Goldwasser encryption. |
44 | * |
45 | */ |
46 | |
47 | /*----- Notes on the BBS generator ----------------------------------------* |
48 | * |
49 | * The Blum-Blum-Shub generator takes the least significant bits from the |
50 | * sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of |
51 | * two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%. |
52 | * For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$% |
05cac080 |
53 | * should be coprime. It is safe to use the least significant |
54 | * %$\log \log n$% bits of each step in the sequence -- an adversary must |
55 | * factor the modulus before being able to work forwards or backwards. The |
56 | * output of the generator cannot be distinguished from a (uniform, |
57 | * independent) random sequence of bits using any polynomial-time test. This |
58 | * is by far the strongest pseudorandom number generator provided in |
59 | * Catacomb, and by far the slowest too. For normal use, the standard |
60 | * Catacomb @rand@ generator should be more than adequate. |
2c52abe6 |
61 | */ |
62 | |
63 | #ifndef CATACOMB_BBS_H |
64 | #define CATACOMB_BBS_H |
65 | |
66 | #ifdef __cplusplus |
67 | extern "C" { |
68 | #endif |
69 | |
70 | /*----- Header files ------------------------------------------------------*/ |
71 | |
72 | #include <mLib/bits.h> |
73 | |
74 | #ifndef CATACOMB_GRAND_H |
75 | # include "grand.h" |
76 | #endif |
77 | |
05cac080 |
78 | #ifndef CATACOMB_KEY_H |
79 | # include "key.h" |
80 | #endif |
81 | |
2c52abe6 |
82 | #ifndef CATACOMB_MP_H |
83 | # include "mp.h" |
84 | #endif |
85 | |
86 | #ifndef CATACOMB_MPBARRETT_H |
87 | # include "mpbarrett.h" |
88 | #endif |
89 | |
4f743df5 |
90 | #ifndef CATACOMB_PGEN_H |
91 | # include "pgen.h" |
92 | #endif |
93 | |
2c52abe6 |
94 | /*----- Data structures ---------------------------------------------------*/ |
95 | |
96 | /* --- Basic generator state --- */ |
97 | |
98 | typedef struct bbs { |
99 | mpbarrett mb; /* Barrett reduction context */ |
100 | mp *x; /* Current quadratic residue */ |
101 | unsigned k; /* Number of bits from each step */ |
102 | unsigned b; /* Number of bits in reservoir */ |
103 | mpw r; /* Reservoir of output bits */ |
104 | } bbs; |
105 | |
106 | /* --- Parameters --- */ |
107 | |
05cac080 |
108 | typedef struct bbs_pub { |
109 | mp *n; |
110 | } bbs_pub; |
111 | |
4f743df5 |
112 | typedef struct bbs_param { |
2c52abe6 |
113 | mp *p, *q; /* Prime factors (3 mod 4) */ |
114 | mp *n; /* Product @pq@ -- a Blum integer */ |
05cac080 |
115 | } bbs_param, bbs_priv; |
116 | |
117 | /*----- Key fetching ------------------------------------------------------*/ |
118 | |
119 | extern const key_fetchdef bbs_pubfetch[]; |
120 | #define BBS_PUBFETCHSZ 3 |
121 | |
122 | extern const key_fetchdef bbs_privfetch[]; |
123 | #define BBS_PRIVFETCHSZ 7 |
2c52abe6 |
124 | |
125 | /*----- The basic generator -----------------------------------------------*/ |
126 | |
127 | /* --- @bbs_create@ --- * |
128 | * |
129 | * Arguments: @bbs *b@ = pointer to BBS generator state to initialize |
130 | * @mp *m@ = modulus (must be a Blum integer) |
131 | * @mp *x@ = initial seed for generator |
132 | * |
133 | * Returns: --- |
134 | * |
135 | * Use: Initializes a BBS generator. The generator is stepped once |
136 | * after initialization, as for @bbs_seed@. |
137 | */ |
138 | |
139 | extern void bbs_create(bbs */*b*/, mp */*m*/, mp */*x*/); |
140 | |
141 | /* --- @bbs_destroy@ --- * |
142 | * |
143 | * Arguments: @bbs *b@ = pointer to BBS generator state |
144 | * |
145 | * Returns: --- |
146 | * |
147 | * Use: Destroys a generator state when it's no longer wanted. |
148 | */ |
149 | |
150 | extern void bbs_destroy(bbs */*b*/); |
151 | |
152 | /* --- @bbs_step@ --- * |
153 | * |
154 | * Arguments: @bbs *b@ = pointer to BBS generator state |
155 | * |
156 | * Returns: --- |
157 | * |
158 | * Use: Steps the generator once. This isn't too useful in client |
159 | * code. |
160 | */ |
161 | |
162 | extern void bbs_step(bbs */*b*/); |
163 | |
164 | /* --- @bbs_set@ --- * |
165 | * |
166 | * Arguments: @bbs *b@ = pointer to BBS generator state |
167 | * @mp *x@ = new residue to set |
168 | * |
169 | * Returns: --- |
170 | * |
171 | * Use: Sets a new quadratic residue. The generator is stepped once. |
172 | */ |
173 | |
174 | extern void bbs_set(bbs */*b*/, mp */*x*/); |
175 | |
176 | /* --- @bbs_seed@ --- * |
177 | * |
178 | * Arguments: @bbs *b@ = pointer to BBS generator state |
179 | * @mp *x@ = new seed to set |
180 | * |
181 | * Returns --- |
182 | * |
183 | * Use: Sets a new seed. The generator is stepped until the residue |
184 | * has clearly wrapped around. |
185 | */ |
186 | |
187 | extern void bbs_seed(bbs */*b*/, mp */*x*/); |
188 | |
189 | /* --- @bbs_bits@ --- * |
190 | * |
191 | * Arguments: @bbs *b@ = pointer to BBS generator state |
192 | * @unsigned bits@ = number of bits wanted |
193 | * |
194 | * Returns: Bits extracted from the BBS generator. |
195 | * |
196 | * Use: Extracts a requested number of bits from the BBS generator. |
197 | */ |
198 | |
199 | extern uint32 bbs_bits(bbs */*b*/, unsigned /*bits*/); |
200 | |
201 | /* --- @bbs_wrap@ --- * |
202 | * |
203 | * Arguments: @bbs *b@ = pointer to BBS generator state |
204 | * |
205 | * Returns: --- |
206 | * |
207 | * Use: Steps the generator if any of the reservoir bits are used. |
208 | * This can be used to `wrap up' after a Blum-Goldwasser |
209 | * encryption, for example, producing the final value to be sent |
210 | * along with the ciphertext. |
211 | * |
212 | * If a generator is seeded, %$b$% bits are extracted, and then |
213 | * @bbs_wrap@ is called, the generator will have been stepped |
05cac080 |
214 | * %$\lceil b/k \rceil$% times. |
2c52abe6 |
215 | */ |
216 | |
217 | extern void bbs_wrap(bbs */*b*/); |
218 | |
219 | /*----- Large forwards and backwards jumps --------------------------------*/ |
220 | |
221 | /* --- @bbs_ff@ --- * |
222 | * |
223 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
4f743df5 |
224 | * @bbs_param *bp@ = pointer to BBS modulus factors |
2c52abe6 |
225 | * @unsigned long n@ = number of steps to make |
226 | * |
227 | * Returns: --- |
228 | * |
229 | * Use: `Fast-forwards' a Blum-Blum-Shub generator by @n@ steps. |
230 | * Requires the factorization of the Blum modulus to do this |
231 | * efficiently. |
232 | */ |
233 | |
4f743df5 |
234 | extern void bbs_ff(bbs */*b*/, bbs_param */*bp*/, unsigned long /*n*/); |
2c52abe6 |
235 | |
236 | /* --- @bbs_rew@ --- * |
237 | * |
238 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
4f743df5 |
239 | * @bbs_param *bp@ = pointer to BBS modulus factors |
2c52abe6 |
240 | * @unsigned long n@ = number of steps to make |
241 | * |
242 | * Returns: --- |
243 | * |
244 | * Use: `Rewinds' a Blum-Blum-Shub generator by @n@ steps. |
245 | * Requires the factorization of the Blum modulus to do this |
246 | * at all. |
247 | */ |
248 | |
4f743df5 |
249 | extern void bbs_rew(bbs */*b*/, bbs_param */*bp*/, unsigned long /*n*/); |
2c52abe6 |
250 | |
251 | /*----- Parameter generation ----------------------------------------------*/ |
252 | |
253 | /* --- @bbs_gen@ --- * |
254 | * |
4f743df5 |
255 | * Arguments: @bbs_param *bp@ = pointer to parameter block |
052b36d0 |
256 | * @unsigned nbits@ = number of bits in the modulus |
257 | * @grand *r@ = pointer to random number source |
258 | * @unsigned n@ = number of attempts to make |
4f743df5 |
259 | * @pgen_proc *event@ = event handler function |
260 | * @void *ectx@ = argument for event handler |
2c52abe6 |
261 | * |
4f743df5 |
262 | * Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@. |
2c52abe6 |
263 | * |
264 | * Use: Finds two prime numbers %$p'$% and %$q'$% such that both are |
265 | * congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and |
266 | * %$(q - 1)/2$% have no common factors. The product %$n = pq$% |
267 | * is eminently suitable for use as a modulus in a Blum-Blum- |
268 | * Shub pseudorandom bit generator. |
269 | */ |
270 | |
052b36d0 |
271 | extern int bbs_gen(bbs_param */*bp*/, unsigned /*nbits*/, grand */*r*/, |
272 | unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/); |
2c52abe6 |
273 | |
274 | /*----- Generic random number generator interface -------------------------*/ |
275 | |
276 | /* --- @bbs_rand@ --- * |
277 | * |
278 | * Arguments: @mp *m@ = modulus |
279 | * @mp *x@ = initial seed |
280 | * |
281 | * Returns: Pointer to a generic generator. |
282 | * |
283 | * Use: Constructs a generic generator interface over a |
284 | * Blum-Blum-Shub generator. |
285 | */ |
286 | |
287 | extern grand *bbs_rand(mp */*m*/, mp */*x*/); |
288 | |
289 | /* --- Blum-Blum-Shub-specific misc op codes --- */ |
290 | |
291 | enum { |
292 | BBS_SET = GRAND_SPECIFIC /* @mp *x@ */ |
293 | }; |
294 | |
295 | /*----- That's all, folks -------------------------------------------------*/ |
296 | |
297 | #ifdef __cplusplus |
298 | } |
299 | #endif |
300 | |
301 | #endif |