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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: bbs.h,v 1.5 2000/07/01 11:20:24 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 1.5 2000/07/01 11:20:24 mdw |
34 | * New functions for freeing public and private keys. Remove bad type name |
35 | * `bbs_param'. |
36 | * |
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37 | * Revision 1.4 2000/06/17 10:45:48 mdw |
38 | * Minor changes for key fetching. Typesetting fixes. |
39 | * |
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40 | * Revision 1.3 2000/02/12 18:21:02 mdw |
41 | * Overhaul of key management (again). |
42 | * |
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43 | * Revision 1.2 1999/12/22 15:52:08 mdw |
44 | * Rename `bbs_params' to `bbs_param' for consistency. |
45 | * |
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46 | * Revision 1.1 1999/12/10 23:14:59 mdw |
47 | * Blum-Blum-Shub generator, and Blum-Goldwasser encryption. |
48 | * |
49 | */ |
50 | |
51 | /*----- Notes on the BBS generator ----------------------------------------* |
52 | * |
53 | * The Blum-Blum-Shub generator takes the least significant bits from the |
54 | * sequence %$x_i = x_{i - 1}^2 \bmod n$%, where %$n = pq$% is the product of |
55 | * two primes %$p$% and %$q$%, each of which are congruent to %$3 \bmod 4$%. |
56 | * For maximum period of the generator, %$(p - 1)/2$% and %$(q - 1)/1$% |
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57 | * should be coprime. It is safe to use the least significant |
58 | * %$\log \log n$% bits of each step in the sequence -- an adversary must |
59 | * factor the modulus before being able to work forwards or backwards. The |
60 | * output of the generator cannot be distinguished from a (uniform, |
61 | * independent) random sequence of bits using any polynomial-time test. This |
62 | * is by far the strongest pseudorandom number generator provided in |
63 | * Catacomb, and by far the slowest too. For normal use, the standard |
64 | * Catacomb @rand@ generator should be more than adequate. |
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65 | */ |
66 | |
67 | #ifndef CATACOMB_BBS_H |
68 | #define CATACOMB_BBS_H |
69 | |
70 | #ifdef __cplusplus |
71 | extern "C" { |
72 | #endif |
73 | |
74 | /*----- Header files ------------------------------------------------------*/ |
75 | |
76 | #include <mLib/bits.h> |
77 | |
78 | #ifndef CATACOMB_GRAND_H |
79 | # include "grand.h" |
80 | #endif |
81 | |
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82 | #ifndef CATACOMB_KEY_H |
83 | # include "key.h" |
84 | #endif |
85 | |
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86 | #ifndef CATACOMB_MP_H |
87 | # include "mp.h" |
88 | #endif |
89 | |
90 | #ifndef CATACOMB_MPBARRETT_H |
91 | # include "mpbarrett.h" |
92 | #endif |
93 | |
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94 | #ifndef CATACOMB_PGEN_H |
95 | # include "pgen.h" |
96 | #endif |
97 | |
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98 | /*----- Data structures ---------------------------------------------------*/ |
99 | |
100 | /* --- Basic generator state --- */ |
101 | |
102 | typedef struct bbs { |
103 | mpbarrett mb; /* Barrett reduction context */ |
104 | mp *x; /* Current quadratic residue */ |
105 | unsigned k; /* Number of bits from each step */ |
106 | unsigned b; /* Number of bits in reservoir */ |
107 | mpw r; /* Reservoir of output bits */ |
108 | } bbs; |
109 | |
110 | /* --- Parameters --- */ |
111 | |
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112 | typedef struct bbs_pub { |
113 | mp *n; |
114 | } bbs_pub; |
115 | |
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116 | typedef struct bbs_priv { |
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117 | mp *p, *q; /* Prime factors (3 mod 4) */ |
118 | mp *n; /* Product @pq@ -- a Blum integer */ |
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119 | } bbs_priv; |
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120 | |
121 | /*----- Key fetching ------------------------------------------------------*/ |
122 | |
123 | extern const key_fetchdef bbs_pubfetch[]; |
124 | #define BBS_PUBFETCHSZ 3 |
125 | |
126 | extern const key_fetchdef bbs_privfetch[]; |
127 | #define BBS_PRIVFETCHSZ 7 |
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128 | |
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129 | /* --- @bbs_pubfree@, @bbs_privfree@ --- * |
130 | * |
131 | * Arguments: @bbs_pub *bp@, @bbs_priv *bp@ = pointer to key block |
132 | * |
133 | * Returns: --- |
134 | * |
135 | * Use: Frees a BBS key block. |
136 | */ |
137 | |
138 | extern void bbs_pubfree(bbs_pub */*bp*/); |
139 | extern void bbs_privfree(bbs_priv */*bp*/); |
140 | |
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141 | /*----- The basic generator -----------------------------------------------*/ |
142 | |
143 | /* --- @bbs_create@ --- * |
144 | * |
145 | * Arguments: @bbs *b@ = pointer to BBS generator state to initialize |
146 | * @mp *m@ = modulus (must be a Blum integer) |
147 | * @mp *x@ = initial seed for generator |
148 | * |
149 | * Returns: --- |
150 | * |
151 | * Use: Initializes a BBS generator. The generator is stepped once |
152 | * after initialization, as for @bbs_seed@. |
153 | */ |
154 | |
155 | extern void bbs_create(bbs */*b*/, mp */*m*/, mp */*x*/); |
156 | |
157 | /* --- @bbs_destroy@ --- * |
158 | * |
159 | * Arguments: @bbs *b@ = pointer to BBS generator state |
160 | * |
161 | * Returns: --- |
162 | * |
163 | * Use: Destroys a generator state when it's no longer wanted. |
164 | */ |
165 | |
166 | extern void bbs_destroy(bbs */*b*/); |
167 | |
168 | /* --- @bbs_step@ --- * |
169 | * |
170 | * Arguments: @bbs *b@ = pointer to BBS generator state |
171 | * |
172 | * Returns: --- |
173 | * |
174 | * Use: Steps the generator once. This isn't too useful in client |
175 | * code. |
176 | */ |
177 | |
178 | extern void bbs_step(bbs */*b*/); |
179 | |
180 | /* --- @bbs_set@ --- * |
181 | * |
182 | * Arguments: @bbs *b@ = pointer to BBS generator state |
183 | * @mp *x@ = new residue to set |
184 | * |
185 | * Returns: --- |
186 | * |
187 | * Use: Sets a new quadratic residue. The generator is stepped once. |
188 | */ |
189 | |
190 | extern void bbs_set(bbs */*b*/, mp */*x*/); |
191 | |
192 | /* --- @bbs_seed@ --- * |
193 | * |
194 | * Arguments: @bbs *b@ = pointer to BBS generator state |
195 | * @mp *x@ = new seed to set |
196 | * |
197 | * Returns --- |
198 | * |
199 | * Use: Sets a new seed. The generator is stepped until the residue |
200 | * has clearly wrapped around. |
201 | */ |
202 | |
203 | extern void bbs_seed(bbs */*b*/, mp */*x*/); |
204 | |
205 | /* --- @bbs_bits@ --- * |
206 | * |
207 | * Arguments: @bbs *b@ = pointer to BBS generator state |
208 | * @unsigned bits@ = number of bits wanted |
209 | * |
210 | * Returns: Bits extracted from the BBS generator. |
211 | * |
212 | * Use: Extracts a requested number of bits from the BBS generator. |
213 | */ |
214 | |
215 | extern uint32 bbs_bits(bbs */*b*/, unsigned /*bits*/); |
216 | |
217 | /* --- @bbs_wrap@ --- * |
218 | * |
219 | * Arguments: @bbs *b@ = pointer to BBS generator state |
220 | * |
221 | * Returns: --- |
222 | * |
223 | * Use: Steps the generator if any of the reservoir bits are used. |
224 | * This can be used to `wrap up' after a Blum-Goldwasser |
225 | * encryption, for example, producing the final value to be sent |
226 | * along with the ciphertext. |
227 | * |
228 | * If a generator is seeded, %$b$% bits are extracted, and then |
229 | * @bbs_wrap@ is called, the generator will have been stepped |
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230 | * %$\lceil b/k \rceil$% times. |
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231 | */ |
232 | |
233 | extern void bbs_wrap(bbs */*b*/); |
234 | |
235 | /*----- Large forwards and backwards jumps --------------------------------*/ |
236 | |
237 | /* --- @bbs_ff@ --- * |
238 | * |
239 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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240 | * @bbs_priv *bp@ = pointer to BBS modulus factors |
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241 | * @unsigned long n@ = number of steps to make |
242 | * |
243 | * Returns: --- |
244 | * |
245 | * Use: `Fast-forwards' a Blum-Blum-Shub generator by @n@ steps. |
246 | * Requires the factorization of the Blum modulus to do this |
247 | * efficiently. |
248 | */ |
249 | |
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250 | extern void bbs_ff(bbs */*b*/, bbs_priv */*bp*/, unsigned long /*n*/); |
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251 | |
252 | /* --- @bbs_rew@ --- * |
253 | * |
254 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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255 | * @bbs_priv *bp@ = pointer to BBS modulus factors |
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256 | * @unsigned long n@ = number of steps to make |
257 | * |
258 | * Returns: --- |
259 | * |
260 | * Use: `Rewinds' a Blum-Blum-Shub generator by @n@ steps. |
261 | * Requires the factorization of the Blum modulus to do this |
262 | * at all. |
263 | */ |
264 | |
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265 | extern void bbs_rew(bbs */*b*/, bbs_priv */*bp*/, unsigned long /*n*/); |
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266 | |
267 | /*----- Parameter generation ----------------------------------------------*/ |
268 | |
269 | /* --- @bbs_gen@ --- * |
270 | * |
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271 | * Arguments: @bbs_priv *bp@ = pointer to parameter block |
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272 | * @unsigned nbits@ = number of bits in the modulus |
273 | * @grand *r@ = pointer to random number source |
274 | * @unsigned n@ = number of attempts to make |
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275 | * @pgen_proc *event@ = event handler function |
276 | * @void *ectx@ = argument for event handler |
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277 | * |
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278 | * Returns: If it worked OK, @PGEN_DONE@, otherwise @PGEN_ABORT@. |
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279 | * |
280 | * Use: Finds two prime numbers %$p'$% and %$q'$% such that both are |
281 | * congruent to %$3 \bmod 4$%, and $(p - 1)/2$% and |
282 | * %$(q - 1)/2$% have no common factors. The product %$n = pq$% |
283 | * is eminently suitable for use as a modulus in a Blum-Blum- |
284 | * Shub pseudorandom bit generator. |
285 | */ |
286 | |
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287 | extern int bbs_gen(bbs_priv */*bp*/, unsigned /*nbits*/, grand */*r*/, |
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288 | unsigned /*n*/, pgen_proc */*event*/, void */*ectx*/); |
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289 | |
290 | /*----- Generic random number generator interface -------------------------*/ |
291 | |
292 | /* --- @bbs_rand@ --- * |
293 | * |
294 | * Arguments: @mp *m@ = modulus |
295 | * @mp *x@ = initial seed |
296 | * |
297 | * Returns: Pointer to a generic generator. |
298 | * |
299 | * Use: Constructs a generic generator interface over a |
300 | * Blum-Blum-Shub generator. |
301 | */ |
302 | |
303 | extern grand *bbs_rand(mp */*m*/, mp */*x*/); |
304 | |
305 | /* --- Blum-Blum-Shub-specific misc op codes --- */ |
306 | |
307 | enum { |
308 | BBS_SET = GRAND_SPECIFIC /* @mp *x@ */ |
309 | }; |
310 | |
311 | /*----- That's all, folks -------------------------------------------------*/ |
312 | |
313 | #ifdef __cplusplus |
314 | } |
315 | #endif |
316 | |
317 | #endif |