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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: bbs-jump.c,v 1.3 2000/06/17 10:44:17 mdw Exp $ |
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4 | * |
5 | * Jumping around a BBS sequence |
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-jump.c,v $ |
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33 | * Revision 1.3 2000/06/17 10:44:17 mdw |
34 | * Typesetting fix. |
35 | * |
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36 | * Revision 1.2 1999/12/22 15:52:08 mdw |
37 | * Rename `bbs_params' to `bbs_param' for consistency. |
38 | * |
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39 | * Revision 1.1 1999/12/10 23:14:59 mdw |
40 | * Blum-Blum-Shub generator, and Blum-Goldwasser encryption. |
41 | * |
42 | */ |
43 | |
44 | /*----- Header files ------------------------------------------------------*/ |
45 | |
46 | #include "bbs.h" |
47 | #include "mp.h" |
48 | #include "mpbarrett.h" |
49 | #include "mpcrt.h" |
50 | #include "mpint.h" |
51 | |
52 | /*----- Main code ---------------------------------------------------------*/ |
53 | |
54 | /* --- @jump@ --- * |
55 | * |
56 | * Arguments: @bbs *b@ = pointer to BBS generator context |
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57 | * @bbs_param *bp@ = pointer to BBS modulus factors |
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58 | * @unsigned long n@ = number of steps to move |
59 | * @mp *px@ = exponent mod @p@ for a one-step jump |
60 | * @mp *qx@ = exponent mod @q@ for a one-step jump |
61 | * |
62 | * Returns: --- |
63 | * |
64 | * Use: Jumps a BBS context a certain number of places (assuming the |
65 | * arguments are right). |
66 | * |
67 | * Let the BBS modulus be %$n = pq$% and the current residue be |
68 | * %$x$%. Then the computations performed are: |
69 | * |
70 | * * Calculate %$x_p = x \bmod p$% and %$x_q = x \bmod q$%. |
71 | * |
72 | * * Determine %$e_p = px^n \bmod (p - 1)$% and similarly |
73 | * %$e_q = qx^n \bmod (p - 1)$%. |
74 | * |
75 | * * Calculate %$x_p' = x_p^{e_p} \bmod p$% and |
76 | * %$x_q' = x_q^{e_q} \bmod q$%. |
77 | * |
78 | * * Combine %$x_p'$% and %$x_q'$% using the Chinese Remainder |
79 | * Theorem. |
80 | * |
81 | * If you want to step the generator forwards, simply set |
82 | * %$px = qx = 2$%. If you want to step backwards, make |
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83 | * %$px = (p + 1)/4$% and %$qx = (q + 1)/4$%. Note that, if |
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84 | * %$x$% is a quadratic residue mod $%p$%, then |
85 | * |
86 | * %$(x^2) ^ {(p + 1)/4}$% |
87 | * %${} = x^{(p + 1)/2}$% |
88 | * %${} = x \cdot x^{(p - 1)/2}$% |
89 | * %${} = x$% |
90 | * |
91 | * Simple, no? (Note that the division works because |
92 | * %$p \equiv 3 \pmod 4$%.) |
93 | */ |
94 | |
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95 | static void jump(bbs *b, bbs_param *bp, unsigned long n, |
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96 | mp *px, mp *qx) |
97 | { |
98 | mp *ep, *eq; |
99 | mp *v[2] = { MP_NEW, MP_NEW }; |
100 | |
101 | /* --- First work out the exponents --- */ |
102 | |
103 | { |
104 | mpbarrett mb; |
105 | mp *m; |
106 | mp *e; |
107 | |
108 | e = mp_fromulong(MP_NEW, n); |
109 | m = mp_sub(MP_NEW, bp->p, MP_ONE); |
110 | mpbarrett_create(&mb, m); |
111 | ep = mpbarrett_exp(&mb, MP_NEW, px, e); |
112 | mpbarrett_destroy(&mb); |
113 | if (qx == px) |
114 | eq = MP_COPY(ep); |
115 | else { |
116 | m = mp_sub(m, bp->q, MP_ONE); |
117 | mpbarrett_create(&mb, m); |
118 | eq = mpbarrett_exp(&mb, MP_NEW, qx, e); |
119 | mpbarrett_destroy(&mb); |
120 | } |
121 | |
122 | mp_drop(m); |
123 | mp_drop(e); |
124 | } |
125 | |
126 | /* --- Now calculate the residues of @x@ --- */ |
127 | |
128 | mp_div(0, &v[0], b->x, bp->p); |
129 | mp_div(0, &v[1], b->x, bp->q); |
130 | |
131 | /* --- Exponentiate --- */ |
132 | |
133 | { |
134 | mpbarrett mb; |
135 | |
136 | mpbarrett_create(&mb, bp->p); |
137 | v[0] = mpbarrett_exp(&mb, v[0], v[0], ep); |
138 | mpbarrett_destroy(&mb); |
139 | |
140 | mpbarrett_create(&mb, bp->q); |
141 | v[1] = mpbarrett_exp(&mb, v[1], v[1], eq); |
142 | mpbarrett_destroy(&mb); |
143 | |
144 | mp_drop(ep); |
145 | mp_drop(eq); |
146 | } |
147 | |
148 | /* --- Sort out the result using the Chinese Remainder Theorem --- */ |
149 | |
150 | { |
151 | mpcrt_mod mv[2]; |
152 | mpcrt c; |
153 | int i; |
154 | |
155 | mv[0].m = MP_COPY(bp->p); |
156 | mv[1].m = MP_COPY(bp->q); |
157 | for (i = 0; i < 2; i++) |
158 | mv[i].n = mv[i].ni = mv[i].nni = MP_NEW; |
159 | mpcrt_create(&c, mv, 2, b->mb.m); |
160 | b->x = mpcrt_solve(&c, b->x, v); |
161 | mpcrt_destroy(&c); |
162 | } |
163 | |
164 | /* --- Tidy away --- */ |
165 | |
166 | mp_drop(v[0]); |
167 | mp_drop(v[1]); |
168 | b->r = b->x->v[0]; |
169 | b->b = b->k; |
170 | } |
171 | |
172 | /* --- @bbs_ff@ --- * |
173 | * |
174 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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175 | * @bbs_param *bp@ = pointer to BBS modulus factors |
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176 | * @unsigned long n@ = number of steps to make |
177 | * |
178 | * Returns: --- |
179 | * |
180 | * Use: `Fast-forwards' a Blum-Blum-Shub generator by @n@ steps. |
181 | * Requires the factorization of the Blum modulus to do this |
182 | * efficiently. |
183 | */ |
184 | |
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185 | void bbs_ff(bbs *b, bbs_param *bp, unsigned long n) |
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186 | { |
187 | jump(b, bp, n, MP_TWO, MP_TWO); |
188 | } |
189 | |
190 | /* --- @bbs_rew@ --- * |
191 | * |
192 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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193 | * @bbs_param *bp@ = pointer to BBS modulus factors |
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194 | * @unsigned long n@ = number of steps to make |
195 | * |
196 | * Returns: --- |
197 | * |
198 | * Use: `Rewinds' a Blum-Blum-Shub generator by @n@ steps. |
199 | * Requires the factorization of the Blum modulus to do this |
200 | * at all. |
201 | */ |
202 | |
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203 | void bbs_rew(bbs *b, bbs_param *bp, unsigned long n) |
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204 | { |
205 | mp *px = mp_lsr(MP_NEW, bp->p, 2); |
206 | mp *qx = mp_lsr(MP_NEW, bp->q, 2); |
207 | px = mp_add(px, px, MP_ONE); |
208 | qx = mp_add(qx, qx, MP_ONE); |
209 | jump(b, bp, n, px, qx); |
210 | mp_drop(px); |
211 | mp_drop(qx); |
212 | } |
213 | |
214 | /*----- Test rig ----------------------------------------------------------*/ |
215 | |
216 | #ifdef TEST_RIG |
217 | |
218 | static int verify(dstr *v) |
219 | { |
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220 | bbs_param bp; |
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221 | bbs b; |
222 | mp *x; |
223 | unsigned long n; |
224 | int ok = 1; |
225 | uint32 p, q, r; |
226 | int i; |
227 | |
228 | bp.p = *(mp **)v[0].buf; |
229 | bp.q = *(mp **)v[1].buf; |
230 | bp.n = mp_mul(MP_NEW, bp.p, bp.q); |
231 | x = *(mp **)v[2].buf; |
232 | n = *(unsigned long *)v[3].buf; |
233 | |
234 | bbs_create(&b, bp.n, x); |
235 | p = bbs_bits(&b, 32); |
236 | |
237 | bbs_seed(&b, x); |
238 | for (i = 0; i < n; i++) |
239 | bbs_step(&b); |
240 | q = bbs_bits(&b, 32); |
241 | bbs_wrap(&b); |
242 | |
243 | bbs_rew(&b, &bp, n + (32 + b.k - 1) / b.k); |
244 | r = bbs_bits(&b, 32); |
245 | |
246 | if (r != p) { |
247 | fputs("\n*** bbs rewind failure\n", stderr); |
248 | fputs("p = ", stderr); mp_writefile(bp.p, stderr, 10); fputc('\n', stderr); |
249 | fputs("q = ", stderr); mp_writefile(bp.q, stderr, 10); fputc('\n', stderr); |
250 | fputs("n = ", stderr); mp_writefile(bp.n, stderr, 10); fputc('\n', stderr); |
251 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
252 | fprintf(stderr, "stepped %lu back\n", n + (32 + b.k - 1) / b.k); |
253 | fprintf(stderr, "expected output = %08lx, found %08lx\n", |
254 | (unsigned long)p, (unsigned long)r); |
255 | ok = 0; |
256 | } |
257 | |
258 | bbs_seed(&b, x); |
259 | bbs_ff(&b, &bp, n); |
260 | r = bbs_bits(&b, 32); |
261 | |
262 | if (q != r) { |
263 | fputs("\n*** bbs fastforward failure\n", stderr); |
264 | fputs("p = ", stderr); mp_writefile(bp.p, stderr, 10); fputc('\n', stderr); |
265 | fputs("q = ", stderr); mp_writefile(bp.q, stderr, 10); fputc('\n', stderr); |
266 | fputs("n = ", stderr); mp_writefile(bp.n, stderr, 10); fputc('\n', stderr); |
267 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
268 | fprintf(stderr, "stepped %lu back\n", n + (32 + b.k - 1) / b.k); |
269 | fprintf(stderr, "expected output = %08lx, found %08lx\n", |
270 | (unsigned long)q, (unsigned long)r); |
271 | ok = 0; |
272 | } |
273 | |
274 | bbs_destroy(&b); |
275 | mp_drop(bp.p); |
276 | mp_drop(bp.q); |
277 | mp_drop(bp.n); |
278 | mp_drop(x); |
279 | |
280 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
281 | return (ok); |
282 | } |
283 | |
284 | static test_chunk tests[] = { |
285 | { "bbs-jump", verify, { &type_mp, &type_mp, &type_mp, &type_ulong, 0 } }, |
286 | { 0, 0, { 0 } } |
287 | }; |
288 | |
289 | int main(int argc, char *argv[]) |
290 | { |
291 | sub_init(); |
292 | test_run(argc, argv, tests, SRCDIR "/tests/bbs"); |
293 | return (0); |
294 | } |
295 | |
296 | #endif |
297 | |
298 | /*----- That's all, folks -------------------------------------------------*/ |