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1 | /* -*-c-*- |
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2 | * |
3 | * Jumping around a BBS sequence |
4 | * |
5 | * (c) 1999 Straylight/Edgeware |
6 | */ |
7 | |
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8 | /*----- Licensing notice --------------------------------------------------* |
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9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
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16 | * |
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17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
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21 | * |
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22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
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28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
30 | #include "bbs.h" |
31 | #include "mp.h" |
32 | #include "mpbarrett.h" |
33 | #include "mpcrt.h" |
34 | #include "mpint.h" |
35 | |
36 | /*----- Main code ---------------------------------------------------------*/ |
37 | |
38 | /* --- @jump@ --- * |
39 | * |
40 | * Arguments: @bbs *b@ = pointer to BBS generator context |
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41 | * @const bbs_priv *bp@ = pointer to BBS modulus factors |
42 | * @mp *n@ = number of steps to move |
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43 | * @mp *px@ = exponent mod @p@ for a one-step jump |
44 | * @mp *qx@ = exponent mod @q@ for a one-step jump |
45 | * |
46 | * Returns: --- |
47 | * |
48 | * Use: Jumps a BBS context a certain number of places (assuming the |
49 | * arguments are right). |
50 | * |
51 | * Let the BBS modulus be %$n = pq$% and the current residue be |
52 | * %$x$%. Then the computations performed are: |
53 | * |
54 | * * Calculate %$x_p = x \bmod p$% and %$x_q = x \bmod q$%. |
55 | * |
56 | * * Determine %$e_p = px^n \bmod (p - 1)$% and similarly |
57 | * %$e_q = qx^n \bmod (p - 1)$%. |
58 | * |
59 | * * Calculate %$x_p' = x_p^{e_p} \bmod p$% and |
60 | * %$x_q' = x_q^{e_q} \bmod q$%. |
61 | * |
62 | * * Combine %$x_p'$% and %$x_q'$% using the Chinese Remainder |
63 | * Theorem. |
64 | * |
65 | * If you want to step the generator forwards, simply set |
66 | * %$px = qx = 2$%. If you want to step backwards, make |
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67 | * %$px = (p + 1)/4$% and %$qx = (q + 1)/4$%. Note that, if |
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68 | * %$x$% is a quadratic residue mod $%p$%, then |
69 | * |
70 | * %$(x^2) ^ {(p + 1)/4}$% |
71 | * %${} = x^{(p + 1)/2}$% |
72 | * %${} = x \cdot x^{(p - 1)/2}$% |
73 | * %${} = x$% |
74 | * |
75 | * Simple, no? (Note that the division works because |
76 | * %$p \equiv 3 \pmod 4$%.) |
77 | */ |
78 | |
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79 | static void jump(bbs *b, const bbs_priv *bp, mp *n, |
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80 | mp *px, mp *qx) |
81 | { |
82 | mp *ep, *eq; |
83 | mp *v[2] = { MP_NEW, MP_NEW }; |
84 | |
85 | /* --- First work out the exponents --- */ |
86 | |
87 | { |
88 | mpbarrett mb; |
89 | mp *m; |
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90 | |
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91 | m = mp_sub(MP_NEW, bp->p, MP_ONE); |
92 | mpbarrett_create(&mb, m); |
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93 | ep = mpbarrett_exp(&mb, MP_NEW, px, n); |
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94 | mpbarrett_destroy(&mb); |
95 | if (qx == px) |
96 | eq = MP_COPY(ep); |
97 | else { |
98 | m = mp_sub(m, bp->q, MP_ONE); |
99 | mpbarrett_create(&mb, m); |
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100 | eq = mpbarrett_exp(&mb, MP_NEW, qx, n); |
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101 | mpbarrett_destroy(&mb); |
102 | } |
103 | |
104 | mp_drop(m); |
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105 | } |
106 | |
107 | /* --- Now calculate the residues of @x@ --- */ |
108 | |
109 | mp_div(0, &v[0], b->x, bp->p); |
110 | mp_div(0, &v[1], b->x, bp->q); |
111 | |
112 | /* --- Exponentiate --- */ |
113 | |
114 | { |
115 | mpbarrett mb; |
116 | |
117 | mpbarrett_create(&mb, bp->p); |
118 | v[0] = mpbarrett_exp(&mb, v[0], v[0], ep); |
119 | mpbarrett_destroy(&mb); |
120 | |
121 | mpbarrett_create(&mb, bp->q); |
122 | v[1] = mpbarrett_exp(&mb, v[1], v[1], eq); |
123 | mpbarrett_destroy(&mb); |
124 | |
125 | mp_drop(ep); |
126 | mp_drop(eq); |
127 | } |
128 | |
129 | /* --- Sort out the result using the Chinese Remainder Theorem --- */ |
130 | |
131 | { |
132 | mpcrt_mod mv[2]; |
133 | mpcrt c; |
134 | int i; |
135 | |
136 | mv[0].m = MP_COPY(bp->p); |
137 | mv[1].m = MP_COPY(bp->q); |
138 | for (i = 0; i < 2; i++) |
139 | mv[i].n = mv[i].ni = mv[i].nni = MP_NEW; |
140 | mpcrt_create(&c, mv, 2, b->mb.m); |
141 | b->x = mpcrt_solve(&c, b->x, v); |
142 | mpcrt_destroy(&c); |
143 | } |
144 | |
145 | /* --- Tidy away --- */ |
146 | |
147 | mp_drop(v[0]); |
148 | mp_drop(v[1]); |
149 | b->r = b->x->v[0]; |
150 | b->b = b->k; |
151 | } |
152 | |
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153 | /* --- @bbs_{ff,rew}{,n}@ --- * |
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154 | * |
155 | * Arguments: @bbs *b@ = pointer to a BBS generator state |
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156 | * @const bbs_priv *bp@ = pointer to BBS modulus factors |
157 | * @mp *n@, @unsigned long n@ = number of steps to make |
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158 | * |
159 | * Returns: --- |
160 | * |
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161 | * Use: `Fast-forwards' or rewinds a Blum-Blum-Shub generator by @n@ |
162 | * steps. The @...n@ versions take an @unsigned long@ argument; |
163 | * the non-@...n@ versions a multiprecision integer. If @n@ is |
164 | * negative then the generator is stepped in the reverse |
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165 | * direction. |
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166 | */ |
167 | |
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168 | static void ff(bbs *b, const bbs_priv *bp, mp *n) |
169 | { jump(b, bp, n, MP_TWO, MP_TWO); } |
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170 | |
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171 | static void rew(bbs *b, const bbs_priv *bp, mp *n) |
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172 | { |
173 | mp *px = mp_lsr(MP_NEW, bp->p, 2); |
174 | mp *qx = mp_lsr(MP_NEW, bp->q, 2); |
175 | px = mp_add(px, px, MP_ONE); |
176 | qx = mp_add(qx, qx, MP_ONE); |
177 | jump(b, bp, n, px, qx); |
178 | mp_drop(px); |
179 | mp_drop(qx); |
180 | } |
181 | |
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182 | void bbs_ff(bbs *b, const bbs_priv *bp, mp *n) |
183 | { |
184 | if (!MP_NEGP(n)) |
185 | ff(b, bp, n); |
186 | else { |
187 | n = mp_neg(MP_NEW, n); |
188 | rew(b, bp, n); |
189 | mp_drop(n); |
190 | } |
191 | } |
192 | |
193 | void bbs_ffn(bbs *b, const bbs_priv *bp, unsigned long n) |
194 | { mp *nn = mp_fromulong(MP_NEW, n); ff(b, bp, nn); mp_drop(nn); } |
195 | |
196 | void bbs_rew(bbs *b, const bbs_priv *bp, mp *n) |
197 | { |
198 | if (!MP_NEGP(n)) |
199 | rew(b, bp, n); |
200 | else { |
201 | n = mp_neg(MP_NEW, n); |
202 | ff(b, bp, n); |
203 | mp_drop(n); |
204 | } |
205 | } |
206 | |
207 | void bbs_rewn(bbs *b, const bbs_priv *bp, unsigned long n) |
208 | { mp *nn = mp_fromulong(MP_NEW, n); bbs_rew(b, bp, nn); mp_drop(nn); } |
209 | |
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210 | /*----- Test rig ----------------------------------------------------------*/ |
211 | |
212 | #ifdef TEST_RIG |
213 | |
214 | static int verify(dstr *v) |
215 | { |
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216 | bbs_priv bp; |
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217 | bbs b; |
218 | mp *x; |
219 | unsigned long n; |
220 | int ok = 1; |
221 | uint32 p, q, r; |
222 | int i; |
223 | |
224 | bp.p = *(mp **)v[0].buf; |
225 | bp.q = *(mp **)v[1].buf; |
226 | bp.n = mp_mul(MP_NEW, bp.p, bp.q); |
227 | x = *(mp **)v[2].buf; |
228 | n = *(unsigned long *)v[3].buf; |
229 | |
230 | bbs_create(&b, bp.n, x); |
231 | p = bbs_bits(&b, 32); |
232 | |
233 | bbs_seed(&b, x); |
234 | for (i = 0; i < n; i++) |
235 | bbs_step(&b); |
236 | q = bbs_bits(&b, 32); |
237 | bbs_wrap(&b); |
238 | |
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239 | bbs_rewn(&b, &bp, n + (32 + b.k - 1) / b.k); |
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240 | r = bbs_bits(&b, 32); |
241 | |
242 | if (r != p) { |
243 | fputs("\n*** bbs rewind failure\n", stderr); |
244 | fputs("p = ", stderr); mp_writefile(bp.p, stderr, 10); fputc('\n', stderr); |
245 | fputs("q = ", stderr); mp_writefile(bp.q, stderr, 10); fputc('\n', stderr); |
246 | fputs("n = ", stderr); mp_writefile(bp.n, stderr, 10); fputc('\n', stderr); |
247 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
248 | fprintf(stderr, "stepped %lu back\n", n + (32 + b.k - 1) / b.k); |
249 | fprintf(stderr, "expected output = %08lx, found %08lx\n", |
250 | (unsigned long)p, (unsigned long)r); |
251 | ok = 0; |
252 | } |
253 | |
254 | bbs_seed(&b, x); |
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255 | bbs_ffn(&b, &bp, n); |
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256 | r = bbs_bits(&b, 32); |
257 | |
258 | if (q != r) { |
259 | fputs("\n*** bbs fastforward failure\n", stderr); |
260 | fputs("p = ", stderr); mp_writefile(bp.p, stderr, 10); fputc('\n', stderr); |
261 | fputs("q = ", stderr); mp_writefile(bp.q, stderr, 10); fputc('\n', stderr); |
262 | fputs("n = ", stderr); mp_writefile(bp.n, stderr, 10); fputc('\n', stderr); |
263 | fputs("x = ", stderr); mp_writefile(x, stderr, 10); fputc('\n', stderr); |
264 | fprintf(stderr, "stepped %lu back\n", n + (32 + b.k - 1) / b.k); |
265 | fprintf(stderr, "expected output = %08lx, found %08lx\n", |
266 | (unsigned long)q, (unsigned long)r); |
267 | ok = 0; |
268 | } |
269 | |
270 | bbs_destroy(&b); |
271 | mp_drop(bp.p); |
272 | mp_drop(bp.q); |
273 | mp_drop(bp.n); |
274 | mp_drop(x); |
275 | |
276 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
277 | return (ok); |
278 | } |
279 | |
280 | static test_chunk tests[] = { |
281 | { "bbs-jump", verify, { &type_mp, &type_mp, &type_mp, &type_ulong, 0 } }, |
282 | { 0, 0, { 0 } } |
283 | }; |
284 | |
285 | int main(int argc, char *argv[]) |
286 | { |
287 | sub_init(); |
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288 | test_run(argc, argv, tests, SRCDIR "/t/bbs"); |
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289 | return (0); |
290 | } |
291 | |
292 | #endif |
293 | |
294 | /*----- That's all, folks -------------------------------------------------*/ |