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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: share.c,v 1.2 2000/06/18 23:05:19 mdw Exp $ |
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4 | * |
5 | * Shamir's secret sharing |
6 | * |
7 | * (c) 2000 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: share.c,v $ |
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33 | * Revision 1.2 2000/06/18 23:05:19 mdw |
34 | * Minor performance tweak: use Barrett reduction rather than Montgomery. |
35 | * Fast secret sharing isn't done here, though: see `gfshare' instead. |
36 | * |
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37 | * Revision 1.1 2000/06/17 12:09:38 mdw |
38 | * Shamir's secret sharing system. |
39 | * |
40 | */ |
41 | |
42 | /*----- Header files ------------------------------------------------------*/ |
43 | |
44 | #include <stdio.h> |
45 | #include <stdlib.h> |
46 | #include <string.h> |
47 | |
48 | #include "grand.h" |
49 | #include "mp.h" |
50 | #include "mpint.h" |
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51 | #include "mpbarrett.h" |
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52 | #include "mprand.h" |
53 | #include "pgen.h" |
54 | #include "rabin.h" |
55 | #include "share.h" |
56 | |
57 | /*----- Main code ---------------------------------------------------------*/ |
58 | |
59 | /* --- @share_create@ --- * |
60 | * |
61 | * Arguments: @share *s@ = pointer to share context to initialize |
62 | * @unsigned t, n@ = threshold parameters for the system |
63 | * |
64 | * Returns: --- |
65 | * |
66 | * Use: Initializes a sharing context. |
67 | */ |
68 | |
69 | void share_create(share *s, unsigned t, unsigned n) |
70 | { |
71 | s->t = t; |
72 | s->n = n; |
73 | s->i = 0; |
74 | s->s = 0; |
75 | s->p = 0; |
76 | s->v = 0; |
77 | } |
78 | |
79 | /* --- @share_destroy@ --- * |
80 | * |
81 | * Arguments: @share *s@ = pointer to share context to destroy |
82 | * |
83 | * Returns: --- |
84 | * |
85 | * Use: Disposes of a sharing context. All memory is freed, all |
86 | * integers are dropped. |
87 | */ |
88 | |
89 | void share_destroy(share *s) |
90 | { |
91 | unsigned n; |
92 | unsigned i; |
93 | |
94 | /* --- Dispose of the share vector --- */ |
95 | |
96 | if (s->v) { |
97 | if (s->i) |
98 | n = s->i; |
99 | else if (s->n) |
100 | n = s->n; |
101 | else |
102 | n = s->t; |
103 | for (i = 0; i < n; i++) { |
104 | if (s->v[i].y) |
105 | mp_drop(s->v[i].y); |
106 | } |
107 | xfree(s->v); |
108 | } |
109 | |
110 | /* --- Other stuff --- */ |
111 | |
112 | if (s->p) |
113 | mp_drop(s->p); |
114 | if (s->s) |
115 | mp_drop(s->s); |
116 | } |
117 | |
118 | /* --- @share_mkshares@ --- * |
119 | * |
120 | * Arguments: @share *s@ = pointer to share context to fill in |
121 | * @grand *r@ = pointer to random number source |
122 | * |
123 | * Returns: --- |
124 | * |
125 | * Use: Generates @c->n@ secret shares, such that any @c->t@ of them |
126 | * may be used to recover the secret. |
127 | * |
128 | * The context structure is expected to be mostly filled in. In |
129 | * particular, @t@, @n@ and @s@ must be initialized. If @p@ is |
130 | * zero, a prime number of appropriate size is generated |
131 | * automatically. If @v@ is zero, a vector of appropriate size |
132 | * is allocated. You should use the macro @SHARE_INIT@ or |
133 | * @share_create@ to construct sharing contexts. |
134 | */ |
135 | |
136 | void share_mkshares(share *s, grand *r) |
137 | { |
138 | mp **v; |
139 | unsigned i; |
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140 | mp u; |
141 | mpw uw; |
142 | mpbarrett mb; |
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143 | |
144 | /* --- If there's no prime, construct one --- */ |
145 | |
146 | if (!s->p) { |
147 | pgen_filterctx pf; |
148 | rabin pr; |
149 | mp *p; |
150 | unsigned bits = (mp_octets(s->s) + 1) * 8; |
151 | |
152 | pf.step = 2; |
153 | p = mprand(MP_NEW, bits, r, 1); |
154 | s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf, |
155 | rabin_iters(bits), pgen_test, &pr); |
156 | } |
157 | |
158 | /* --- Construct the coefficients --- */ |
159 | |
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160 | mpbarrett_create(&mb, s->p); |
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161 | v = xmalloc(s->t * sizeof(mp *)); |
162 | for (i = 0; i < s->t - 1; i++) |
163 | v[i] = mprand_range(MP_NEW, s->p, r, 0); |
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164 | v[s->t - 1] = s->s; |
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165 | |
166 | /* --- Construct the shares --- */ |
167 | |
168 | if (!s->v) |
169 | s->v = xmalloc(s->n * sizeof(share_pt)); |
170 | |
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171 | mp_build(&u, &uw, &uw + 1); |
172 | for (uw = 1; uw <= s->n; uw++) { |
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173 | mp *m = MP_ZERO; |
174 | unsigned j; |
175 | |
176 | /* --- Evaluate the polynomial at %$x = i + 1$% --- */ |
177 | |
178 | for (j = 0; j < s->t; j++) { |
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179 | m = mp_mul(m, m, &u); |
180 | m = mpbarrett_reduce(&mb, m, m); |
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181 | m = mp_add(m, m, v[j]); |
182 | if (MP_CMP(m, >=, s->p)) |
183 | m = mp_sub(m, m, s->p); |
184 | } |
185 | |
186 | /* --- Reduce the final result --- */ |
187 | |
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188 | s->v[uw - 1].x = uw - 1; |
189 | s->v[uw - 1].y = m; |
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190 | } |
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191 | mpbarrett_destroy(&mb); |
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192 | |
193 | /* --- Dispose of various bits of old rubbish --- */ |
194 | |
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195 | for (i = 0; i < s->t - 1; i++) |
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196 | mp_drop(v[i]); |
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197 | xfree(v); |
198 | } |
199 | |
200 | /* --- @share_add@ --- * |
201 | * |
202 | * Arguments: @share *s@ = pointer to sharing context |
203 | * @unsigned x@ = which share number this is |
204 | * @mp *y@ = the share value |
205 | * |
206 | * Returns: Number of shares required before recovery may be performed. |
207 | * |
208 | * Use: Adds a share to the context. The context must have been |
209 | * initialized with the correct prime @p@ and threshold @t@. |
210 | */ |
211 | |
212 | unsigned share_add(share *s, unsigned x, mp *y) |
213 | { |
214 | /* --- If no vector has been allocated, create one --- */ |
215 | |
216 | if (!s->v) { |
217 | s->v = xmalloc(s->t * sizeof(share_pt)); |
218 | s->i = 0; |
219 | } |
220 | |
221 | assert(((void)"Share context is full", s->i < s->t)); |
222 | |
223 | /* --- Store the share in the vector --- */ |
224 | |
225 | s->v[s->i].x = x; |
226 | s->v[s->i].y = mp_copy(y); |
227 | s->i++; |
228 | |
229 | /* --- Done --- */ |
230 | |
231 | return (s->t - s->i); |
232 | } |
233 | |
234 | /* --- @share_combine@ --- * |
235 | * |
236 | * Arguments: @share *s@ = pointer to share context |
237 | * |
238 | * Returns: The secret, as a multiprecision integer. |
239 | * |
240 | * Use: Reconstructs a secret, given enough shares. |
241 | */ |
242 | |
243 | mp *share_combine(share *s) |
244 | { |
245 | mp *a = MP_ZERO; |
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246 | mpbarrett mb; |
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247 | unsigned i, j; |
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248 | mp ii, jj; |
249 | mpw iiw, jjw; |
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250 | mp *m = MP_NEW; |
251 | |
252 | /* --- Sanity checking --- */ |
253 | |
254 | assert(((void)"Not enough shares yet", s->i == s->t)); |
255 | |
256 | /* --- Initialization --- */ |
257 | |
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258 | mpbarrett_create(&mb, s->p); |
259 | mp_build(&ii, &iiw, &iiw + 1); |
260 | mp_build(&jj, &jjw, &jjw + 1); |
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261 | |
262 | /* --- Grind through the shares --- */ |
263 | |
264 | for (i = 0; i < s->t; i++) { |
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265 | mp *c = MP_ONE; |
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266 | |
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267 | iiw = s->v[i].x + 1; |
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268 | for (j = 0; j < s->t; j++) { |
269 | if (i == j) |
270 | continue; |
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271 | jjw = s->v[j].x + 1; |
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272 | if (s->v[j].x >= s->v[i].x) |
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273 | m = mp_sub(m, &jj, &ii); |
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274 | else { |
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275 | m = mp_sub(m, &ii, &jj); |
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276 | m = mp_sub(m, s->p, m); |
277 | } |
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278 | mp_gcd(0, 0, &m, s->p, m); |
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279 | c = mp_mul(c, c, &jj); |
280 | c = mpbarrett_reduce(&mb, c, c); |
281 | c = mp_mul(c, c, m); |
282 | c = mpbarrett_reduce(&mb, c, c); |
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283 | } |
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284 | c = mp_mul(c, c, s->v[i].y); |
285 | c = mpbarrett_reduce(&mb, c, c); |
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286 | a = mp_add(a, a, c); |
287 | mp_drop(c); |
288 | } |
289 | |
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290 | a = mpbarrett_reduce(&mb, a, a); |
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291 | s->s = mp_copy(a); |
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292 | if (m) |
293 | mp_drop(m); |
294 | mpbarrett_destroy(&mb); |
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295 | return (a); |
296 | } |
297 | |
298 | /*----- Test rig ----------------------------------------------------------*/ |
299 | |
300 | #ifdef TEST_RIG |
301 | |
302 | #include "fibrand.h" |
303 | |
304 | static int verify(grand *r) |
305 | { |
306 | unsigned n = r->ops->range(r, 16) + 8; |
307 | unsigned t = r->ops->range(r, n - 1) + 1; |
308 | unsigned len = r->ops->range(r, 160); |
309 | |
310 | share_pt *v = xmalloc(t * sizeof(share_pt)); |
311 | unsigned *p = xmalloc(n * sizeof(unsigned)); |
312 | mp *sec = mprand(MP_NEW, len, r, 0); |
313 | share s; |
314 | mp *pp; |
315 | mp *ss; |
316 | unsigned i; |
317 | |
318 | int ok = 1; |
319 | |
320 | for (i = 0; i < n; i++) |
321 | p[i] = i; |
322 | for (i = 0; i < t; i++) { |
323 | unsigned long j = r->ops->range(r, n - i); |
324 | unsigned x = p[i]; |
325 | p[i] = p[i + j]; |
326 | p[i + j] = x; |
327 | } |
328 | |
329 | share_create(&s, t, n); |
330 | s.s = mp_copy(sec); |
331 | share_mkshares(&s, r); |
332 | for (i = 0; i < t; i++) { |
333 | v[i].x = s.v[p[i]].x; |
334 | v[i].y = mp_copy(s.v[p[i]].y); |
335 | } |
336 | pp = mp_copy(s.p); |
337 | share_destroy(&s); |
338 | |
339 | assert(mparena_count(MPARENA_GLOBAL) == t + 2); |
340 | |
341 | share_create(&s, t, n); |
342 | s.p = pp; |
343 | for (i = 0; i < t; i++) { |
344 | share_add(&s, v[i].x, v[i].y); |
345 | } |
346 | ss = share_combine(&s); |
347 | share_destroy(&s); |
348 | |
349 | if (MP_CMP(sec, !=, ss)) { |
350 | ok = 0; |
351 | fprintf(stderr, "\nbad recombination of shares\n"); |
352 | }; |
353 | |
354 | mp_drop(sec); |
355 | mp_drop(ss); |
356 | |
357 | for (i = 0; i < t; i++) |
358 | mp_drop(v[i].y); |
359 | |
360 | xfree(v); |
361 | xfree(p); |
362 | |
363 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
364 | return (ok); |
365 | } |
366 | |
367 | int main(void) |
368 | { |
369 | grand *r = fibrand_create(0); |
370 | unsigned i; |
371 | int ok = 1; |
372 | |
373 | fputs("share: ", stdout); |
374 | for (i = 0; i < 40; i++) { |
375 | if (!verify(r)) |
376 | ok = 0; |
377 | fputc('.', stdout); |
378 | fflush(stdout); |
379 | } |
380 | |
381 | if (ok) |
382 | fputs(" ok\n", stdout); |
383 | else |
384 | fputs(" failed\n", stdout); |
385 | return (ok ? EXIT_SUCCESS : EXIT_FAILURE); |
386 | } |
387 | |
388 | #endif |
389 | |
390 | /*----- That's all, folks -------------------------------------------------*/ |