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1 | /* -*-c-*- |
2 | * |
22bab86c |
3 | * $Id: share.c,v 1.4 2000/10/08 12:16:17 mdw Exp $ |
71dfe576 |
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 $ |
22bab86c |
33 | * Revision 1.4 2000/10/08 12:16:17 mdw |
34 | * Use @MP_EQ@ instead of @MP_CMP@. |
35 | * |
3d64a35c |
36 | * Revision 1.3 2000/06/24 18:29:05 mdw |
37 | * Interface change: allow shares to be extracted from a context on demand, |
38 | * rather than building them all up-front. |
39 | * |
ad74e5b4 |
40 | * Revision 1.2 2000/06/18 23:05:19 mdw |
41 | * Minor performance tweak: use Barrett reduction rather than Montgomery. |
42 | * Fast secret sharing isn't done here, though: see `gfshare' instead. |
43 | * |
71dfe576 |
44 | * Revision 1.1 2000/06/17 12:09:38 mdw |
45 | * Shamir's secret sharing system. |
46 | * |
47 | */ |
48 | |
49 | /*----- Header files ------------------------------------------------------*/ |
50 | |
51 | #include <stdio.h> |
52 | #include <stdlib.h> |
53 | #include <string.h> |
54 | |
55 | #include "grand.h" |
56 | #include "mp.h" |
57 | #include "mpint.h" |
ad74e5b4 |
58 | #include "mpbarrett.h" |
71dfe576 |
59 | #include "mprand.h" |
60 | #include "pgen.h" |
61 | #include "rabin.h" |
62 | #include "share.h" |
63 | |
64 | /*----- Main code ---------------------------------------------------------*/ |
65 | |
66 | /* --- @share_create@ --- * |
67 | * |
68 | * Arguments: @share *s@ = pointer to share context to initialize |
3d64a35c |
69 | * @unsigned t@ = threshold for the system |
71dfe576 |
70 | * |
71 | * Returns: --- |
72 | * |
73 | * Use: Initializes a sharing context. |
74 | */ |
75 | |
3d64a35c |
76 | void share_create(share *s, unsigned t) |
71dfe576 |
77 | { |
78 | s->t = t; |
71dfe576 |
79 | s->i = 0; |
80 | s->s = 0; |
81 | s->p = 0; |
82 | s->v = 0; |
83 | } |
84 | |
85 | /* --- @share_destroy@ --- * |
86 | * |
87 | * Arguments: @share *s@ = pointer to share context to destroy |
88 | * |
89 | * Returns: --- |
90 | * |
91 | * Use: Disposes of a sharing context. All memory is freed, all |
92 | * integers are dropped. |
93 | */ |
94 | |
95 | void share_destroy(share *s) |
96 | { |
71dfe576 |
97 | unsigned i; |
98 | |
99 | /* --- Dispose of the share vector --- */ |
100 | |
101 | if (s->v) { |
3d64a35c |
102 | for (i = 0; i < s->t; i++) { |
71dfe576 |
103 | if (s->v[i].y) |
104 | mp_drop(s->v[i].y); |
105 | } |
106 | xfree(s->v); |
107 | } |
108 | |
109 | /* --- Other stuff --- */ |
110 | |
111 | if (s->p) |
112 | mp_drop(s->p); |
113 | if (s->s) |
114 | mp_drop(s->s); |
115 | } |
116 | |
117 | /* --- @share_mkshares@ --- * |
118 | * |
119 | * Arguments: @share *s@ = pointer to share context to fill in |
120 | * @grand *r@ = pointer to random number source |
121 | * |
122 | * Returns: --- |
123 | * |
3d64a35c |
124 | * Use: Initializes a sharing context to be able to create shares. |
71dfe576 |
125 | * The context structure is expected to be mostly filled in. In |
3d64a35c |
126 | * particular, @t@ and @s@ must be initialized. If @p@ is zero, |
127 | * a prime number of appropriate size is generated |
71dfe576 |
128 | * automatically. If @v@ is zero, a vector of appropriate size |
129 | * is allocated. You should use the macro @SHARE_INIT@ or |
130 | * @share_create@ to construct sharing contexts. |
131 | */ |
132 | |
133 | void share_mkshares(share *s, grand *r) |
134 | { |
71dfe576 |
135 | unsigned i; |
71dfe576 |
136 | |
137 | /* --- If there's no prime, construct one --- */ |
138 | |
139 | if (!s->p) { |
140 | pgen_filterctx pf; |
141 | rabin pr; |
142 | mp *p; |
143 | unsigned bits = (mp_octets(s->s) + 1) * 8; |
144 | |
145 | pf.step = 2; |
146 | p = mprand(MP_NEW, bits, r, 1); |
147 | s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf, |
148 | rabin_iters(bits), pgen_test, &pr); |
149 | } |
150 | |
3d64a35c |
151 | /* --- Construct the polynomial --- */ |
71dfe576 |
152 | |
3d64a35c |
153 | if (!s->v) |
154 | s->v = xmalloc(s->t * sizeof(share_pt)); |
71dfe576 |
155 | for (i = 0; i < s->t - 1; i++) |
3d64a35c |
156 | s->v[i].y = mprand_range(MP_NEWSEC, s->p, r, 0); |
157 | s->v[s->t - 1].y = mp_copy(s->s); |
158 | } |
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159 | |
3d64a35c |
160 | /* --- @share_get@ --- * |
161 | * |
162 | * Arguments: @share *s@ = pointer to share conext |
163 | * @mp *d@ = destination for the share |
164 | * @unsigned x@ = share index to fetch |
165 | * |
166 | * Returns: The share, as requested. |
167 | * |
168 | * Use: Extracts a share from the system. You may extract @MPW_MAX@ |
169 | * shares, or @s->p@ shares from the system, whichever is |
170 | * smaller. Shares are indexed from 0. |
171 | */ |
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172 | |
3d64a35c |
173 | mp *share_get(share *s, mp *d, unsigned x) |
174 | { |
175 | mpbarrett mb; |
176 | mpw uw = x + 1; |
177 | mp u; |
178 | unsigned i; |
71dfe576 |
179 | |
3d64a35c |
180 | /* --- Various bits of initialization --- */ |
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181 | |
3d64a35c |
182 | mp_build(&u, &uw, &uw + 1); |
183 | if (d) |
184 | mp_drop(d); |
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185 | |
3d64a35c |
186 | /* --- Evaluate the polynomial at %$x = i + 1$% --- */ |
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187 | |
3d64a35c |
188 | d = MP_ZERO; |
189 | mpbarrett_create(&mb, s->p); |
190 | for (i = 0; i < s->t; i++) { |
191 | d = mp_mul(d, d, &u); |
192 | d = mp_add(d, d, s->v[i].y); |
193 | d = mpbarrett_reduce(&mb, d, d); |
71dfe576 |
194 | } |
ad74e5b4 |
195 | mpbarrett_destroy(&mb); |
71dfe576 |
196 | |
3d64a35c |
197 | return (d); |
71dfe576 |
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) { |
3d64a35c |
217 | unsigned i; |
71dfe576 |
218 | s->v = xmalloc(s->t * sizeof(share_pt)); |
219 | s->i = 0; |
3d64a35c |
220 | for (i = 0; i < s->t; i++) |
221 | s->v[i].y = 0; |
71dfe576 |
222 | } |
223 | |
224 | assert(((void)"Share context is full", s->i < s->t)); |
225 | |
226 | /* --- Store the share in the vector --- */ |
227 | |
3d64a35c |
228 | s->v[s->i].x = x + 1; |
71dfe576 |
229 | s->v[s->i].y = mp_copy(y); |
230 | s->i++; |
231 | |
232 | /* --- Done --- */ |
233 | |
234 | return (s->t - s->i); |
235 | } |
236 | |
237 | /* --- @share_combine@ --- * |
238 | * |
239 | * Arguments: @share *s@ = pointer to share context |
240 | * |
241 | * Returns: The secret, as a multiprecision integer. |
242 | * |
243 | * Use: Reconstructs a secret, given enough shares. |
244 | */ |
245 | |
246 | mp *share_combine(share *s) |
247 | { |
248 | mp *a = MP_ZERO; |
ad74e5b4 |
249 | mpbarrett mb; |
71dfe576 |
250 | unsigned i, j; |
ad74e5b4 |
251 | mp ii, jj; |
252 | mpw iiw, jjw; |
71dfe576 |
253 | mp *m = MP_NEW; |
254 | |
255 | /* --- Sanity checking --- */ |
256 | |
257 | assert(((void)"Not enough shares yet", s->i == s->t)); |
258 | |
259 | /* --- Initialization --- */ |
260 | |
ad74e5b4 |
261 | mpbarrett_create(&mb, s->p); |
262 | mp_build(&ii, &iiw, &iiw + 1); |
263 | mp_build(&jj, &jjw, &jjw + 1); |
71dfe576 |
264 | |
265 | /* --- Grind through the shares --- */ |
266 | |
267 | for (i = 0; i < s->t; i++) { |
ad74e5b4 |
268 | mp *c = MP_ONE; |
71dfe576 |
269 | |
3d64a35c |
270 | iiw = s->v[i].x; |
71dfe576 |
271 | for (j = 0; j < s->t; j++) { |
272 | if (i == j) |
273 | continue; |
3d64a35c |
274 | jjw = s->v[j].x; |
71dfe576 |
275 | if (s->v[j].x >= s->v[i].x) |
ad74e5b4 |
276 | m = mp_sub(m, &jj, &ii); |
71dfe576 |
277 | else { |
ad74e5b4 |
278 | m = mp_sub(m, &ii, &jj); |
71dfe576 |
279 | m = mp_sub(m, s->p, m); |
280 | } |
71dfe576 |
281 | mp_gcd(0, 0, &m, s->p, m); |
ad74e5b4 |
282 | c = mp_mul(c, c, &jj); |
283 | c = mpbarrett_reduce(&mb, c, c); |
284 | c = mp_mul(c, c, m); |
285 | c = mpbarrett_reduce(&mb, c, c); |
71dfe576 |
286 | } |
ad74e5b4 |
287 | c = mp_mul(c, c, s->v[i].y); |
288 | c = mpbarrett_reduce(&mb, c, c); |
71dfe576 |
289 | a = mp_add(a, a, c); |
290 | mp_drop(c); |
291 | } |
292 | |
ad74e5b4 |
293 | a = mpbarrett_reduce(&mb, a, a); |
71dfe576 |
294 | s->s = mp_copy(a); |
ad74e5b4 |
295 | if (m) |
296 | mp_drop(m); |
297 | mpbarrett_destroy(&mb); |
71dfe576 |
298 | return (a); |
299 | } |
300 | |
301 | /*----- Test rig ----------------------------------------------------------*/ |
302 | |
303 | #ifdef TEST_RIG |
304 | |
305 | #include "fibrand.h" |
306 | |
307 | static int verify(grand *r) |
308 | { |
309 | unsigned n = r->ops->range(r, 16) + 8; |
310 | unsigned t = r->ops->range(r, n - 1) + 1; |
311 | unsigned len = r->ops->range(r, 160); |
312 | |
3d64a35c |
313 | mp **v = xmalloc(t * sizeof(mp *)); |
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314 | unsigned *p = xmalloc(n * sizeof(unsigned)); |
315 | mp *sec = mprand(MP_NEW, len, r, 0); |
316 | share s; |
317 | mp *pp; |
318 | mp *ss; |
319 | unsigned i; |
320 | |
321 | int ok = 1; |
322 | |
323 | for (i = 0; i < n; i++) |
324 | p[i] = i; |
325 | for (i = 0; i < t; i++) { |
326 | unsigned long j = r->ops->range(r, n - i); |
327 | unsigned x = p[i]; |
328 | p[i] = p[i + j]; |
329 | p[i + j] = x; |
330 | } |
331 | |
3d64a35c |
332 | share_create(&s, t); |
71dfe576 |
333 | s.s = mp_copy(sec); |
334 | share_mkshares(&s, r); |
3d64a35c |
335 | for (i = 0; i < t; i++) |
336 | v[i] = share_get(&s, MP_NEW, p[i]); |
71dfe576 |
337 | pp = mp_copy(s.p); |
338 | share_destroy(&s); |
3d64a35c |
339 | assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2); |
71dfe576 |
340 | |
3d64a35c |
341 | share_create(&s, t); |
71dfe576 |
342 | s.p = pp; |
3d64a35c |
343 | for (i = 0; i < t; i++) |
344 | share_add(&s, p[i], v[i]); |
71dfe576 |
345 | ss = share_combine(&s); |
346 | share_destroy(&s); |
347 | |
22bab86c |
348 | if (!MP_EQ(sec, ss)) { |
71dfe576 |
349 | ok = 0; |
350 | fprintf(stderr, "\nbad recombination of shares\n"); |
351 | }; |
352 | |
353 | mp_drop(sec); |
354 | mp_drop(ss); |
355 | |
356 | for (i = 0; i < t; i++) |
3d64a35c |
357 | mp_drop(v[i]); |
71dfe576 |
358 | |
359 | xfree(v); |
360 | xfree(p); |
361 | |
3d64a35c |
362 | assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == 0); |
71dfe576 |
363 | return (ok); |
364 | } |
365 | |
366 | int main(void) |
367 | { |
368 | grand *r = fibrand_create(0); |
369 | unsigned i; |
370 | int ok = 1; |
371 | |
372 | fputs("share: ", stdout); |
373 | for (i = 0; i < 40; i++) { |
374 | if (!verify(r)) |
375 | ok = 0; |
376 | fputc('.', stdout); |
377 | fflush(stdout); |
378 | } |
379 | |
380 | if (ok) |
381 | fputs(" ok\n", stdout); |
382 | else |
383 | fputs(" failed\n", stdout); |
384 | return (ok ? EXIT_SUCCESS : EXIT_FAILURE); |
385 | } |
386 | |
387 | #endif |
388 | |
389 | /*----- That's all, folks -------------------------------------------------*/ |