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1 | /* -*-c-*- |
2 | * |
5d4fee2a |
3 | * $Id: share.c,v 1.5 2000/12/06 20:30:10 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 $ |
5d4fee2a |
33 | * Revision 1.5 2000/12/06 20:30:10 mdw |
34 | * Change secret sharing interface: present the secret at share |
35 | * construction time. |
36 | * |
22bab86c |
37 | * Revision 1.4 2000/10/08 12:16:17 mdw |
38 | * Use @MP_EQ@ instead of @MP_CMP@. |
39 | * |
3d64a35c |
40 | * Revision 1.3 2000/06/24 18:29:05 mdw |
41 | * Interface change: allow shares to be extracted from a context on demand, |
42 | * rather than building them all up-front. |
43 | * |
ad74e5b4 |
44 | * Revision 1.2 2000/06/18 23:05:19 mdw |
45 | * Minor performance tweak: use Barrett reduction rather than Montgomery. |
46 | * Fast secret sharing isn't done here, though: see `gfshare' instead. |
47 | * |
71dfe576 |
48 | * Revision 1.1 2000/06/17 12:09:38 mdw |
49 | * Shamir's secret sharing system. |
50 | * |
51 | */ |
52 | |
53 | /*----- Header files ------------------------------------------------------*/ |
54 | |
55 | #include <stdio.h> |
56 | #include <stdlib.h> |
57 | #include <string.h> |
58 | |
59 | #include "grand.h" |
60 | #include "mp.h" |
61 | #include "mpint.h" |
ad74e5b4 |
62 | #include "mpbarrett.h" |
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63 | #include "mprand.h" |
64 | #include "pgen.h" |
65 | #include "rabin.h" |
66 | #include "share.h" |
67 | |
68 | /*----- Main code ---------------------------------------------------------*/ |
69 | |
70 | /* --- @share_create@ --- * |
71 | * |
72 | * Arguments: @share *s@ = pointer to share context to initialize |
3d64a35c |
73 | * @unsigned t@ = threshold for the system |
71dfe576 |
74 | * |
75 | * Returns: --- |
76 | * |
77 | * Use: Initializes a sharing context. |
78 | */ |
79 | |
3d64a35c |
80 | void share_create(share *s, unsigned t) |
71dfe576 |
81 | { |
82 | s->t = t; |
71dfe576 |
83 | s->i = 0; |
71dfe576 |
84 | s->p = 0; |
85 | s->v = 0; |
86 | } |
87 | |
88 | /* --- @share_destroy@ --- * |
89 | * |
90 | * Arguments: @share *s@ = pointer to share context to destroy |
91 | * |
92 | * Returns: --- |
93 | * |
94 | * Use: Disposes of a sharing context. All memory is freed, all |
95 | * integers are dropped. |
96 | */ |
97 | |
98 | void share_destroy(share *s) |
99 | { |
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100 | unsigned i; |
101 | |
102 | /* --- Dispose of the share vector --- */ |
103 | |
104 | if (s->v) { |
3d64a35c |
105 | for (i = 0; i < s->t; i++) { |
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106 | if (s->v[i].y) |
107 | mp_drop(s->v[i].y); |
108 | } |
109 | xfree(s->v); |
110 | } |
111 | |
112 | /* --- Other stuff --- */ |
113 | |
114 | if (s->p) |
115 | mp_drop(s->p); |
71dfe576 |
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 |
5d4fee2a |
122 | * @mp *n@ = the secret to share |
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123 | * |
124 | * Returns: --- |
125 | * |
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126 | * Use: Initializes a sharing context to be able to create shares. |
71dfe576 |
127 | * The context structure is expected to be mostly filled in. In |
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128 | * particular, @t@ must be initialized. If @p@ is zero, a prime |
129 | * number of appropriate size is generated automatically. If |
130 | * @v@ is zero, a vector of appropriate size is allocated. You |
131 | * should use the macro @SHARE_INIT@ or @share_create@ to |
132 | * construct sharing contexts. |
71dfe576 |
133 | */ |
134 | |
5d4fee2a |
135 | void share_mkshares(share *s, grand *r, mp *n) |
71dfe576 |
136 | { |
71dfe576 |
137 | unsigned i; |
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138 | |
139 | /* --- If there's no prime, construct one --- */ |
140 | |
141 | if (!s->p) { |
142 | pgen_filterctx pf; |
143 | rabin pr; |
144 | mp *p; |
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145 | unsigned bits = (mp_octets(n) + 1) * 8; |
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146 | |
147 | pf.step = 2; |
148 | p = mprand(MP_NEW, bits, r, 1); |
149 | s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf, |
150 | rabin_iters(bits), pgen_test, &pr); |
151 | } |
152 | |
3d64a35c |
153 | /* --- Construct the polynomial --- */ |
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154 | |
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155 | if (!s->v) |
156 | s->v = xmalloc(s->t * sizeof(share_pt)); |
71dfe576 |
157 | for (i = 0; i < s->t - 1; i++) |
3d64a35c |
158 | s->v[i].y = mprand_range(MP_NEWSEC, s->p, r, 0); |
5d4fee2a |
159 | s->v[s->t - 1].y = mp_copy(n); |
3d64a35c |
160 | } |
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161 | |
3d64a35c |
162 | /* --- @share_get@ --- * |
163 | * |
164 | * Arguments: @share *s@ = pointer to share conext |
165 | * @mp *d@ = destination for the share |
166 | * @unsigned x@ = share index to fetch |
167 | * |
168 | * Returns: The share, as requested. |
169 | * |
170 | * Use: Extracts a share from the system. You may extract @MPW_MAX@ |
171 | * shares, or @s->p@ shares from the system, whichever is |
172 | * smaller. Shares are indexed from 0. |
173 | */ |
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174 | |
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175 | mp *share_get(share *s, mp *d, unsigned x) |
176 | { |
177 | mpbarrett mb; |
178 | mpw uw = x + 1; |
179 | mp u; |
180 | unsigned i; |
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181 | |
3d64a35c |
182 | /* --- Various bits of initialization --- */ |
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183 | |
3d64a35c |
184 | mp_build(&u, &uw, &uw + 1); |
185 | if (d) |
186 | mp_drop(d); |
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187 | |
3d64a35c |
188 | /* --- Evaluate the polynomial at %$x = i + 1$% --- */ |
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189 | |
3d64a35c |
190 | d = MP_ZERO; |
191 | mpbarrett_create(&mb, s->p); |
192 | for (i = 0; i < s->t; i++) { |
193 | d = mp_mul(d, d, &u); |
194 | d = mp_add(d, d, s->v[i].y); |
195 | d = mpbarrett_reduce(&mb, d, d); |
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196 | } |
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197 | mpbarrett_destroy(&mb); |
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198 | |
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199 | return (d); |
71dfe576 |
200 | } |
201 | |
202 | /* --- @share_add@ --- * |
203 | * |
204 | * Arguments: @share *s@ = pointer to sharing context |
205 | * @unsigned x@ = which share number this is |
206 | * @mp *y@ = the share value |
207 | * |
208 | * Returns: Number of shares required before recovery may be performed. |
209 | * |
210 | * Use: Adds a share to the context. The context must have been |
211 | * initialized with the correct prime @p@ and threshold @t@. |
212 | */ |
213 | |
214 | unsigned share_add(share *s, unsigned x, mp *y) |
215 | { |
216 | /* --- If no vector has been allocated, create one --- */ |
217 | |
218 | if (!s->v) { |
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219 | unsigned i; |
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220 | s->v = xmalloc(s->t * sizeof(share_pt)); |
221 | s->i = 0; |
3d64a35c |
222 | for (i = 0; i < s->t; i++) |
223 | s->v[i].y = 0; |
71dfe576 |
224 | } |
225 | |
226 | assert(((void)"Share context is full", s->i < s->t)); |
227 | |
228 | /* --- Store the share in the vector --- */ |
229 | |
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230 | s->v[s->i].x = x + 1; |
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231 | s->v[s->i].y = mp_copy(y); |
232 | s->i++; |
233 | |
234 | /* --- Done --- */ |
235 | |
236 | return (s->t - s->i); |
237 | } |
238 | |
239 | /* --- @share_combine@ --- * |
240 | * |
241 | * Arguments: @share *s@ = pointer to share context |
242 | * |
243 | * Returns: The secret, as a multiprecision integer. |
244 | * |
245 | * Use: Reconstructs a secret, given enough shares. |
246 | */ |
247 | |
248 | mp *share_combine(share *s) |
249 | { |
250 | mp *a = MP_ZERO; |
ad74e5b4 |
251 | mpbarrett mb; |
71dfe576 |
252 | unsigned i, j; |
ad74e5b4 |
253 | mp ii, jj; |
254 | mpw iiw, jjw; |
71dfe576 |
255 | mp *m = MP_NEW; |
256 | |
257 | /* --- Sanity checking --- */ |
258 | |
259 | assert(((void)"Not enough shares yet", s->i == s->t)); |
260 | |
261 | /* --- Initialization --- */ |
262 | |
ad74e5b4 |
263 | mpbarrett_create(&mb, s->p); |
264 | mp_build(&ii, &iiw, &iiw + 1); |
265 | mp_build(&jj, &jjw, &jjw + 1); |
71dfe576 |
266 | |
267 | /* --- Grind through the shares --- */ |
268 | |
269 | for (i = 0; i < s->t; i++) { |
ad74e5b4 |
270 | mp *c = MP_ONE; |
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271 | |
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272 | iiw = s->v[i].x; |
71dfe576 |
273 | for (j = 0; j < s->t; j++) { |
274 | if (i == j) |
275 | continue; |
3d64a35c |
276 | jjw = s->v[j].x; |
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277 | if (s->v[j].x >= s->v[i].x) |
ad74e5b4 |
278 | m = mp_sub(m, &jj, &ii); |
71dfe576 |
279 | else { |
ad74e5b4 |
280 | m = mp_sub(m, &ii, &jj); |
71dfe576 |
281 | m = mp_sub(m, s->p, m); |
282 | } |
71dfe576 |
283 | mp_gcd(0, 0, &m, s->p, m); |
ad74e5b4 |
284 | c = mp_mul(c, c, &jj); |
285 | c = mpbarrett_reduce(&mb, c, c); |
286 | c = mp_mul(c, c, m); |
287 | c = mpbarrett_reduce(&mb, c, c); |
71dfe576 |
288 | } |
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289 | c = mp_mul(c, c, s->v[i].y); |
290 | c = mpbarrett_reduce(&mb, c, c); |
71dfe576 |
291 | a = mp_add(a, a, c); |
292 | mp_drop(c); |
293 | } |
294 | |
ad74e5b4 |
295 | a = mpbarrett_reduce(&mb, a, a); |
ad74e5b4 |
296 | if (m) |
297 | mp_drop(m); |
298 | mpbarrett_destroy(&mb); |
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299 | return (a); |
300 | } |
301 | |
302 | /*----- Test rig ----------------------------------------------------------*/ |
303 | |
304 | #ifdef TEST_RIG |
305 | |
306 | #include "fibrand.h" |
307 | |
308 | static int verify(grand *r) |
309 | { |
310 | unsigned n = r->ops->range(r, 16) + 8; |
311 | unsigned t = r->ops->range(r, n - 1) + 1; |
312 | unsigned len = r->ops->range(r, 160); |
313 | |
3d64a35c |
314 | mp **v = xmalloc(t * sizeof(mp *)); |
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315 | unsigned *p = xmalloc(n * sizeof(unsigned)); |
316 | mp *sec = mprand(MP_NEW, len, r, 0); |
317 | share s; |
318 | mp *pp; |
319 | mp *ss; |
320 | unsigned i; |
321 | |
322 | int ok = 1; |
323 | |
324 | for (i = 0; i < n; i++) |
325 | p[i] = i; |
326 | for (i = 0; i < t; i++) { |
327 | unsigned long j = r->ops->range(r, n - i); |
328 | unsigned x = p[i]; |
329 | p[i] = p[i + j]; |
330 | p[i + j] = x; |
331 | } |
332 | |
3d64a35c |
333 | share_create(&s, t); |
5d4fee2a |
334 | share_mkshares(&s, r, sec); |
3d64a35c |
335 | for (i = 0; i < t; i++) |
336 | v[i] = share_get(&s, MP_NEW, p[i]); |
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337 | pp = mp_copy(s.p); |
338 | share_destroy(&s); |
3d64a35c |
339 | assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2); |
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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]); |
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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 -------------------------------------------------*/ |