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1 | /* -*-c-*- |
2 | * |
3d64a35c |
3 | * $Id: share.c,v 1.3 2000/06/24 18:29:05 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 $ |
3d64a35c |
33 | * Revision 1.3 2000/06/24 18:29:05 mdw |
34 | * Interface change: allow shares to be extracted from a context on demand, |
35 | * rather than building them all up-front. |
36 | * |
ad74e5b4 |
37 | * Revision 1.2 2000/06/18 23:05:19 mdw |
38 | * Minor performance tweak: use Barrett reduction rather than Montgomery. |
39 | * Fast secret sharing isn't done here, though: see `gfshare' instead. |
40 | * |
71dfe576 |
41 | * Revision 1.1 2000/06/17 12:09:38 mdw |
42 | * Shamir's secret sharing system. |
43 | * |
44 | */ |
45 | |
46 | /*----- Header files ------------------------------------------------------*/ |
47 | |
48 | #include <stdio.h> |
49 | #include <stdlib.h> |
50 | #include <string.h> |
51 | |
52 | #include "grand.h" |
53 | #include "mp.h" |
54 | #include "mpint.h" |
ad74e5b4 |
55 | #include "mpbarrett.h" |
71dfe576 |
56 | #include "mprand.h" |
57 | #include "pgen.h" |
58 | #include "rabin.h" |
59 | #include "share.h" |
60 | |
61 | /*----- Main code ---------------------------------------------------------*/ |
62 | |
63 | /* --- @share_create@ --- * |
64 | * |
65 | * Arguments: @share *s@ = pointer to share context to initialize |
3d64a35c |
66 | * @unsigned t@ = threshold for the system |
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67 | * |
68 | * Returns: --- |
69 | * |
70 | * Use: Initializes a sharing context. |
71 | */ |
72 | |
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73 | void share_create(share *s, unsigned t) |
71dfe576 |
74 | { |
75 | s->t = t; |
71dfe576 |
76 | s->i = 0; |
77 | s->s = 0; |
78 | s->p = 0; |
79 | s->v = 0; |
80 | } |
81 | |
82 | /* --- @share_destroy@ --- * |
83 | * |
84 | * Arguments: @share *s@ = pointer to share context to destroy |
85 | * |
86 | * Returns: --- |
87 | * |
88 | * Use: Disposes of a sharing context. All memory is freed, all |
89 | * integers are dropped. |
90 | */ |
91 | |
92 | void share_destroy(share *s) |
93 | { |
71dfe576 |
94 | unsigned i; |
95 | |
96 | /* --- Dispose of the share vector --- */ |
97 | |
98 | if (s->v) { |
3d64a35c |
99 | for (i = 0; i < s->t; i++) { |
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100 | if (s->v[i].y) |
101 | mp_drop(s->v[i].y); |
102 | } |
103 | xfree(s->v); |
104 | } |
105 | |
106 | /* --- Other stuff --- */ |
107 | |
108 | if (s->p) |
109 | mp_drop(s->p); |
110 | if (s->s) |
111 | mp_drop(s->s); |
112 | } |
113 | |
114 | /* --- @share_mkshares@ --- * |
115 | * |
116 | * Arguments: @share *s@ = pointer to share context to fill in |
117 | * @grand *r@ = pointer to random number source |
118 | * |
119 | * Returns: --- |
120 | * |
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121 | * Use: Initializes a sharing context to be able to create shares. |
71dfe576 |
122 | * The context structure is expected to be mostly filled in. In |
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123 | * particular, @t@ and @s@ must be initialized. If @p@ is zero, |
124 | * a prime number of appropriate size is generated |
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125 | * automatically. If @v@ is zero, a vector of appropriate size |
126 | * is allocated. You should use the macro @SHARE_INIT@ or |
127 | * @share_create@ to construct sharing contexts. |
128 | */ |
129 | |
130 | void share_mkshares(share *s, grand *r) |
131 | { |
71dfe576 |
132 | unsigned i; |
71dfe576 |
133 | |
134 | /* --- If there's no prime, construct one --- */ |
135 | |
136 | if (!s->p) { |
137 | pgen_filterctx pf; |
138 | rabin pr; |
139 | mp *p; |
140 | unsigned bits = (mp_octets(s->s) + 1) * 8; |
141 | |
142 | pf.step = 2; |
143 | p = mprand(MP_NEW, bits, r, 1); |
144 | s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf, |
145 | rabin_iters(bits), pgen_test, &pr); |
146 | } |
147 | |
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148 | /* --- Construct the polynomial --- */ |
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149 | |
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150 | if (!s->v) |
151 | s->v = xmalloc(s->t * sizeof(share_pt)); |
71dfe576 |
152 | for (i = 0; i < s->t - 1; i++) |
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153 | s->v[i].y = mprand_range(MP_NEWSEC, s->p, r, 0); |
154 | s->v[s->t - 1].y = mp_copy(s->s); |
155 | } |
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156 | |
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157 | /* --- @share_get@ --- * |
158 | * |
159 | * Arguments: @share *s@ = pointer to share conext |
160 | * @mp *d@ = destination for the share |
161 | * @unsigned x@ = share index to fetch |
162 | * |
163 | * Returns: The share, as requested. |
164 | * |
165 | * Use: Extracts a share from the system. You may extract @MPW_MAX@ |
166 | * shares, or @s->p@ shares from the system, whichever is |
167 | * smaller. Shares are indexed from 0. |
168 | */ |
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169 | |
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170 | mp *share_get(share *s, mp *d, unsigned x) |
171 | { |
172 | mpbarrett mb; |
173 | mpw uw = x + 1; |
174 | mp u; |
175 | unsigned i; |
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176 | |
3d64a35c |
177 | /* --- Various bits of initialization --- */ |
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178 | |
3d64a35c |
179 | mp_build(&u, &uw, &uw + 1); |
180 | if (d) |
181 | mp_drop(d); |
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182 | |
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183 | /* --- Evaluate the polynomial at %$x = i + 1$% --- */ |
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184 | |
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185 | d = MP_ZERO; |
186 | mpbarrett_create(&mb, s->p); |
187 | for (i = 0; i < s->t; i++) { |
188 | d = mp_mul(d, d, &u); |
189 | d = mp_add(d, d, s->v[i].y); |
190 | d = mpbarrett_reduce(&mb, d, d); |
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191 | } |
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192 | mpbarrett_destroy(&mb); |
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193 | |
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194 | return (d); |
71dfe576 |
195 | } |
196 | |
197 | /* --- @share_add@ --- * |
198 | * |
199 | * Arguments: @share *s@ = pointer to sharing context |
200 | * @unsigned x@ = which share number this is |
201 | * @mp *y@ = the share value |
202 | * |
203 | * Returns: Number of shares required before recovery may be performed. |
204 | * |
205 | * Use: Adds a share to the context. The context must have been |
206 | * initialized with the correct prime @p@ and threshold @t@. |
207 | */ |
208 | |
209 | unsigned share_add(share *s, unsigned x, mp *y) |
210 | { |
211 | /* --- If no vector has been allocated, create one --- */ |
212 | |
213 | if (!s->v) { |
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214 | unsigned i; |
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215 | s->v = xmalloc(s->t * sizeof(share_pt)); |
216 | s->i = 0; |
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217 | for (i = 0; i < s->t; i++) |
218 | s->v[i].y = 0; |
71dfe576 |
219 | } |
220 | |
221 | assert(((void)"Share context is full", s->i < s->t)); |
222 | |
223 | /* --- Store the share in the vector --- */ |
224 | |
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225 | s->v[s->i].x = x + 1; |
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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; |
ad74e5b4 |
246 | mpbarrett mb; |
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247 | unsigned i, j; |
ad74e5b4 |
248 | mp ii, jj; |
249 | mpw iiw, jjw; |
71dfe576 |
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 | |
ad74e5b4 |
258 | mpbarrett_create(&mb, s->p); |
259 | mp_build(&ii, &iiw, &iiw + 1); |
260 | mp_build(&jj, &jjw, &jjw + 1); |
71dfe576 |
261 | |
262 | /* --- Grind through the shares --- */ |
263 | |
264 | for (i = 0; i < s->t; i++) { |
ad74e5b4 |
265 | mp *c = MP_ONE; |
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266 | |
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267 | iiw = s->v[i].x; |
71dfe576 |
268 | for (j = 0; j < s->t; j++) { |
269 | if (i == j) |
270 | continue; |
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271 | jjw = s->v[j].x; |
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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); |
71dfe576 |
274 | else { |
ad74e5b4 |
275 | m = mp_sub(m, &ii, &jj); |
71dfe576 |
276 | m = mp_sub(m, s->p, m); |
277 | } |
71dfe576 |
278 | mp_gcd(0, 0, &m, s->p, m); |
ad74e5b4 |
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); |
71dfe576 |
283 | } |
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284 | c = mp_mul(c, c, s->v[i].y); |
285 | c = mpbarrett_reduce(&mb, c, c); |
71dfe576 |
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 | |
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310 | mp **v = xmalloc(t * sizeof(mp *)); |
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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 | |
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329 | share_create(&s, t); |
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330 | s.s = mp_copy(sec); |
331 | share_mkshares(&s, r); |
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332 | for (i = 0; i < t; i++) |
333 | v[i] = share_get(&s, MP_NEW, p[i]); |
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334 | pp = mp_copy(s.p); |
335 | share_destroy(&s); |
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336 | assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2); |
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337 | |
3d64a35c |
338 | share_create(&s, t); |
71dfe576 |
339 | s.p = pp; |
3d64a35c |
340 | for (i = 0; i < t; i++) |
341 | share_add(&s, p[i], v[i]); |
71dfe576 |
342 | ss = share_combine(&s); |
343 | share_destroy(&s); |
344 | |
345 | if (MP_CMP(sec, !=, ss)) { |
346 | ok = 0; |
347 | fprintf(stderr, "\nbad recombination of shares\n"); |
348 | }; |
349 | |
350 | mp_drop(sec); |
351 | mp_drop(ss); |
352 | |
353 | for (i = 0; i < t; i++) |
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354 | mp_drop(v[i]); |
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355 | |
356 | xfree(v); |
357 | xfree(p); |
358 | |
3d64a35c |
359 | assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == 0); |
71dfe576 |
360 | return (ok); |
361 | } |
362 | |
363 | int main(void) |
364 | { |
365 | grand *r = fibrand_create(0); |
366 | unsigned i; |
367 | int ok = 1; |
368 | |
369 | fputs("share: ", stdout); |
370 | for (i = 0; i < 40; i++) { |
371 | if (!verify(r)) |
372 | ok = 0; |
373 | fputc('.', stdout); |
374 | fflush(stdout); |
375 | } |
376 | |
377 | if (ok) |
378 | fputs(" ok\n", stdout); |
379 | else |
380 | fputs(" failed\n", stdout); |
381 | return (ok ? EXIT_SUCCESS : EXIT_FAILURE); |
382 | } |
383 | |
384 | #endif |
385 | |
386 | /*----- That's all, folks -------------------------------------------------*/ |