71dfe576 |
1 | /* -*-c-*- |
2 | * |
3 | * $Id: share.c,v 1.1 2000/06/17 12:09:38 mdw Exp $ |
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 $ |
33 | * Revision 1.1 2000/06/17 12:09:38 mdw |
34 | * Shamir's secret sharing system. |
35 | * |
36 | */ |
37 | |
38 | /*----- Header files ------------------------------------------------------*/ |
39 | |
40 | #include <stdio.h> |
41 | #include <stdlib.h> |
42 | #include <string.h> |
43 | |
44 | #include "grand.h" |
45 | #include "mp.h" |
46 | #include "mpint.h" |
47 | #include "mpmont.h" |
48 | #include "mprand.h" |
49 | #include "pgen.h" |
50 | #include "rabin.h" |
51 | #include "share.h" |
52 | |
53 | /*----- Main code ---------------------------------------------------------*/ |
54 | |
55 | /* --- @share_create@ --- * |
56 | * |
57 | * Arguments: @share *s@ = pointer to share context to initialize |
58 | * @unsigned t, n@ = threshold parameters for the system |
59 | * |
60 | * Returns: --- |
61 | * |
62 | * Use: Initializes a sharing context. |
63 | */ |
64 | |
65 | void share_create(share *s, unsigned t, unsigned n) |
66 | { |
67 | s->t = t; |
68 | s->n = n; |
69 | s->i = 0; |
70 | s->s = 0; |
71 | s->p = 0; |
72 | s->v = 0; |
73 | } |
74 | |
75 | /* --- @share_destroy@ --- * |
76 | * |
77 | * Arguments: @share *s@ = pointer to share context to destroy |
78 | * |
79 | * Returns: --- |
80 | * |
81 | * Use: Disposes of a sharing context. All memory is freed, all |
82 | * integers are dropped. |
83 | */ |
84 | |
85 | void share_destroy(share *s) |
86 | { |
87 | unsigned n; |
88 | unsigned i; |
89 | |
90 | /* --- Dispose of the share vector --- */ |
91 | |
92 | if (s->v) { |
93 | if (s->i) |
94 | n = s->i; |
95 | else if (s->n) |
96 | n = s->n; |
97 | else |
98 | n = s->t; |
99 | for (i = 0; i < n; i++) { |
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 | * |
121 | * Use: Generates @c->n@ secret shares, such that any @c->t@ of them |
122 | * may be used to recover the secret. |
123 | * |
124 | * The context structure is expected to be mostly filled in. In |
125 | * particular, @t@, @n@ and @s@ must be initialized. If @p@ is |
126 | * zero, a prime number of appropriate size is generated |
127 | * automatically. If @v@ is zero, a vector of appropriate size |
128 | * is allocated. You should use the macro @SHARE_INIT@ or |
129 | * @share_create@ to construct sharing contexts. |
130 | */ |
131 | |
132 | void share_mkshares(share *s, grand *r) |
133 | { |
134 | mp **v; |
135 | unsigned i; |
136 | mp *u; |
137 | mpmont mm; |
138 | |
139 | /* --- If there's no prime, construct one --- */ |
140 | |
141 | if (!s->p) { |
142 | pgen_filterctx pf; |
143 | rabin pr; |
144 | mp *p; |
145 | unsigned bits = (mp_octets(s->s) + 1) * 8; |
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 | |
153 | /* --- Construct the coefficients --- */ |
154 | |
155 | mpmont_create(&mm, s->p); |
156 | v = xmalloc(s->t * sizeof(mp *)); |
157 | for (i = 0; i < s->t - 1; i++) |
158 | v[i] = mprand_range(MP_NEW, s->p, r, 0); |
159 | v[s->t - 1] = mpmont_mul(&mm, MP_NEW, s->s, mm.r2); |
160 | |
161 | /* --- Construct the shares --- */ |
162 | |
163 | if (!s->v) |
164 | s->v = xmalloc(s->n * sizeof(share_pt)); |
165 | |
166 | u = mp_copy(mm.r); |
167 | for (i = 0; i < s->n; i++) { |
168 | mp *m = MP_ZERO; |
169 | unsigned j; |
170 | |
171 | /* --- Evaluate the polynomial at %$x = i + 1$% --- */ |
172 | |
173 | for (j = 0; j < s->t; j++) { |
174 | m = mpmont_mul(&mm, m, m, u); |
175 | m = mp_add(m, m, v[j]); |
176 | if (MP_CMP(m, >=, s->p)) |
177 | m = mp_sub(m, m, s->p); |
178 | } |
179 | |
180 | /* --- Reduce the final result --- */ |
181 | |
182 | s->v[i].x = i; |
183 | s->v[i].y = mpmont_reduce(&mm, m, m); |
184 | |
185 | /* --- Compute the next point in Montgomery space --- */ |
186 | |
187 | u = mp_add(u, u, mm.r); |
188 | if (MP_CMP(u, >=, s->p)) |
189 | u = mp_sub(u, u, s->p); |
190 | } |
191 | mpmont_destroy(&mm); |
192 | |
193 | /* --- Dispose of various bits of old rubbish --- */ |
194 | |
195 | for (i = 0; i < s->t; i++) |
196 | mp_drop(v[i]); |
197 | mp_drop(u); |
198 | xfree(v); |
199 | } |
200 | |
201 | /* --- @share_add@ --- * |
202 | * |
203 | * Arguments: @share *s@ = pointer to sharing context |
204 | * @unsigned x@ = which share number this is |
205 | * @mp *y@ = the share value |
206 | * |
207 | * Returns: Number of shares required before recovery may be performed. |
208 | * |
209 | * Use: Adds a share to the context. The context must have been |
210 | * initialized with the correct prime @p@ and threshold @t@. |
211 | */ |
212 | |
213 | unsigned share_add(share *s, unsigned x, mp *y) |
214 | { |
215 | /* --- If no vector has been allocated, create one --- */ |
216 | |
217 | if (!s->v) { |
218 | s->v = xmalloc(s->t * sizeof(share_pt)); |
219 | s->i = 0; |
220 | } |
221 | |
222 | assert(((void)"Share context is full", s->i < s->t)); |
223 | |
224 | /* --- Store the share in the vector --- */ |
225 | |
226 | s->v[s->i].x = x; |
227 | s->v[s->i].y = mp_copy(y); |
228 | s->i++; |
229 | |
230 | /* --- Done --- */ |
231 | |
232 | return (s->t - s->i); |
233 | } |
234 | |
235 | /* --- @share_combine@ --- * |
236 | * |
237 | * Arguments: @share *s@ = pointer to share context |
238 | * |
239 | * Returns: The secret, as a multiprecision integer. |
240 | * |
241 | * Use: Reconstructs a secret, given enough shares. |
242 | */ |
243 | |
244 | mp *share_combine(share *s) |
245 | { |
246 | mp *a = MP_ZERO; |
247 | mpmont mm; |
248 | unsigned i, j; |
249 | mp *ii = MP_NEW, *jj = MP_NEW; |
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 | |
258 | mpmont_create(&mm, s->p); |
259 | |
260 | /* --- Grind through the shares --- */ |
261 | |
262 | for (i = 0; i < s->t; i++) { |
263 | mp *c = mp_copy(mm.r); |
264 | |
265 | ii = mp_fromuint(ii, s->v[i].x + 1); |
266 | for (j = 0; j < s->t; j++) { |
267 | if (i == j) |
268 | continue; |
269 | jj = mp_fromuint(jj, s->v[j].x + 1); |
270 | if (s->v[j].x >= s->v[i].x) |
271 | m = mp_sub(m, jj, ii); |
272 | else { |
273 | m = mp_sub(m, ii, jj); |
274 | m = mp_sub(m, s->p, m); |
275 | } |
276 | jj = mpmont_mul(&mm, jj, jj, mm.r2); |
277 | mp_gcd(0, 0, &m, s->p, m); |
278 | m = mpmont_mul(&mm, m, m, mm.r2); |
279 | m = mpmont_mul(&mm, m, m, jj); |
280 | c = mpmont_mul(&mm, c, c, m); |
281 | } |
282 | m = mpmont_mul(&mm, m, s->v[i].y, mm.r2); |
283 | c = mpmont_mul(&mm, c, c, m); |
284 | a = mp_add(a, a, c); |
285 | mp_drop(c); |
286 | } |
287 | |
288 | a = mpmont_reduce(&mm, a, a); |
289 | s->s = mp_copy(a); |
290 | mp_drop(ii); |
291 | if (jj) |
292 | mp_drop(jj); |
293 | mp_drop(m); |
294 | mpmont_destroy(&mm); |
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 -------------------------------------------------*/ |