3 * $Id: share.c,v 1.3 2000/06/24 18:29:05 mdw Exp $
5 * Shamir's secret sharing
7 * (c) 2000 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
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.
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.
41 * Revision 1.1 2000/06/17 12:09:38 mdw
42 * Shamir's secret sharing system.
46 /*----- Header files ------------------------------------------------------*/
55 #include "mpbarrett.h"
61 /*----- Main code ---------------------------------------------------------*/
63 /* --- @share_create@ --- *
65 * Arguments: @share *s@ = pointer to share context to initialize
66 * @unsigned t@ = threshold for the system
70 * Use: Initializes a sharing context.
73 void share_create(share *s, unsigned t)
82 /* --- @share_destroy@ --- *
84 * Arguments: @share *s@ = pointer to share context to destroy
88 * Use: Disposes of a sharing context. All memory is freed, all
89 * integers are dropped.
92 void share_destroy(share *s)
96 /* --- Dispose of the share vector --- */
99 for (i = 0; i < s->t; i++) {
106 /* --- Other stuff --- */
114 /* --- @share_mkshares@ --- *
116 * Arguments: @share *s@ = pointer to share context to fill in
117 * @grand *r@ = pointer to random number source
121 * Use: Initializes a sharing context to be able to create shares.
122 * The context structure is expected to be mostly filled in. In
123 * particular, @t@ and @s@ must be initialized. If @p@ is zero,
124 * a prime number of appropriate size is generated
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.
130 void share_mkshares(share *s, grand *r)
134 /* --- If there's no prime, construct one --- */
140 unsigned bits = (mp_octets(s->s) + 1) * 8;
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);
148 /* --- Construct the polynomial --- */
151 s->v = xmalloc(s->t * sizeof(share_pt));
152 for (i = 0; i < s->t - 1; i++)
153 s->v[i].y = mprand_range(MP_NEWSEC, s->p, r, 0);
154 s->v[s->t - 1].y = mp_copy(s->s);
157 /* --- @share_get@ --- *
159 * Arguments: @share *s@ = pointer to share conext
160 * @mp *d@ = destination for the share
161 * @unsigned x@ = share index to fetch
163 * Returns: The share, as requested.
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.
170 mp *share_get(share *s, mp *d, unsigned x)
177 /* --- Various bits of initialization --- */
179 mp_build(&u, &uw, &uw + 1);
183 /* --- Evaluate the polynomial at %$x = i + 1$% --- */
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);
192 mpbarrett_destroy(&mb);
197 /* --- @share_add@ --- *
199 * Arguments: @share *s@ = pointer to sharing context
200 * @unsigned x@ = which share number this is
201 * @mp *y@ = the share value
203 * Returns: Number of shares required before recovery may be performed.
205 * Use: Adds a share to the context. The context must have been
206 * initialized with the correct prime @p@ and threshold @t@.
209 unsigned share_add(share *s, unsigned x, mp *y)
211 /* --- If no vector has been allocated, create one --- */
215 s->v = xmalloc(s->t * sizeof(share_pt));
217 for (i = 0; i < s->t; i++)
221 assert(((void)"Share context is full", s->i < s->t));
223 /* --- Store the share in the vector --- */
225 s->v[s->i].x = x + 1;
226 s->v[s->i].y = mp_copy(y);
231 return (s->t - s->i);
234 /* --- @share_combine@ --- *
236 * Arguments: @share *s@ = pointer to share context
238 * Returns: The secret, as a multiprecision integer.
240 * Use: Reconstructs a secret, given enough shares.
243 mp *share_combine(share *s)
252 /* --- Sanity checking --- */
254 assert(((void)"Not enough shares yet", s->i == s->t));
256 /* --- Initialization --- */
258 mpbarrett_create(&mb, s->p);
259 mp_build(&ii, &iiw, &iiw + 1);
260 mp_build(&jj, &jjw, &jjw + 1);
262 /* --- Grind through the shares --- */
264 for (i = 0; i < s->t; i++) {
268 for (j = 0; j < s->t; j++) {
272 if (s->v[j].x >= s->v[i].x)
273 m = mp_sub(m, &jj, &ii);
275 m = mp_sub(m, &ii, &jj);
276 m = mp_sub(m, s->p, m);
278 mp_gcd(0, 0, &m, s->p, m);
279 c = mp_mul(c, c, &jj);
280 c = mpbarrett_reduce(&mb, c, c);
282 c = mpbarrett_reduce(&mb, c, c);
284 c = mp_mul(c, c, s->v[i].y);
285 c = mpbarrett_reduce(&mb, c, c);
290 a = mpbarrett_reduce(&mb, a, a);
294 mpbarrett_destroy(&mb);
298 /*----- Test rig ----------------------------------------------------------*/
304 static int verify(grand *r)
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);
310 mp **v = xmalloc(t * sizeof(mp *));
311 unsigned *p = xmalloc(n * sizeof(unsigned));
312 mp *sec = mprand(MP_NEW, len, r, 0);
320 for (i = 0; i < n; i++)
322 for (i = 0; i < t; i++) {
323 unsigned long j = r->ops->range(r, n - i);
331 share_mkshares(&s, r);
332 for (i = 0; i < t; i++)
333 v[i] = share_get(&s, MP_NEW, p[i]);
336 assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2);
340 for (i = 0; i < t; i++)
341 share_add(&s, p[i], v[i]);
342 ss = share_combine(&s);
345 if (MP_CMP(sec, !=, ss)) {
347 fprintf(stderr, "\nbad recombination of shares\n");
353 for (i = 0; i < t; i++)
359 assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == 0);
365 grand *r = fibrand_create(0);
369 fputs("share: ", stdout);
370 for (i = 0; i < 40; i++) {
378 fputs(" ok\n", stdout);
380 fputs(" failed\n", stdout);
381 return (ok ? EXIT_SUCCESS : EXIT_FAILURE);
386 /*----- That's all, folks -------------------------------------------------*/