3 * Shamir's secret sharing
5 * (c) 2000 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Header files ------------------------------------------------------*/
37 #include "mpbarrett.h"
43 /*----- Main code ---------------------------------------------------------*/
45 /* --- @share_create@ --- *
47 * Arguments: @share *s@ = pointer to share context to initialize
48 * @unsigned t@ = threshold for the system
52 * Use: Initializes a sharing context.
55 void share_create(share *s, unsigned t)
63 /* --- @share_destroy@ --- *
65 * Arguments: @share *s@ = pointer to share context to destroy
69 * Use: Disposes of a sharing context. All memory is freed, all
70 * integers are dropped.
73 void share_destroy(share *s)
77 /* --- Dispose of the share vector --- */
80 for (i = 0; i < s->t; i++)
85 /* --- Other stuff --- */
90 /* --- @share_mkshares@ --- *
92 * Arguments: @share *s@ = pointer to share context to fill in
93 * @grand *r@ = pointer to random number source
94 * @mp *n@ = the secret to share
98 * Use: Initializes a sharing context to be able to create shares.
99 * The context structure is expected to be mostly filled in. In
100 * particular, @t@ must be initialized. If @p@ is zero, a prime
101 * number of appropriate size is generated automatically. If
102 * @v@ is zero, a vector of appropriate size is allocated. You
103 * should use the macro @SHARE_INIT@ or @share_create@ to
104 * construct sharing contexts.
107 void share_mkshares(share *s, grand *r, mp *n)
111 /* --- If there's no prime, construct one --- */
117 unsigned bits = (mp_octets(n) + 1) * 8;
120 p = mprand(MP_NEW, bits, r, 1);
121 s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf,
122 rabin_iters(bits), pgen_test, &pr);
125 /* --- Construct the polynomial --- */
128 s->v = xmalloc(s->t * sizeof(share_pt));
129 for (i = 0; i < s->t - 1; i++)
130 s->v[i].y = mprand_range(MP_NEWSEC, s->p, r, 0);
131 s->v[s->t - 1].y = mp_copy(n);
134 /* --- @share_get@ --- *
136 * Arguments: @share *s@ = pointer to share conext
137 * @mp *d@ = destination for the share
138 * @unsigned x@ = share index to fetch
140 * Returns: The share, as requested.
142 * Use: Extracts a share from the system. You may extract @MPW_MAX@
143 * shares, or @s->p@ shares from the system, whichever is
144 * smaller. Shares are indexed from 0.
147 mp *share_get(share *s, mp *d, unsigned x)
154 /* --- Various bits of initialization --- */
156 mp_build(&u, &uw, &uw + 1);
159 /* --- Evaluate the polynomial at %$x = i + 1$% --- */
162 mpbarrett_create(&mb, s->p);
163 for (i = 0; i < s->t; i++) {
164 d = mp_mul(d, d, &u);
165 d = mp_add(d, d, s->v[i].y);
166 d = mpbarrett_reduce(&mb, d, d);
168 mpbarrett_destroy(&mb);
173 /* --- @share_addedp@ --- *
175 * Arguments: @share *s@ = pointer to sharing context
176 * @unsigned x@ = which share number to check
178 * Returns: Nonzero if share @x@ has been added already, zero if it
182 int share_addedp(share *s, unsigned x)
186 for (i = 0; i < s->i; i++) {
187 if (s->v[i].x == x + 1)
193 /* --- @share_add@ --- *
195 * Arguments: @share *s@ = pointer to sharing context
196 * @unsigned x@ = which share number this is
197 * @mp *y@ = the share value
199 * Returns: Number of shares required before recovery may be performed.
201 * Use: Adds a share to the context. The context must have been
202 * initialized with the correct prime @p@ and threshold @t@.
205 unsigned share_add(share *s, unsigned x, mp *y)
207 assert(((void)"Share context is full", s->i < s->t));
208 assert(((void)"Share already present", !share_addedp(s, x)));
210 /* --- If no vector has been allocated, create one --- */
214 s->v = xmalloc(s->t * sizeof(share_pt));
216 for (i = 0; i < s->t; i++)
220 /* --- Store the share in the vector --- */
222 s->v[s->i].x = x + 1;
223 s->v[s->i].y = mp_copy(y);
228 return (s->t - s->i);
231 /* --- @share_combine@ --- *
233 * Arguments: @share *s@ = pointer to share context
235 * Returns: The secret, as a multiprecision integer.
237 * Use: Reconstructs a secret, given enough shares.
240 mp *share_combine(share *s)
249 /* --- Sanity checking --- */
251 assert(((void)"Not enough shares yet", s->i == s->t));
253 /* --- Initialization --- */
255 mpbarrett_create(&mb, s->p);
256 mp_build(&ii, &iiw, &iiw + 1);
257 mp_build(&jj, &jjw, &jjw + 1);
259 /* --- Grind through the shares --- */
261 for (i = 0; i < s->t; i++) {
265 for (j = 0; j < s->t; j++) {
269 if (s->v[j].x >= s->v[i].x)
270 m = mp_sub(m, &jj, &ii);
272 m = mp_sub(m, &ii, &jj);
273 m = mp_sub(m, s->p, m);
275 m = mp_modinv(m, m, s->p);
276 c = mp_mul(c, c, &jj);
277 c = mpbarrett_reduce(&mb, c, c);
279 c = mpbarrett_reduce(&mb, c, c);
281 c = mp_mul(c, c, s->v[i].y);
282 c = mpbarrett_reduce(&mb, c, c);
287 a = mpbarrett_reduce(&mb, a, a);
289 mpbarrett_destroy(&mb);
293 /*----- Test rig ----------------------------------------------------------*/
299 static int verify(grand *r)
301 unsigned n = r->ops->range(r, 16) + 8;
302 unsigned t = r->ops->range(r, n - 1) + 1;
303 unsigned len = r->ops->range(r, 160);
305 mp **v = xmalloc(t * sizeof(mp *));
306 unsigned *p = xmalloc(n * sizeof(unsigned));
307 mp *sec = mprand(MP_NEW, len, r, 0);
315 for (i = 0; i < n; i++)
317 for (i = 0; i < t; i++) {
318 unsigned long j = r->ops->range(r, n - i);
325 share_mkshares(&s, r, sec);
326 for (i = 0; i < t; i++)
327 v[i] = share_get(&s, MP_NEW, p[i]);
330 assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2);
334 for (i = 0; i < t; i++)
335 share_add(&s, p[i], v[i]);
336 ss = share_combine(&s);
339 if (!MP_EQ(sec, ss)) {
341 fprintf(stderr, "\nbad recombination of shares\n");
347 for (i = 0; i < t; i++)
353 assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == 0);
359 grand *r = fibrand_create(0);
363 fputs("share: ", stdout);
364 for (i = 0; i < 40; i++) {
372 fputs(" ok\n", stdout);
374 fputs(" failed\n", stdout);
375 return (ok ? EXIT_SUCCESS : EXIT_FAILURE);
380 /*----- That's all, folks -------------------------------------------------*/