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 /*----- Header files ------------------------------------------------------*/
39 #include "mpbarrett.h"
45 /*----- Main code ---------------------------------------------------------*/
47 /* --- @share_create@ --- *
49 * Arguments: @share *s@ = pointer to share context to initialize
50 * @unsigned t@ = threshold for the system
54 * Use: Initializes a sharing context.
57 void share_create(share *s, unsigned t)
65 /* --- @share_destroy@ --- *
67 * Arguments: @share *s@ = pointer to share context to destroy
71 * Use: Disposes of a sharing context. All memory is freed, all
72 * integers are dropped.
75 void share_destroy(share *s)
79 /* --- Dispose of the share vector --- */
82 for (i = 0; i < s->t; i++)
87 /* --- Other stuff --- */
92 /* --- @share_mkshares@ --- *
94 * Arguments: @share *s@ = pointer to share context to fill in
95 * @grand *r@ = pointer to random number source
96 * @mp *n@ = the secret to share
100 * Use: Initializes a sharing context to be able to create shares.
101 * The context structure is expected to be mostly filled in. In
102 * particular, @t@ must be initialized. If @p@ is zero, a prime
103 * number of appropriate size is generated automatically. If
104 * @v@ is zero, a vector of appropriate size is allocated. You
105 * should use the macro @SHARE_INIT@ or @share_create@ to
106 * construct sharing contexts.
109 void share_mkshares(share *s, grand *r, mp *n)
113 /* --- If there's no prime, construct one --- */
119 unsigned bits = (mp_octets(n) + 1) * 8;
122 p = mprand(MP_NEW, bits, r, 1);
123 s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf,
124 rabin_iters(bits), pgen_test, &pr);
127 /* --- Construct the polynomial --- */
130 s->v = xmalloc(s->t * sizeof(share_pt));
131 for (i = 0; i < s->t - 1; i++)
132 s->v[i].y = mprand_range(MP_NEWSEC, s->p, r, 0);
133 s->v[s->t - 1].y = mp_copy(n);
136 /* --- @share_get@ --- *
138 * Arguments: @share *s@ = pointer to share conext
139 * @mp *d@ = destination for the share
140 * @unsigned x@ = share index to fetch
142 * Returns: The share, as requested.
144 * Use: Extracts a share from the system. You may extract @MPW_MAX@
145 * shares, or @s->p@ shares from the system, whichever is
146 * smaller. Shares are indexed from 0.
149 mp *share_get(share *s, mp *d, unsigned x)
156 /* --- Various bits of initialization --- */
158 mp_build(&u, &uw, &uw + 1);
161 /* --- Evaluate the polynomial at %$x = i + 1$% --- */
164 mpbarrett_create(&mb, s->p);
165 for (i = 0; i < s->t; i++) {
166 d = mp_mul(d, d, &u);
167 d = mp_add(d, d, s->v[i].y);
168 d = mpbarrett_reduce(&mb, d, d);
170 mpbarrett_destroy(&mb);
175 /* --- @share_addedp@ --- *
177 * Arguments: @share *s@ = pointer to sharing context
178 * @unsigned x@ = which share number to check
180 * Returns: Nonzero if share @x@ has been added already, zero if it
184 int share_addedp(share *s, unsigned x)
188 for (i = 0; i < s->i; i++) {
189 if (s->v[i].x == x + 1)
195 /* --- @share_add@ --- *
197 * Arguments: @share *s@ = pointer to sharing context
198 * @unsigned x@ = which share number this is
199 * @mp *y@ = the share value
201 * Returns: Number of shares required before recovery may be performed.
203 * Use: Adds a share to the context. The context must have been
204 * initialized with the correct prime @p@ and threshold @t@.
207 unsigned share_add(share *s, unsigned x, mp *y)
209 assert(((void)"Share context is full", s->i < s->t));
210 assert(((void)"Share already present", !share_addedp(s, x)));
212 /* --- If no vector has been allocated, create one --- */
216 s->v = xmalloc(s->t * sizeof(share_pt));
218 for (i = 0; i < s->t; i++)
222 /* --- Store the share in the vector --- */
224 s->v[s->i].x = x + 1;
225 s->v[s->i].y = mp_copy(y);
230 return (s->t - s->i);
233 /* --- @share_combine@ --- *
235 * Arguments: @share *s@ = pointer to share context
237 * Returns: The secret, as a multiprecision integer.
239 * Use: Reconstructs a secret, given enough shares.
242 mp *share_combine(share *s)
251 /* --- Sanity checking --- */
253 assert(((void)"Not enough shares yet", s->i == s->t));
255 /* --- Initialization --- */
257 mpbarrett_create(&mb, s->p);
258 mp_build(&ii, &iiw, &iiw + 1);
259 mp_build(&jj, &jjw, &jjw + 1);
261 /* --- Grind through the shares --- */
263 for (i = 0; i < s->t; i++) {
267 for (j = 0; j < s->t; j++) {
271 if (s->v[j].x >= s->v[i].x)
272 m = mp_sub(m, &jj, &ii);
274 m = mp_sub(m, &ii, &jj);
275 m = mp_sub(m, s->p, m);
277 m = mp_modinv(m, m, s->p);
278 c = mp_mul(c, c, &jj);
279 c = mpbarrett_reduce(&mb, c, c);
281 c = mpbarrett_reduce(&mb, c, c);
283 c = mp_mul(c, c, s->v[i].y);
284 c = mpbarrett_reduce(&mb, c, c);
289 a = mpbarrett_reduce(&mb, a, a);
291 mpbarrett_destroy(&mb);
295 /*----- Test rig ----------------------------------------------------------*/
301 static int verify(grand *r)
303 unsigned n = r->ops->range(r, 16) + 8;
304 unsigned t = r->ops->range(r, n - 1) + 1;
305 unsigned len = r->ops->range(r, 160);
307 mp **v = xmalloc(t * sizeof(mp *));
308 unsigned *p = xmalloc(n * sizeof(unsigned));
309 mp *sec = mprand(MP_NEW, len, r, 0);
317 for (i = 0; i < n; i++)
319 for (i = 0; i < t; i++) {
320 unsigned long j = r->ops->range(r, n - i);
327 share_mkshares(&s, r, sec);
328 for (i = 0; i < t; i++)
329 v[i] = share_get(&s, MP_NEW, p[i]);
332 assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2);
336 for (i = 0; i < t; i++)
337 share_add(&s, p[i], v[i]);
338 ss = share_combine(&s);
341 if (!MP_EQ(sec, ss)) {
343 fprintf(stderr, "\nbad recombination of shares\n");
349 for (i = 0; i < t; i++)
355 assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == 0);
361 grand *r = fibrand_create(0);
365 fputs("share: ", stdout);
366 for (i = 0; i < 40; i++) {
374 fputs(" ok\n", stdout);
376 fputs(" failed\n", stdout);
377 return (ok ? EXIT_SUCCESS : EXIT_FAILURE);
382 /*----- That's all, folks -------------------------------------------------*/