3 * $Id: share.c,v 1.6 2001/02/03 16:05:41 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 1.6 2001/02/03 16:05:41 mdw
34 * Now @mp_drop@ checks its argument is non-NULL before attempting to free
35 * it. Note that the macro version @MP_DROP@ doesn't do this.
37 * Revision 1.5 2000/12/06 20:30:10 mdw
38 * Change secret sharing interface: present the secret at share
41 * Revision 1.4 2000/10/08 12:16:17 mdw
42 * Use @MP_EQ@ instead of @MP_CMP@.
44 * Revision 1.3 2000/06/24 18:29:05 mdw
45 * Interface change: allow shares to be extracted from a context on demand,
46 * rather than building them all up-front.
48 * Revision 1.2 2000/06/18 23:05:19 mdw
49 * Minor performance tweak: use Barrett reduction rather than Montgomery.
50 * Fast secret sharing isn't done here, though: see `gfshare' instead.
52 * Revision 1.1 2000/06/17 12:09:38 mdw
53 * Shamir's secret sharing system.
57 /*----- Header files ------------------------------------------------------*/
66 #include "mpbarrett.h"
72 /*----- Main code ---------------------------------------------------------*/
74 /* --- @share_create@ --- *
76 * Arguments: @share *s@ = pointer to share context to initialize
77 * @unsigned t@ = threshold for the system
81 * Use: Initializes a sharing context.
84 void share_create(share
*s
, unsigned t
)
92 /* --- @share_destroy@ --- *
94 * Arguments: @share *s@ = pointer to share context to destroy
98 * Use: Disposes of a sharing context. All memory is freed, all
99 * integers are dropped.
102 void share_destroy(share
*s
)
106 /* --- Dispose of the share vector --- */
109 for (i
= 0; i
< s
->t
; i
++)
114 /* --- Other stuff --- */
119 /* --- @share_mkshares@ --- *
121 * Arguments: @share *s@ = pointer to share context to fill in
122 * @grand *r@ = pointer to random number source
123 * @mp *n@ = the secret to share
127 * Use: Initializes a sharing context to be able to create shares.
128 * The context structure is expected to be mostly filled in. In
129 * particular, @t@ must be initialized. If @p@ is zero, a prime
130 * number of appropriate size is generated automatically. If
131 * @v@ is zero, a vector of appropriate size is allocated. You
132 * should use the macro @SHARE_INIT@ or @share_create@ to
133 * construct sharing contexts.
136 void share_mkshares(share
*s
, grand
*r
, mp
*n
)
140 /* --- If there's no prime, construct one --- */
146 unsigned bits
= (mp_octets(n
) + 1) * 8;
149 p
= mprand(MP_NEW
, bits
, r
, 1);
150 s
->p
= pgen("p", p
, p
, 0, 0, 0, pgen_filter
, &pf
,
151 rabin_iters(bits
), pgen_test
, &pr
);
154 /* --- Construct the polynomial --- */
157 s
->v
= xmalloc(s
->t
* sizeof(share_pt
));
158 for (i
= 0; i
< s
->t
- 1; i
++)
159 s
->v
[i
].y
= mprand_range(MP_NEWSEC
, s
->p
, r
, 0);
160 s
->v
[s
->t
- 1].y
= mp_copy(n
);
163 /* --- @share_get@ --- *
165 * Arguments: @share *s@ = pointer to share conext
166 * @mp *d@ = destination for the share
167 * @unsigned x@ = share index to fetch
169 * Returns: The share, as requested.
171 * Use: Extracts a share from the system. You may extract @MPW_MAX@
172 * shares, or @s->p@ shares from the system, whichever is
173 * smaller. Shares are indexed from 0.
176 mp
*share_get(share
*s
, mp
*d
, unsigned x
)
183 /* --- Various bits of initialization --- */
185 mp_build(&u
, &uw
, &uw
+ 1);
188 /* --- Evaluate the polynomial at %$x = i + 1$% --- */
191 mpbarrett_create(&mb
, s
->p
);
192 for (i
= 0; i
< s
->t
; i
++) {
193 d
= mp_mul(d
, d
, &u
);
194 d
= mp_add(d
, d
, s
->v
[i
].y
);
195 d
= mpbarrett_reduce(&mb
, d
, d
);
197 mpbarrett_destroy(&mb
);
202 /* --- @share_add@ --- *
204 * Arguments: @share *s@ = pointer to sharing context
205 * @unsigned x@ = which share number this is
206 * @mp *y@ = the share value
208 * Returns: Number of shares required before recovery may be performed.
210 * Use: Adds a share to the context. The context must have been
211 * initialized with the correct prime @p@ and threshold @t@.
214 unsigned share_add(share
*s
, unsigned x
, mp
*y
)
216 /* --- If no vector has been allocated, create one --- */
220 s
->v
= xmalloc(s
->t
* sizeof(share_pt
));
222 for (i
= 0; i
< s
->t
; i
++)
226 assert(((void)"Share context is full", s
->i
< s
->t
));
228 /* --- Store the share in the vector --- */
230 s
->v
[s
->i
].x
= x
+ 1;
231 s
->v
[s
->i
].y
= mp_copy(y
);
236 return (s
->t
- s
->i
);
239 /* --- @share_combine@ --- *
241 * Arguments: @share *s@ = pointer to share context
243 * Returns: The secret, as a multiprecision integer.
245 * Use: Reconstructs a secret, given enough shares.
248 mp
*share_combine(share
*s
)
257 /* --- Sanity checking --- */
259 assert(((void)"Not enough shares yet", s
->i
== s
->t
));
261 /* --- Initialization --- */
263 mpbarrett_create(&mb
, s
->p
);
264 mp_build(&ii
, &iiw
, &iiw
+ 1);
265 mp_build(&jj
, &jjw
, &jjw
+ 1);
267 /* --- Grind through the shares --- */
269 for (i
= 0; i
< s
->t
; i
++) {
273 for (j
= 0; j
< s
->t
; j
++) {
277 if (s
->v
[j
].x
>= s
->v
[i
].x
)
278 m
= mp_sub(m
, &jj
, &ii
);
280 m
= mp_sub(m
, &ii
, &jj
);
281 m
= mp_sub(m
, s
->p
, m
);
283 mp_gcd(0, 0, &m
, s
->p
, m
);
284 c
= mp_mul(c
, c
, &jj
);
285 c
= mpbarrett_reduce(&mb
, c
, c
);
287 c
= mpbarrett_reduce(&mb
, c
, c
);
289 c
= mp_mul(c
, c
, s
->v
[i
].y
);
290 c
= mpbarrett_reduce(&mb
, c
, c
);
295 a
= mpbarrett_reduce(&mb
, a
, a
);
297 mpbarrett_destroy(&mb
);
301 /*----- Test rig ----------------------------------------------------------*/
307 static int verify(grand
*r
)
309 unsigned n
= r
->ops
->range(r
, 16) + 8;
310 unsigned t
= r
->ops
->range(r
, n
- 1) + 1;
311 unsigned len
= r
->ops
->range(r
, 160);
313 mp
**v
= xmalloc(t
* sizeof(mp
*));
314 unsigned *p
= xmalloc(n
* sizeof(unsigned));
315 mp
*sec
= mprand(MP_NEW
, len
, r
, 0);
323 for (i
= 0; i
< n
; i
++)
325 for (i
= 0; i
< t
; i
++) {
326 unsigned long j
= r
->ops
->range(r
, n
- i
);
333 share_mkshares(&s
, r
, sec
);
334 for (i
= 0; i
< t
; i
++)
335 v
[i
] = share_get(&s
, MP_NEW
, p
[i
]);
338 assert(mparena_count(MPARENA_GLOBAL
) + mparena_count(MPARENA_SECURE
) == t
+ 2);
342 for (i
= 0; i
< t
; i
++)
343 share_add(&s
, p
[i
], v
[i
]);
344 ss
= share_combine(&s
);
347 if (!MP_EQ(sec
, ss
)) {
349 fprintf(stderr
, "\nbad recombination of shares\n");
355 for (i
= 0; i
< t
; i
++)
361 assert(mparena_count(MPARENA_GLOBAL
) + mparena_count(MPARENA_SECURE
) == 0);
367 grand
*r
= fibrand_create(0);
371 fputs("share: ", stdout
);
372 for (i
= 0; i
< 40; i
++) {
380 fputs(" ok\n", stdout
);
382 fputs(" failed\n", stdout
);
383 return (ok ? EXIT_SUCCESS
: EXIT_FAILURE
);
388 /*----- That's all, folks -------------------------------------------------*/