git.distorted.org.uk Git - u/mdw/catacomb/blob - misc/share.c

   1 /* -*-c-*-
   2  *
   3  * Shamir's secret sharing
   4  *
   5  * (c) 2000 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  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.
  16  *
  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.
  21  *
  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,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include <stdio.h>
  31 #include <stdlib.h>
  32 #include <string.h>
  33
  34 #include "grand.h"
  35 #include "mp.h"
  36 #include "mpint.h"
  37 #include "mpbarrett.h"
  38 #include "mprand.h"
  39 #include "pgen.h"
  40 #include "rabin.h"
  41 #include "share.h"
  42
  43 /*----- Main code ---------------------------------------------------------*/
  44
  45 /* --- @share_create@ --- *
  46  *
  47  * Arguments:   @share *s@ = pointer to share context to initialize
  48  *              @unsigned t@ = threshold for the system
  49  *
  50  * Returns:     ---
  51  *
  52  * Use:         Initializes a sharing context.
  53  */
  54
  55 void share_create(share *s, unsigned t)
  56 {
  57   s->t = t;
  58   s->i = 0;
  59   s->p = 0;
  60   s->v = 0;
  61 }
  62
  63 /* --- @share_destroy@ --- *
  64  *
  65  * Arguments:   @share *s@ = pointer to share context to destroy
  66  *
  67  * Returns:     ---
  68  *
  69  * Use:         Disposes of a sharing context.  All memory is freed, all
  70  *              integers are dropped.
  71  */
  72
  73 void share_destroy(share *s)
  74 {
  75   unsigned i;
  76
  77   /* --- Dispose of the share vector --- */
  78
  79   if (s->v) {
  80     for (i = 0; i < s->t; i++)
  81       mp_drop(s->v[i].y);
  82     xfree(s->v);
  83   }
  84
  85   /* --- Other stuff --- */
  86
  87   mp_drop(s->p);
  88 }
  89
  90 /* --- @share_mkshares@ --- *
  91  *
  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
  95  *
  96  * Returns:     ---
  97  *
  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.
 105  */
 106
 107 void share_mkshares(share *s, grand *r, mp *n)
 108 {
 109   unsigned i;
 110
 111   /* --- If there's no prime, construct one --- */
 112
 113   if (!s->p) {
 114     pgen_filterctx pf;
 115     rabin pr;
 116     mp *p;
 117     unsigned bits = (mp_octets(n) + 1) * 8;
 118
 119     pf.step = 2;
 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);
 123   }
 124
 125   /* --- Construct the polynomial --- */
 126
 127   if (!s->v)
 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);
 132 }
 133
 134 /* --- @share_get@ --- *
 135  *
 136  * Arguments:   @share *s@ = pointer to share conext
 137  *              @mp *d@ = destination for the share
 138  *              @unsigned x@ = share index to fetch
 139  *
 140  * Returns:     The share, as requested.
 141  *
 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.
 145  */
 146
 147 mp *share_get(share *s, mp *d, unsigned x)
 148 {
 149   mpbarrett mb;
 150   mpw uw = x + 1;
 151   mp u;
 152   unsigned i;
 153
 154   /* --- Various bits of initialization --- */
 155
 156   mp_build(&u, &uw, &uw + 1);
 157   mp_drop(d);
 158
 159   /* --- Evaluate the polynomial at %$x = i + 1$% --- */
 160
 161   d = MP_ZERO;
 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);
 167   }
 168   mpbarrett_destroy(&mb);
 169
 170   return (d);
 171 }
 172
 173 /* --- @share_addedp@ --- *
 174  *
 175  * Arguments:   @share *s@ = pointer to sharing context
 176  *              @unsigned x@ = which share number to check
 177  *
 178  * Returns:     Nonzero if share @x@ has been added already, zero if it
 179  *              hasn't.
 180  */
 181
 182 int share_addedp(share *s, unsigned x)
 183 {
 184   unsigned i;
 185
 186   for (i = 0; i < s->i; i++) {
 187     if (s->v[i].x == x + 1)
 188       return (1);
 189   }
 190   return (0);
 191 }
 192
 193 /* --- @share_add@ --- *
 194  *
 195  * Arguments:   @share *s@ = pointer to sharing context
 196  *              @unsigned x@ = which share number this is
 197  *              @mp *y@ = the share value
 198  *
 199  * Returns:     Number of shares required before recovery may be performed.
 200  *
 201  * Use:         Adds a share to the context.  The context must have been
 202  *              initialized with the correct prime @p@ and threshold @t@.
 203  */
 204
 205 unsigned share_add(share *s, unsigned x, mp *y)
 206 {
 207   assert(((void)"Share context is full", s->i < s->t));
 208   assert(((void)"Share already present", !share_addedp(s, x)));
 209
 210   /* --- If no vector has been allocated, create one --- */
 211
 212   if (!s->v) {
 213     unsigned i;
 214     s->v = xmalloc(s->t * sizeof(share_pt));
 215     s->i = 0;
 216     for (i = 0; i < s->t; i++)
 217       s->v[i].y = 0;
 218   }
 219
 220   /* --- Store the share in the vector --- */
 221
 222   s->v[s->i].x = x + 1;
 223   s->v[s->i].y = mp_copy(y);
 224   s->i++;
 225
 226   /* --- Done --- */
 227
 228   return (s->t - s->i);
 229 }
 230
 231 /* --- @share_combine@ --- *
 232  *
 233  * Arguments:   @share *s@ = pointer to share context
 234  *
 235  * Returns:     The secret, as a multiprecision integer.
 236  *
 237  * Use:         Reconstructs a secret, given enough shares.
 238  */
 239
 240 mp *share_combine(share *s)
 241 {
 242   mp *a = MP_ZERO;
 243   mpbarrett mb;
 244   unsigned i, j;
 245   mp ii, jj;
 246   mpw iiw, jjw;
 247   mp *m = MP_NEW;
 248
 249   /* --- Sanity checking --- */
 250
 251   assert(((void)"Not enough shares yet", s->i == s->t));
 252
 253   /* --- Initialization --- */
 254
 255   mpbarrett_create(&mb, s->p);
 256   mp_build(&ii, &iiw, &iiw + 1);
 257   mp_build(&jj, &jjw, &jjw + 1);
 258
 259   /* --- Grind through the shares --- */
 260
 261   for (i = 0; i < s->t; i++) {
 262     mp *c = MP_ONE;
 263
 264     iiw = s->v[i].x;
 265     for (j = 0; j < s->t; j++) {
 266       if (i == j)
 267         continue;
 268       jjw = s->v[j].x;
 269       if (s->v[j].x >= s->v[i].x)
 270         m = mp_sub(m, &jj, &ii);
 271       else {
 272         m = mp_sub(m, &ii, &jj);
 273         m = mp_sub(m, s->p, m);
 274       }
 275       m = mp_modinv(m, m, s->p);
 276       c = mp_mul(c, c, &jj);
 277       c = mpbarrett_reduce(&mb, c, c);
 278       c = mp_mul(c, c, m);
 279       c = mpbarrett_reduce(&mb, c, c);
 280     }
 281     c = mp_mul(c, c, s->v[i].y);
 282     c = mpbarrett_reduce(&mb, c, c);
 283     a = mp_add(a, a, c);
 284     mp_drop(c);
 285   }
 286
 287   a = mpbarrett_reduce(&mb, a, a);
 288   mp_drop(m);
 289   mpbarrett_destroy(&mb);
 290   return (a);
 291 }
 292
 293 /*----- Test rig ----------------------------------------------------------*/
 294
 295 #ifdef TEST_RIG
 296
 297 #include "fibrand.h"
 298
 299 static int verify(grand *r)
 300 {
 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);
 304
 305   mp **v = xmalloc(t * sizeof(mp *));
 306   unsigned *p = xmalloc(n * sizeof(unsigned));
 307   mp *sec = mprand(MP_NEW, len, r, 0);
 308   share s;
 309   mp *pp;
 310   mp *ss;
 311   unsigned i;
 312
 313   int ok = 1;
 314
 315   for (i = 0; i < n; i++)
 316     p[i] = i;
 317   for (i = 0; i < t; i++) {
 318     unsigned long j = r->ops->range(r, n - i);
 319     unsigned x = p[i];
 320     p[i] = p[i + j];
 321     p[i + j] = x;
 322   }
 323
 324   share_create(&s, t);
 325   share_mkshares(&s, r, sec);
 326   for (i = 0; i < t; i++)
 327     v[i] = share_get(&s, MP_NEW, p[i]);
 328   pp = mp_copy(s.p);
 329   share_destroy(&s);
 330   assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == t + 2);
 331
 332   share_create(&s, t);
 333   s.p = pp;
 334   for (i = 0; i < t; i++)
 335     share_add(&s, p[i], v[i]);
 336   ss = share_combine(&s);
 337   share_destroy(&s);
 338
 339   if (!MP_EQ(sec, ss)) {
 340     ok = 0;
 341     fprintf(stderr, "\nbad recombination of shares\n");
 342   };
 343
 344   mp_drop(sec);
 345   mp_drop(ss);
 346
 347   for (i = 0; i < t; i++)
 348     mp_drop(v[i]);
 349
 350   xfree(v);
 351   xfree(p);
 352
 353   assert(mparena_count(MPARENA_GLOBAL) + mparena_count(MPARENA_SECURE) == 0);
 354   return (ok);
 355 }
 356
 357 int main(void)
 358 {
 359   grand *r = fibrand_create(0);
 360   unsigned i;
 361   int ok = 1;
 362
 363   fputs("share: ", stdout);
 364   for (i = 0; i < 40; i++) {
 365     if (!verify(r))
 366       ok = 0;
 367     fputc('.', stdout);
 368     fflush(stdout);
 369   }
 370
 371   if (ok)
 372     fputs(" ok\n", stdout);
 373   else
 374     fputs(" failed\n", stdout);
 375   return (ok ? EXIT_SUCCESS : EXIT_FAILURE);
 376 }
 377
 378 #endif
 379
 380 /*----- That's all, folks -------------------------------------------------*/