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   1 /* -*-c-*-
   2  *
   3  * $Id: gfshare.c,v 1.7 2001/06/16 23:42:17 mdw Exp $
   4  *
   5  * Secret sharing over %$\gf{2^8}$%
   6  *
   7  * (c) 2000 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  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.
  18  *
  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.
  23  *
  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,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: gfshare.c,v $
  33  * Revision 1.7  2001/06/16 23:42:17  mdw
  34  * Typesetting fixes.
  35  *
  36  * Revision 1.6  2000/12/06 20:30:10  mdw
  37  * Change secret sharing interface: present the secret at share
  38  * construction time.
  39  *
  40  * Revision 1.5  2000/06/24 19:11:47  mdw
  41  * Fix daft error in the comment for @gfshare_get@.
  42  *
  43  * Revision 1.4  2000/06/24 18:29:05  mdw
  44  * Interface change: allow shares to be extracted from a context on demand,
  45  * rather than building them all up-front.
  46  *
  47  * Revision 1.3  2000/06/22 18:04:13  mdw
  48  * Improve secret reconstruction -- compute coefficients as needed rather
  49  * than making a big array of them.
  50  *
  51  * Revision 1.2  2000/06/18 23:12:15  mdw
  52  * Change typesetting of Galois Field names.
  53  *
  54  * Revision 1.1  2000/06/17 10:56:30  mdw
  55  * Fast but nonstandard secret sharing system.
  56  *
  57  */
  58
  59 /*----- Header files ------------------------------------------------------*/
  60
  61 #include <assert.h>
  62 #include <stdarg.h>
  63 #include <stdio.h>
  64 #include <string.h>
  65
  66 #include <mLib/alloc.h>
  67 #include <mLib/bits.h>
  68
  69 #include "arena.h"
  70 #include "gfshare.h"
  71 #include "gfshare-tab.h"
  72 #include "grand.h"
  73
  74 /*----- Static variables --------------------------------------------------*/
  75
  76 static octet gflog[] = GFSHARE_LOG, gfexp[] = GFSHARE_EXP;
  77
  78 /*----- Main code ---------------------------------------------------------*/
  79
  80 /* --- @gfshare_create@ --- *
  81  *
  82  * Arguments:   @gfshare *s@ = pointer to share context to initialize
  83  *              @unsigned t@ = threshold for the system
  84  *              @size_t sz@ = size of the secret
  85  *
  86  * Returns:     ---
  87  *
  88  * Use:         Initializes a sharing context.
  89  */
  90
  91 void gfshare_create(gfshare *s, unsigned t, size_t sz)
  92 {
  93   s->t = t;
  94   s->i = 0;
  95   s->sz = sz;
  96   s->v = 0;
  97 }
  98
  99 /* --- @gfshare_destroy@ --- *
 100  *
 101  * Arguments:   @gfshare *s@ = pointer to share context to destroy
 102  *
 103  * Returns:     ---
 104  *
 105  * Use:         Disposes of a sharing context.  The allocations for the
 106  *              individual shares and the vector @v@ are freed; the secret is
 107  *              left alone.
 108  */
 109
 110 void gfshare_destroy(gfshare *s)
 111 {
 112   if (s->v)
 113     XS_FREE(s->v);
 114 }
 115
 116 /* --- @gfshare_mkshares@ --- *
 117  *
 118  * Arguments:   @gfshare *s@ = pointer to share context to fill in
 119  *              @grand *r@ = pointer to random number source
 120  *              @const void *buf@ = pointer to the secret to share
 121  *
 122  * Returns:     ---
 123  *
 124  * Use:         Initializes a sharing context to be able to create shares.
 125  *              The context structure is expected to be mostly filled in.  In
 126  *              particular, @t@ must be initialized.  If @v@ is zero, a
 127  *              vector of appropriate size is allocated.  You should use the
 128  *              macro @GFSHARE_INIT@ or @gfshare_create@ to construct sharing
 129  *              contexts.
 130  */
 131
 132 void gfshare_mkshares(gfshare *s, grand *r, const void *buf)
 133 {
 134   s->v = XS_ALLOC(s->sz * s->t);
 135   r->ops->fill(r, s->v, s->sz * (s->t - 1));
 136   memcpy(s->v + s->sz * (s->t - 1), buf, s->sz);
 137 }
 138
 139 /* --- @gfshare_get@ --- *
 140  *
 141  * Arguments:   @gfshare *s@ = pointer to share conext
 142  *              @unsigned x@ = share index to fetch
 143  *              @void *buf@ = pointer to output buffer
 144  *
 145  * Returns:     ---
 146  *
 147  * Use:         Extracts a share from the system.  You may extract up to 255
 148  *              shares from the system.  Shares are indexed from 0.
 149  */
 150
 151 void gfshare_get(gfshare *s, unsigned x, void *buf)
 152 {
 153   unsigned i;
 154   const octet *p = s->v;
 155   unsigned ilog = gflog[x + 1];
 156
 157   /* --- Evaluate the polynomial at %$x = i + 1$% --- */
 158
 159   memcpy(buf, p, s->sz);
 160   p += s->sz;
 161
 162   for (i = 1; i < s->t; i++) {
 163     octet *q = buf;
 164     unsigned k;
 165     for (k = 0; k < s->sz; k++) {
 166       unsigned qq = *q;
 167       if (qq)
 168         qq = gfexp[ilog + gflog[qq]];
 169       *q++ = qq ^ *p++;
 170     }
 171   }
 172 }
 173
 174 /* --- @gfshare_add@ --- *
 175  *
 176  * Arguments:   @gfshare *s@ = pointer to sharing context
 177  *              @unsigned x@ = which share number this is
 178  *              @const void *y@ = the share value
 179  *
 180  * Returns:     Number of shares required before recovery may be performed.
 181  *
 182  * Use:         Adds a share to the context.  The context must have been
 183  *              initialized with the correct threshold @t@.
 184  */
 185
 186 unsigned gfshare_add(gfshare *s, unsigned x, const void *y)
 187 {
 188   octet *p;
 189
 190   /* --- If no vector has been allocated, create one --- */
 191
 192   if (!s->v) {
 193     s->v = XS_ALLOC(s->t * (s->sz + 1));
 194     s->i = 0;
 195   }
 196
 197   assert(((void)"Share context is full", s->i < s->t));
 198
 199   /* --- Store the share in the vector --- */
 200
 201   p = s->v + s->i * (s->sz + 1);
 202   *p++ = x + 1;
 203   memcpy(p, y, s->sz);
 204   s->i++;
 205
 206   /* --- Done --- */
 207
 208   return (s->t - s->i);
 209 }
 210
 211 /* --- @gfshare_combine@ --- *
 212  *
 213  * Arguments:   @gfshare *s@ = pointer to share context
 214  *              @void *buf@ = pointer to output buffer for the secret
 215  *
 216  * Returns:     ---
 217  *
 218  * Use:         Reconstructs a secret, given enough shares.
 219  */
 220
 221 void gfshare_combine(gfshare *s, void *buf)
 222 {
 223   unsigned i, j;
 224   unsigned xi, xj;
 225
 226   /* --- Sanity checking --- */
 227
 228   assert(((void)"Not enough shares yet", s->i == s->t));
 229
 230   /* --- Grind through the shares --- */
 231
 232   memset(buf, 0, s->sz);
 233
 234   for (i = 0; i < s->t; i++) {
 235     octet *p = buf;
 236     octet *q = s->v + i * (s->sz + 1);
 237     unsigned c = 0, ci = 0;
 238
 239     /* --- Compute the magic coefficient --- */
 240
 241     xi = *q++;
 242     for (j = 0; j < s->t; j++) {
 243       if (i == j)
 244         continue;
 245       xj = s->v[j * (s->sz + 1)];
 246       c += gflog[xj];
 247       if (c >= 0xff)
 248         c -= 0xff;
 249       ci += gflog[xi ^ xj];
 250       if (ci >= 0xff)
 251         ci -= 0xff;
 252     }
 253     if (ci > c)
 254       c += 0xff;
 255     c -= ci;
 256
 257     /* --- Work out another layer of the secret --- */
 258
 259     p = buf;
 260     for (j = 0; j < s->sz; j++) {
 261       if (*q)
 262         *p ^= gfexp[c + gflog[*q]];
 263       p++, q++;
 264     }
 265   }
 266 }
 267
 268 /*----- Test rig ----------------------------------------------------------*/
 269
 270 #ifdef TEST_RIG
 271
 272 #include "fibrand.h"
 273
 274 static int verify(grand *r)
 275 {
 276   unsigned n = r->ops->range(r, 16) + 8;
 277   unsigned t = r->ops->range(r, n - 1) + 1;
 278   unsigned len = r->ops->range(r, 32) + 1;
 279
 280   octet *v = xmalloc(t * len);
 281   unsigned *p = xmalloc(n * sizeof(unsigned));
 282   octet *sec = xmalloc(len), *sbuf = xmalloc(len);
 283   gfshare s;
 284   unsigned i;
 285
 286   int ok = 1;
 287
 288   for (i = 0; i < n; i++)
 289     p[i] = i;
 290   for (i = 0; i < t; i++) {
 291     unsigned long j = r->ops->range(r, n - i);
 292     unsigned x = p[i];
 293     p[i] = p[i + j];
 294     p[i + j] = x;
 295   }
 296
 297   r->ops->fill(r, sec, len);
 298
 299   gfshare_create(&s, t, len);
 300
 301   gfshare_mkshares(&s, r, sec);
 302   for (i = 0; i < t; i++)
 303     gfshare_get(&s, p[i], v + (i * len));
 304   gfshare_destroy(&s);
 305
 306   gfshare_create(&s, t, len);
 307   for (i = 0; i < t; i++)
 308     gfshare_add(&s, p[i], v + (i * len));
 309   gfshare_combine(&s, sbuf);
 310   gfshare_destroy(&s);
 311
 312   if (memcmp(sec, sbuf, len) != 0) {
 313     ok = 0;
 314     fprintf(stderr, "\nbad recombination of shares\n");
 315   };
 316
 317   xfree(sec);
 318   xfree(sbuf);
 319
 320   xfree(v);
 321   xfree(p);
 322
 323   return (ok);
 324 }
 325
 326 int main(void)
 327 {
 328   grand *r = fibrand_create(0);
 329   unsigned i;
 330   int ok = 1;
 331
 332   fputs("gfshare: ", stdout);
 333   for (i = 0; i < 40; i++) {
 334     if (!verify(r))
 335       ok = 0;
 336     fputc('.', stdout);
 337     fflush(stdout);
 338   }
 339
 340   if (ok)
 341     fputs(" ok\n", stdout);
 342   else
 343     fputs(" failed\n", stdout);
 344   return (ok ? EXIT_SUCCESS : EXIT_FAILURE);
 345 }
 346
 347 #endif
 348
 349 /*----- That's all, folks -------------------------------------------------*/