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