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