| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: share.c,v 1.2 2000/06/18 23:05:19 mdw Exp $ |
| 4 | * |
| 5 | * Shamir's secret sharing |
| 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: share.c,v $ |
| 33 | * Revision 1.2 2000/06/18 23:05:19 mdw |
| 34 | * Minor performance tweak: use Barrett reduction rather than Montgomery. |
| 35 | * Fast secret sharing isn't done here, though: see `gfshare' instead. |
| 36 | * |
| 37 | * Revision 1.1 2000/06/17 12:09:38 mdw |
| 38 | * Shamir's secret sharing system. |
| 39 | * |
| 40 | */ |
| 41 | |
| 42 | /*----- Header files ------------------------------------------------------*/ |
| 43 | |
| 44 | #include <stdio.h> |
| 45 | #include <stdlib.h> |
| 46 | #include <string.h> |
| 47 | |
| 48 | #include "grand.h" |
| 49 | #include "mp.h" |
| 50 | #include "mpint.h" |
| 51 | #include "mpbarrett.h" |
| 52 | #include "mprand.h" |
| 53 | #include "pgen.h" |
| 54 | #include "rabin.h" |
| 55 | #include "share.h" |
| 56 | |
| 57 | /*----- Main code ---------------------------------------------------------*/ |
| 58 | |
| 59 | /* --- @share_create@ --- * |
| 60 | * |
| 61 | * Arguments: @share *s@ = pointer to share context to initialize |
| 62 | * @unsigned t, n@ = threshold parameters for the system |
| 63 | * |
| 64 | * Returns: --- |
| 65 | * |
| 66 | * Use: Initializes a sharing context. |
| 67 | */ |
| 68 | |
| 69 | void share_create(share *s, unsigned t, unsigned n) |
| 70 | { |
| 71 | s->t = t; |
| 72 | s->n = n; |
| 73 | s->i = 0; |
| 74 | s->s = 0; |
| 75 | s->p = 0; |
| 76 | s->v = 0; |
| 77 | } |
| 78 | |
| 79 | /* --- @share_destroy@ --- * |
| 80 | * |
| 81 | * Arguments: @share *s@ = pointer to share context to destroy |
| 82 | * |
| 83 | * Returns: --- |
| 84 | * |
| 85 | * Use: Disposes of a sharing context. All memory is freed, all |
| 86 | * integers are dropped. |
| 87 | */ |
| 88 | |
| 89 | void share_destroy(share *s) |
| 90 | { |
| 91 | unsigned n; |
| 92 | unsigned i; |
| 93 | |
| 94 | /* --- Dispose of the share vector --- */ |
| 95 | |
| 96 | if (s->v) { |
| 97 | if (s->i) |
| 98 | n = s->i; |
| 99 | else if (s->n) |
| 100 | n = s->n; |
| 101 | else |
| 102 | n = s->t; |
| 103 | for (i = 0; i < n; i++) { |
| 104 | if (s->v[i].y) |
| 105 | mp_drop(s->v[i].y); |
| 106 | } |
| 107 | xfree(s->v); |
| 108 | } |
| 109 | |
| 110 | /* --- Other stuff --- */ |
| 111 | |
| 112 | if (s->p) |
| 113 | mp_drop(s->p); |
| 114 | if (s->s) |
| 115 | mp_drop(s->s); |
| 116 | } |
| 117 | |
| 118 | /* --- @share_mkshares@ --- * |
| 119 | * |
| 120 | * Arguments: @share *s@ = pointer to share context to fill in |
| 121 | * @grand *r@ = pointer to random number source |
| 122 | * |
| 123 | * Returns: --- |
| 124 | * |
| 125 | * Use: Generates @c->n@ secret shares, such that any @c->t@ of them |
| 126 | * may be used to recover the secret. |
| 127 | * |
| 128 | * The context structure is expected to be mostly filled in. In |
| 129 | * particular, @t@, @n@ and @s@ must be initialized. If @p@ is |
| 130 | * zero, a prime number of appropriate size is generated |
| 131 | * automatically. If @v@ is zero, a vector of appropriate size |
| 132 | * is allocated. You should use the macro @SHARE_INIT@ or |
| 133 | * @share_create@ to construct sharing contexts. |
| 134 | */ |
| 135 | |
| 136 | void share_mkshares(share *s, grand *r) |
| 137 | { |
| 138 | mp **v; |
| 139 | unsigned i; |
| 140 | mp u; |
| 141 | mpw uw; |
| 142 | mpbarrett mb; |
| 143 | |
| 144 | /* --- If there's no prime, construct one --- */ |
| 145 | |
| 146 | if (!s->p) { |
| 147 | pgen_filterctx pf; |
| 148 | rabin pr; |
| 149 | mp *p; |
| 150 | unsigned bits = (mp_octets(s->s) + 1) * 8; |
| 151 | |
| 152 | pf.step = 2; |
| 153 | p = mprand(MP_NEW, bits, r, 1); |
| 154 | s->p = pgen("p", p, p, 0, 0, 0, pgen_filter, &pf, |
| 155 | rabin_iters(bits), pgen_test, &pr); |
| 156 | } |
| 157 | |
| 158 | /* --- Construct the coefficients --- */ |
| 159 | |
| 160 | mpbarrett_create(&mb, s->p); |
| 161 | v = xmalloc(s->t * sizeof(mp *)); |
| 162 | for (i = 0; i < s->t - 1; i++) |
| 163 | v[i] = mprand_range(MP_NEW, s->p, r, 0); |
| 164 | v[s->t - 1] = s->s; |
| 165 | |
| 166 | /* --- Construct the shares --- */ |
| 167 | |
| 168 | if (!s->v) |
| 169 | s->v = xmalloc(s->n * sizeof(share_pt)); |
| 170 | |
| 171 | mp_build(&u, &uw, &uw + 1); |
| 172 | for (uw = 1; uw <= s->n; uw++) { |
| 173 | mp *m = MP_ZERO; |
| 174 | unsigned j; |
| 175 | |
| 176 | /* --- Evaluate the polynomial at %$x = i + 1$% --- */ |
| 177 | |
| 178 | for (j = 0; j < s->t; j++) { |
| 179 | m = mp_mul(m, m, &u); |
| 180 | m = mpbarrett_reduce(&mb, m, m); |
| 181 | m = mp_add(m, m, v[j]); |
| 182 | if (MP_CMP(m, >=, s->p)) |
| 183 | m = mp_sub(m, m, s->p); |
| 184 | } |
| 185 | |
| 186 | /* --- Reduce the final result --- */ |
| 187 | |
| 188 | s->v[uw - 1].x = uw - 1; |
| 189 | s->v[uw - 1].y = m; |
| 190 | } |
| 191 | mpbarrett_destroy(&mb); |
| 192 | |
| 193 | /* --- Dispose of various bits of old rubbish --- */ |
| 194 | |
| 195 | for (i = 0; i < s->t - 1; i++) |
| 196 | mp_drop(v[i]); |
| 197 | xfree(v); |
| 198 | } |
| 199 | |
| 200 | /* --- @share_add@ --- * |
| 201 | * |
| 202 | * Arguments: @share *s@ = pointer to sharing context |
| 203 | * @unsigned x@ = which share number this is |
| 204 | * @mp *y@ = the share value |
| 205 | * |
| 206 | * Returns: Number of shares required before recovery may be performed. |
| 207 | * |
| 208 | * Use: Adds a share to the context. The context must have been |
| 209 | * initialized with the correct prime @p@ and threshold @t@. |
| 210 | */ |
| 211 | |
| 212 | unsigned share_add(share *s, unsigned x, mp *y) |
| 213 | { |
| 214 | /* --- If no vector has been allocated, create one --- */ |
| 215 | |
| 216 | if (!s->v) { |
| 217 | s->v = xmalloc(s->t * sizeof(share_pt)); |
| 218 | s->i = 0; |
| 219 | } |
| 220 | |
| 221 | assert(((void)"Share context is full", s->i < s->t)); |
| 222 | |
| 223 | /* --- Store the share in the vector --- */ |
| 224 | |
| 225 | s->v[s->i].x = x; |
| 226 | s->v[s->i].y = mp_copy(y); |
| 227 | s->i++; |
| 228 | |
| 229 | /* --- Done --- */ |
| 230 | |
| 231 | return (s->t - s->i); |
| 232 | } |
| 233 | |
| 234 | /* --- @share_combine@ --- * |
| 235 | * |
| 236 | * Arguments: @share *s@ = pointer to share context |
| 237 | * |
| 238 | * Returns: The secret, as a multiprecision integer. |
| 239 | * |
| 240 | * Use: Reconstructs a secret, given enough shares. |
| 241 | */ |
| 242 | |
| 243 | mp *share_combine(share *s) |
| 244 | { |
| 245 | mp *a = MP_ZERO; |
| 246 | mpbarrett mb; |
| 247 | unsigned i, j; |
| 248 | mp ii, jj; |
| 249 | mpw iiw, jjw; |
| 250 | mp *m = MP_NEW; |
| 251 | |
| 252 | /* --- Sanity checking --- */ |
| 253 | |
| 254 | assert(((void)"Not enough shares yet", s->i == s->t)); |
| 255 | |
| 256 | /* --- Initialization --- */ |
| 257 | |
| 258 | mpbarrett_create(&mb, s->p); |
| 259 | mp_build(&ii, &iiw, &iiw + 1); |
| 260 | mp_build(&jj, &jjw, &jjw + 1); |
| 261 | |
| 262 | /* --- Grind through the shares --- */ |
| 263 | |
| 264 | for (i = 0; i < s->t; i++) { |
| 265 | mp *c = MP_ONE; |
| 266 | |
| 267 | iiw = s->v[i].x + 1; |
| 268 | for (j = 0; j < s->t; j++) { |
| 269 | if (i == j) |
| 270 | continue; |
| 271 | jjw = s->v[j].x + 1; |
| 272 | if (s->v[j].x >= s->v[i].x) |
| 273 | m = mp_sub(m, &jj, &ii); |
| 274 | else { |
| 275 | m = mp_sub(m, &ii, &jj); |
| 276 | m = mp_sub(m, s->p, m); |
| 277 | } |
| 278 | mp_gcd(0, 0, &m, s->p, m); |
| 279 | c = mp_mul(c, c, &jj); |
| 280 | c = mpbarrett_reduce(&mb, c, c); |
| 281 | c = mp_mul(c, c, m); |
| 282 | c = mpbarrett_reduce(&mb, c, c); |
| 283 | } |
| 284 | c = mp_mul(c, c, s->v[i].y); |
| 285 | c = mpbarrett_reduce(&mb, c, c); |
| 286 | a = mp_add(a, a, c); |
| 287 | mp_drop(c); |
| 288 | } |
| 289 | |
| 290 | a = mpbarrett_reduce(&mb, a, a); |
| 291 | s->s = mp_copy(a); |
| 292 | if (m) |
| 293 | mp_drop(m); |
| 294 | mpbarrett_destroy(&mb); |
| 295 | return (a); |
| 296 | } |
| 297 | |
| 298 | /*----- Test rig ----------------------------------------------------------*/ |
| 299 | |
| 300 | #ifdef TEST_RIG |
| 301 | |
| 302 | #include "fibrand.h" |
| 303 | |
| 304 | static int verify(grand *r) |
| 305 | { |
| 306 | unsigned n = r->ops->range(r, 16) + 8; |
| 307 | unsigned t = r->ops->range(r, n - 1) + 1; |
| 308 | unsigned len = r->ops->range(r, 160); |
| 309 | |
| 310 | share_pt *v = xmalloc(t * sizeof(share_pt)); |
| 311 | unsigned *p = xmalloc(n * sizeof(unsigned)); |
| 312 | mp *sec = mprand(MP_NEW, len, r, 0); |
| 313 | share s; |
| 314 | mp *pp; |
| 315 | mp *ss; |
| 316 | unsigned i; |
| 317 | |
| 318 | int ok = 1; |
| 319 | |
| 320 | for (i = 0; i < n; i++) |
| 321 | p[i] = i; |
| 322 | for (i = 0; i < t; i++) { |
| 323 | unsigned long j = r->ops->range(r, n - i); |
| 324 | unsigned x = p[i]; |
| 325 | p[i] = p[i + j]; |
| 326 | p[i + j] = x; |
| 327 | } |
| 328 | |
| 329 | share_create(&s, t, n); |
| 330 | s.s = mp_copy(sec); |
| 331 | share_mkshares(&s, r); |
| 332 | for (i = 0; i < t; i++) { |
| 333 | v[i].x = s.v[p[i]].x; |
| 334 | v[i].y = mp_copy(s.v[p[i]].y); |
| 335 | } |
| 336 | pp = mp_copy(s.p); |
| 337 | share_destroy(&s); |
| 338 | |
| 339 | assert(mparena_count(MPARENA_GLOBAL) == t + 2); |
| 340 | |
| 341 | share_create(&s, t, n); |
| 342 | s.p = pp; |
| 343 | for (i = 0; i < t; i++) { |
| 344 | share_add(&s, v[i].x, v[i].y); |
| 345 | } |
| 346 | ss = share_combine(&s); |
| 347 | share_destroy(&s); |
| 348 | |
| 349 | if (MP_CMP(sec, !=, ss)) { |
| 350 | ok = 0; |
| 351 | fprintf(stderr, "\nbad recombination of shares\n"); |
| 352 | }; |
| 353 | |
| 354 | mp_drop(sec); |
| 355 | mp_drop(ss); |
| 356 | |
| 357 | for (i = 0; i < t; i++) |
| 358 | mp_drop(v[i].y); |
| 359 | |
| 360 | xfree(v); |
| 361 | xfree(p); |
| 362 | |
| 363 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 364 | return (ok); |
| 365 | } |
| 366 | |
| 367 | int main(void) |
| 368 | { |
| 369 | grand *r = fibrand_create(0); |
| 370 | unsigned i; |
| 371 | int ok = 1; |
| 372 | |
| 373 | fputs("share: ", stdout); |
| 374 | for (i = 0; i < 40; i++) { |
| 375 | if (!verify(r)) |
| 376 | ok = 0; |
| 377 | fputc('.', stdout); |
| 378 | fflush(stdout); |
| 379 | } |
| 380 | |
| 381 | if (ok) |
| 382 | fputs(" ok\n", stdout); |
| 383 | else |
| 384 | fputs(" failed\n", stdout); |
| 385 | return (ok ? EXIT_SUCCESS : EXIT_FAILURE); |
| 386 | } |
| 387 | |
| 388 | #endif |
| 389 | |
| 390 | /*----- That's all, folks -------------------------------------------------*/ |