git.distorted.org.uk Git - u/mdw/catacomb/blob - ec-info.c

   1 /* -*-c-*-
   2  *
   3  * $Id$
   4  *
   5  * Elliptic curve information management
   6  *
   7  * (c) 2004 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 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "ec.h"
  33 #include "ectab.h"
  34 #include "gf.h"
  35 #include "pgen.h"
  36 #include "mprand.h"
  37 #include "mpint.h"
  38 #include "rabin.h"
  39
  40 /*----- Main code ---------------------------------------------------------*/
  41
  42 /* --- @ec_curveparse@ --- *
  43  *
  44  * Arguments:   @qd_parse *qd@ = parser context
  45  *
  46  * Returns:     Elliptic curve pointer if OK, or null.
  47  *
  48  * Use:         Parses an elliptic curve description, which has the form
  49  *
  50  *                * a field description
  51  *                * an optional `;'
  52  *                * `prime', `primeproj', `bin', or `binproj'
  53  *                * an optional `:'
  54  *                * the %$a$% parameter
  55  *                * an optional `,'
  56  *                * the %$b$% parameter
  57  */
  58
  59 ec_curve *ec_curveparse(qd_parse *qd)
  60 {
  61   mp *a = MP_NEW, *b = MP_NEW;
  62   ec_curve *c;
  63   field *f;
  64
  65   if ((f = field_parse(qd)) == 0) goto fail;
  66   qd_delim(qd, ';');
  67   switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
  68     case 0:
  69       if (F_TYPE(f) != FTY_PRIME) {
  70         qd->e = "field not prime";
  71         goto fail;
  72       }
  73       qd_delim(qd, ':');
  74       if ((a = qd_getmp(qd)) == 0) goto fail;
  75       qd_delim(qd, ',');
  76       if ((b = qd_getmp(qd)) == 0) goto fail;
  77       c = ec_prime(f, a, b);
  78       break;
  79     case 1:
  80       if (F_TYPE(f) != FTY_PRIME) {
  81         qd->e = "field not prime";
  82         goto fail;
  83       }
  84       qd_delim(qd, ':');
  85       if ((a = qd_getmp(qd)) == 0) goto fail;
  86       qd_delim(qd, ',');
  87       if ((b = qd_getmp(qd)) == 0) goto fail;
  88       c = ec_primeproj(f, a, b);
  89       break;
  90     case 2:
  91       if (F_TYPE(f) != FTY_BINARY) {
  92         qd->e = "field not binary";
  93         goto fail;
  94       }
  95       qd_delim(qd, ':');
  96       if ((a = qd_getmp(qd)) == 0) goto fail;
  97       qd_delim(qd, ',');
  98       if ((b = qd_getmp(qd)) == 0) goto fail;
  99       c = ec_bin(f, a, b);
 100       break;
 101     case 3:
 102       if (F_TYPE(f) != FTY_BINARY) {
 103         qd->e = "field not binary";
 104         goto fail;
 105       }
 106       qd_delim(qd, ':');
 107       if ((a = qd_getmp(qd)) == 0) goto fail;
 108       qd_delim(qd, ',');
 109       if ((b = qd_getmp(qd)) == 0) goto fail;
 110       c = ec_binproj(f, a, b);
 111       break;
 112     default:
 113       goto fail;
 114   }
 115   if (!c) {
 116     qd->e = "bad curve parameters";
 117     goto fail;
 118   }
 119   if (a) MP_DROP(a);
 120   if (b) MP_DROP(b);
 121   return (c);
 122
 123 fail:
 124   if (f) F_DESTROY(f);
 125   if (a) MP_DROP(a);
 126   if (b) MP_DROP(b);
 127   return (0);
 128 }
 129
 130 /* --- @ec_ptparse@ --- *
 131  *
 132  * Arguments:   @qd_parse *qd@ = parser context
 133  *              @ec *p@ = where to put the point
 134  *
 135  * Returns:     The point address, or null.
 136  *
 137  * Use:         Parses an elliptic curve point.  This has the form
 138  *
 139  *                * %$x$%-coordinate
 140  *                * optional `,'
 141  *                * %$y$%-coordinate
 142  */
 143
 144 ec *ec_ptparse(qd_parse *qd, ec *p)
 145 {
 146   mp *x = MP_NEW, *y = MP_NEW;
 147
 148   if (qd_enum(qd, "inf") >= 0) {
 149     EC_SETINF(p);
 150     return (p);
 151   }
 152   if ((x = qd_getmp(qd)) == 0) goto fail;
 153   qd_delim(qd, ',');
 154   if ((y = qd_getmp(qd)) == 0) goto fail;
 155   EC_DESTROY(p);
 156   p->x = x;
 157   p->y = y;
 158   p->z = 0;
 159   return (p);
 160
 161 fail:
 162   if (x) MP_DROP(x);
 163   if (y) MP_DROP(y);
 164   return (0);
 165 }
 166
 167 /* --- @ec_infofromdata@ --- *
 168  *
 169  * Arguments:   @ec_info *ei@ = where to write the information
 170  *              @ecdata *ed@ = raw data
 171  *
 172  * Returns:     ---
 173  *
 174  * Use:         Loads elliptic curve information about one of the standard
 175  *              curves.
 176  */
 177
 178 void ec_infofromdata(ec_info *ei, ecdata *ed)
 179 {
 180   field *f;
 181
 182   switch (ed->ftag) {
 183     case FTAG_PRIME:
 184       f = field_prime(&ed->p);
 185       ei->c = ec_primeproj(f, &ed->a, &ed->b);
 186       break;
 187     case FTAG_NICEPRIME:
 188       f = field_niceprime(&ed->p);
 189       ei->c = ec_primeproj(f, &ed->a, &ed->b);
 190       break;
 191     case FTAG_BINPOLY:
 192       f = field_binpoly(&ed->p);
 193       ei->c = ec_binproj(f, &ed->a, &ed->b);
 194       break;
 195     case FTAG_BINNORM:
 196       f = field_binnorm(&ed->p, &ed->beta);
 197       ei->c = ec_binproj(f, &ed->a, &ed->b);
 198       break;
 199     default:
 200       abort();
 201   }
 202
 203   assert(f); assert(ei->c);
 204   EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0;
 205   ei->r = &ed->r; ei->h = &ed->h;
 206 }
 207
 208 /* --- @ec_infoparse@ --- *
 209  *
 210  * Arguments:   @qd_parse *qd@ = parser context
 211  *              @ec_info *ei@ = curve information block, currently
 212  *                      uninitialized
 213  *
 214  * Returns:     Zero on success, nonzero on failure.
 215  *
 216  * Use:         Parses an elliptic curve information string, and stores the
 217  *              information in @ei@.  This is either the name of a standard
 218  *              curve, or it has the form
 219  *
 220  *                * elliptic curve description
 221  *                * optional `;'
 222  *                * common point
 223  *                * optional `:'
 224  *                * group order
 225  *                * optional `*'
 226  *                * cofactor
 227  */
 228
 229 int ec_infoparse(qd_parse *qd, ec_info *ei)
 230 {
 231   ec_curve *c = 0;
 232   field *f;
 233   ec g = EC_INIT;
 234   const ecentry *ee;
 235   mp *r = MP_NEW, *h = MP_NEW;
 236
 237   for (ee = ectab; ee->name; ee++) {
 238     if (qd_enum(qd, ee->name) >= 0) {
 239       ec_infofromdata(ei, ee->data);
 240       goto found;
 241     }
 242   }
 243
 244   if ((c = ec_curveparse(qd)) == 0) goto fail;
 245   qd_delim(qd, ';'); if (!ec_ptparse(qd, &g)) goto fail;
 246   qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail;
 247   qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail;
 248   ei->c = c; ei->g = g; ei->r = r; ei->h = h;
 249
 250 found:
 251   return (0);
 252
 253 fail:
 254   EC_DESTROY(&g);
 255   if (r) MP_DROP(r);
 256   if (h) MP_DROP(h);
 257   if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); }
 258   return (-1);
 259 }
 260
 261 /* --- @ec_getinfo@ --- *
 262  *
 263  * Arguments:   @ec_info *ei@ = where to write the information
 264  *              @const char *p@ = string describing a curve
 265  *
 266  * Returns:     Null on success, or a pointer to an error message.
 267  *
 268  * Use:         Parses out information about a curve.  The string is either a
 269  *              standard curve name, or a curve info string.
 270  */
 271
 272 const char *ec_getinfo(ec_info *ei, const char *p)
 273 {
 274   qd_parse qd;
 275
 276   qd.p = p;
 277   qd.e = 0;
 278   if (ec_infoparse(&qd, ei))
 279     return (qd.e);
 280   if (!qd_eofp(&qd)) {
 281     ec_freeinfo(ei);
 282     return ("junk found at end of string");
 283   }
 284   return (0);
 285 }
 286
 287 /* --- @ec_sameinfop@ --- *
 288  *
 289  * Arguments:   @ec_info *ei, *ej@ = two elliptic curve parameter sets
 290  *
 291  * Returns:     Nonzero if the curves are identical (not just isomorphic).
 292  *
 293  * Use:         Checks for sameness of curve parameters.
 294  */
 295
 296 int ec_sameinfop(ec_info *ei, ec_info *ej)
 297 {
 298   return (ec_samep(ei->c, ej->c) &&
 299           MP_EQ(ei->r, ej->r) && MP_EQ(ei->h, ej->h) &&
 300           EC_EQ(&ei->g, &ej->g));
 301 }
 302
 303 /* --- @ec_freeinfo@ --- *
 304  *
 305  * Arguments:   @ec_info *ei@ = elliptic curve information block to free
 306  *
 307  * Returns:     ---
 308  *
 309  * Use:         Frees the information block.
 310  */
 311
 312 void ec_freeinfo(ec_info *ei)
 313 {
 314   field *f;
 315
 316   EC_DESTROY(&ei->g);
 317   MP_DROP(ei->r);
 318   MP_DROP(ei->h);
 319   f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f);
 320 }
 321
 322 /* --- @ec_checkinfo@ --- *
 323  *
 324  * Arguments:   @const ec_info *ei@ = elliptic curve information block
 325  *
 326  * Returns:     Null if OK, or pointer to error message.
 327  *
 328  * Use:         Checks an elliptic curve according to the rules in SEC1.
 329  */
 330
 331 static const char *gencheck(const ec_info *ei, grand *gr, mp *q)
 332 {
 333   ec_curve *c = ei->c;
 334   field *f = c->f;
 335   int i, j, n;
 336   mp *qq;
 337   mp *nn;
 338   mp *x, *y;
 339   ec p;
 340   int rc;
 341
 342   /* --- Check %$G \in E$% --- */
 343
 344   if (EC_ATINF(&ei->g)) return ("generator at infinity");
 345   if (ec_check(c, &ei->g)) return ("generator not on curve");
 346
 347   /* --- Check %$r$% is prime --- */
 348
 349   if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
 350
 351   /* --- Check that the cofactor is correct --- *
 352    *
 353    * Let %$q$% be the size of the field, and let %$n = h r = \#E(\gf{q})$% be
 354    * the number of %$\gf{q}$%-rational points on our curve.  Hasse's theorem
 355    * tells us that
 356    *
 357    *   %$|q + 1 - n| \le 2\sqrt{q}$%
 358    *
 359    * or, if we square both sides,
 360    *
 361    *   %$(q + 1 - n)^2 \le 4 q$%.
 362    *
 363    * We'd like the cofactor to be uniquely determined by this equation, which
 364    * is possible as long as it's not too big.  (If it is, we have to mess
 365    * about with Weil pairings, which is no fun.)  For this, we need the
 366    * following inequalities:
 367    *
 368    *   * %$A = (q + 1 - n)^2 \le 4 q$% (both lower and upper bounds from
 369    *     Hasse's theorem);
 370    *
 371    *   * %$B = (q + 1 - n - r)^2 > 4 q$% (check %$h - 1$% isn't possible);
 372    *     and
 373    *
 374    *   * %$C = (q + 1 - n + r)^2 > 4 q$% (check %$h + 1$% isn't possible).
 375    */
 376
 377   rc = 1;
 378   qq = mp_add(MP_NEW, q, MP_ONE);
 379   nn = mp_mul(MP_NEW, ei->r, ei->h);
 380   nn = mp_sub(nn, qq, nn);
 381   qq = mp_lsl(qq, q, 2);
 382
 383   y = mp_sqr(MP_NEW, nn);
 384   if (MP_CMP(y, >, qq)) rc = 0;
 385
 386   x = mp_sub(MP_NEW, nn, ei->r);
 387   y = mp_sqr(y, x);
 388   if (MP_CMP(y, <=, qq)) rc = 0;
 389
 390   x = mp_add(x, nn, ei->r);
 391   y = mp_sqr(y, x);
 392   if (MP_CMP(y, <=, qq)) rc = 0;
 393
 394   MP_DROP(x);
 395   MP_DROP(y);
 396   MP_DROP(nn);
 397   MP_DROP(qq);
 398   if (!rc) return ("incorrect or ambiguous cofactor");
 399
 400   /* --- Check %$n G = O$% --- */
 401
 402   EC_CREATE(&p);
 403   ec_mul(c, &p, &ei->g, ei->r);
 404   rc = EC_ATINF(&p);
 405   EC_DESTROY(&p);
 406   if (!rc) return ("incorrect group order");
 407
 408   /* --- Check %$q^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
 409    *
 410    * Actually, give up if %$q^B \ge 2^{2000}$% because that's probably
 411    * good enough for jazz.
 412    */
 413
 414   x = MP_NEW;
 415   mp_div(0, &x, q, ei->r);
 416   n = mp_bits(ei->r) - 1;
 417   for (i = 0, j = n; i < 20; i++, j += n) {
 418     if (j >= 2000)
 419       break;
 420     if (MP_EQ(x, MP_ONE)) {
 421       MP_DROP(x);
 422       return("curve embedding degree too low");
 423     }
 424     x = mp_mul(x, x, f->m);
 425     mp_div(0, &x, x, ei->r);
 426   }
 427   MP_DROP(x);
 428
 429   /* --- Done --- */
 430
 431   return (0);
 432 }
 433
 434 static int primeeltp(mp *x, field *f)
 435   { return (!MP_NEGP(x) && MP_CMP(x, <, f->m)); }
 436
 437 static const char *primecheck(const ec_info *ei, grand *gr)
 438 {
 439   ec_curve *c = ei->c;
 440   field *f = c->f;
 441   mp *x, *y;
 442   int rc;
 443   const char *err;
 444
 445   /* --- Check %$p$% is an odd prime --- */
 446
 447   if (!pgen_primep(f->m, gr)) return ("p not prime");
 448
 449   /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
 450
 451   if (!primeeltp(c->a, f)) return ("a out of range");
 452   if (!primeeltp(c->b, f)) return ("b out of range");
 453   if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
 454   if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
 455
 456   /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
 457
 458   x = F_SQR(f, MP_NEW, c->a);
 459   x = F_MUL(f, x, x, c->a);
 460   x = F_QDL(f, x, x);
 461   y = F_SQR(f, MP_NEW, c->b);
 462   y = F_TPL(f, y, y);
 463   y = F_TPL(f, y, y);
 464   y = F_TPL(f, y, y);
 465   x = F_ADD(f, x, x, y);
 466   rc = F_ZEROP(f, x);
 467   MP_DROP(x);
 468   MP_DROP(y);
 469   if (rc) return ("not an elliptic curve");
 470
 471   /* --- Now do the general checks --- */
 472
 473   err = gencheck(ei, gr, f->m);
 474   return (err);
 475 }
 476
 477 static const char *bincheck(const ec_info *ei, grand *gr)
 478 {
 479   ec_curve *c = ei->c;
 480   field *f = c->f;
 481   mp *x;
 482   int rc;
 483   const char *err;
 484
 485   /* --- Check that %$m$% is prime --- */
 486
 487   x = mp_fromuint(MP_NEW, f->nbits);
 488   rc = pfilt_smallfactor(x);
 489   mp_drop(x);
 490   if (rc != PGEN_DONE) return ("degree not prime");
 491
 492   /* --- Check that %$p$% is irreducible --- */
 493
 494   if (!gf_irreduciblep(f->m)) return ("p not irreducible");
 495
 496   /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
 497
 498   if (mp_bits(c->a) > f->nbits) return ("a out of range");
 499   if (mp_bits(c->b) > f->nbits) return ("a out of range");
 500   if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
 501   if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
 502
 503   /* --- Check that %$b \ne 0$% --- */
 504
 505   if (F_ZEROP(f, c->b)) return ("b is zero");
 506
 507   /* --- Now do the general checks --- */
 508
 509   x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
 510   err = gencheck(ei, gr, x);
 511   mp_drop(x);
 512   return (err);
 513 }
 514
 515 const char *ec_checkinfo(const ec_info *ei, grand *gr)
 516 {
 517   switch (F_TYPE(ei->c->f)) {
 518     case FTY_PRIME: return (primecheck(ei, gr)); break;
 519     case FTY_BINARY: return (bincheck(ei, gr)); break;
 520   }
 521   return ("unknown curve type");
 522 }
 523
 524 /*----- Test rig ----------------------------------------------------------*/
 525
 526 #ifdef TEST_RIG
 527
 528 #include "fibrand.h"
 529
 530 int main(int argc, char *argv[])
 531 {
 532   const ecentry *ee;
 533   const char *e;
 534   int ok = 1;
 535   int i;
 536   grand *gr;
 537
 538   gr = fibrand_create(0);
 539   if (argc > 1) {
 540     for (i = 1; i < argc; i++) {
 541       ec_info ei;
 542       if ((e = ec_getinfo(&ei, argv[i])) != 0)
 543         fprintf(stderr, "bad curve spec `%s': %s\n", argv[i], e);
 544       else {
 545         e = ec_checkinfo(&ei, gr);
 546         ec_freeinfo(&ei);
 547         if (!e)
 548           printf("OK %s\n", argv[i]);
 549         else {
 550           printf("BAD %s: %s\n", argv[i], e);
 551           ok = 0;
 552         }
 553       }
 554       assert(mparena_count(MPARENA_GLOBAL) == 0);
 555     }
 556   } else {
 557     fputs("checking standard curves:", stdout);
 558     fflush(stdout);
 559     for (ee = ectab; ee->name; ee++) {
 560       ec_info ei;
 561       ec_infofromdata(&ei, ee->data);
 562       e = ec_checkinfo(&ei, gr);
 563       ec_freeinfo(&ei);
 564       if (e) {
 565         printf(" [%s fails: %s]", ee->name, e);
 566         ok = 0;
 567       } else
 568         printf(" %s", ee->name);
 569       fflush(stdout);
 570       assert(mparena_count(MPARENA_GLOBAL) == 0);
 571     }
 572     fputs(ok ? " ok\n" : " failed\n", stdout);
 573   }
 574   gr->ops->destroy(gr);
 575   return (!ok);
 576 }
 577
 578 #endif
 579
 580 /*----- That's all, folks -------------------------------------------------*/