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 int primeeltp(mp *x, field *f)
 332 {
 333   return (!MP_NEGP(x) && MP_CMP(x, <, f->m));
 334 }
 335
 336 static const char *primecheck(const ec_info *ei, grand *gr)
 337 {
 338   ec_curve *c = ei->c;
 339   field *f = c->f;
 340   int i;
 341   mp *x, *y;
 342   ec p;
 343   int rc;
 344
 345   /* --- Check %$p$% is an odd prime --- */
 346
 347   if (!pgen_primep(f->m, gr)) return ("p not prime");
 348
 349   /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
 350
 351   if (!primeeltp(c->a, f)) return ("a out of range");
 352   if (!primeeltp(c->b, f)) return ("b out of range");
 353   if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
 354   if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
 355
 356   /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
 357
 358   x = F_SQR(f, MP_NEW, c->a);
 359   x = F_MUL(f, x, x, c->a);
 360   x = F_QDL(f, x, x);
 361   y = F_SQR(f, MP_NEW, c->b);
 362   y = F_TPL(f, y, y);
 363   y = F_TPL(f, y, y);
 364   y = F_TPL(f, y, y);
 365   x = F_ADD(f, x, x, y);
 366   rc = F_ZEROP(f, x);
 367   MP_DROP(x);
 368   MP_DROP(y);
 369   if (rc) return ("not an elliptic curve");
 370
 371   /* --- Check %$G \in E$% --- */
 372
 373   if (EC_ATINF(&ei->g)) return ("generator at infinity");
 374   if (ec_check(c, &ei->g)) return ("generator not on curve");
 375
 376   /* --- Check %$r$% is prime --- */
 377
 378   if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
 379
 380   /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
 381    *
 382    * This seems to work with the approximate-sqrt in the library, but might
 383    * not be so good in some cases.  Throw in some extra significate figures
 384    * for good measure.
 385    */
 386
 387   x = mp_lsl(MP_NEW, f->m, 128);
 388   x = mp_sqrt(x, x);
 389   y = mp_lsl(MP_NEW, MP_ONE, 64);
 390   x = mp_add(x, x, y);
 391   x = mp_sqr(x, x);
 392   mp_div(&x, 0, x, ei->r);
 393   x = mp_lsr(x, x, 128);
 394   rc = MP_EQ(x, ei->h);
 395   MP_DROP(x);
 396   MP_DROP(y);
 397   if (!rc) return ("incorrect cofactor");
 398
 399   /* --- Check %$n G = O$% --- */
 400
 401   EC_CREATE(&p);
 402   ec_mul(c, &p, &ei->g, ei->r);
 403   rc = EC_ATINF(&p);
 404   EC_DESTROY(&p);
 405   if (!rc) return ("incorrect group order");
 406
 407   /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
 408    *
 409    * The spec says %$q$%, not %$p$%, but I think that's a misprint.
 410    */
 411
 412   x = MP_NEW;
 413   mp_div(0, &x, f->m, ei->r);
 414   i = 20;
 415   while (i) {
 416     if (MP_EQ(x, MP_ONE)) break;
 417     x = mp_mul(x, x, f->m);
 418     mp_div(0, &x, x, ei->r);
 419     i--;
 420   }
 421   MP_DROP(x);
 422   if (i) return ("curve is weak");
 423
 424   /* --- Check %$0 < h \le 4$% --- */
 425
 426   if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
 427     return ("cofactor out of range");
 428
 429   /* --- Done --- */
 430
 431   return (0);
 432 }
 433
 434 static const char *bincheck(const ec_info *ei, grand *gr)
 435 {
 436   ec_curve *c = ei->c;
 437   field *f = c->f;
 438   int i;
 439   mp *x, *y;
 440   ec p;
 441   int rc;
 442
 443   /* --- Check that %$m$% is prime --- */
 444
 445   x = mp_fromuint(MP_NEW, f->nbits);
 446   rc = pfilt_smallfactor(x);
 447   mp_drop(x);
 448   if (rc != PGEN_DONE) return ("degree not prime");
 449
 450   /* --- Check that %$p$% is irreducible --- */
 451
 452   if (!gf_irreduciblep(f->m)) return ("p not irreducible");
 453
 454   /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
 455
 456   if (mp_bits(c->a) > f->nbits) return ("a out of range");
 457   if (mp_bits(c->b) > f->nbits) return ("a out of range");
 458   if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
 459   if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
 460
 461   /* --- Check that %$b \ne 0$% --- */
 462
 463   if (F_ZEROP(f, c->b)) return ("b is zero");
 464
 465   /* --- Check that %$G \in E$% --- */
 466
 467   if (EC_ATINF(&ei->g)) return ("generator at infinity");
 468   if (ec_check(c, &ei->g)) return ("generator not on curve");
 469
 470   /* --- Check %$r$% is prime --- */
 471
 472   if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
 473
 474   /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
 475    *
 476    * This seems to work with the approximate-sqrt in the library, but might
 477    * not be so good in some cases.  Throw in some extra significate figures
 478    * for good measure.
 479    */
 480
 481   x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
 482   x = mp_sqrt(x, x);
 483   y = mp_lsl(MP_NEW, MP_ONE, 64);
 484   x = mp_add(x, x, y);
 485   x = mp_sqr(x, x);
 486   mp_div(&x, 0, x, ei->r);
 487   x = mp_lsr(x, x, 128);
 488   rc = MP_EQ(x, ei->h);
 489   MP_DROP(x);
 490   MP_DROP(y);
 491   if (!rc) return ("incorrect cofactor");
 492
 493   /* --- Check %$n G = O$% --- */
 494
 495   EC_CREATE(&p);
 496   ec_mul(c, &p, &ei->g, ei->r);
 497   rc = EC_ATINF(&p);
 498   EC_DESTROY(&p);
 499   if (!rc) return ("incorrect group order");
 500
 501   /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
 502
 503   x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
 504   mp_div(0, &x, x, ei->r);
 505   i = 20;
 506   while (i) {
 507     if (MP_EQ(x, MP_ONE)) break;
 508     x = mp_mul(x, x, f->m);
 509     mp_div(0, &x, x, ei->r);
 510     i--;
 511   }
 512   MP_DROP(x);
 513   if (i) return ("curve is weak");
 514
 515   /* --- Check %$0 < h \le 4$% --- */
 516
 517   if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
 518     return ("cofactor out of range");
 519
 520   /* --- Done --- */
 521
 522   return (0);
 523 }
 524
 525 const char *ec_checkinfo(const ec_info *ei, grand *gr)
 526 {
 527   switch (F_TYPE(ei->c->f)) {
 528     case FTY_PRIME: return (primecheck(ei, gr)); break;
 529     case FTY_BINARY: return (bincheck(ei, gr)); break;
 530   }
 531   return ("unknown curve type");
 532 }
 533
 534 /*----- Test rig ----------------------------------------------------------*/
 535
 536 #ifdef TEST_RIG
 537
 538 #include "fibrand.h"
 539
 540 int main(int argc, char *argv[])
 541 {
 542   const ecentry *ee;
 543   const char *e;
 544   int ok = 1;
 545   int i;
 546   grand *gr;
 547
 548   gr = fibrand_create(0);
 549   if (argc > 1) {
 550     for (i = 1; i < argc; i++) {
 551       ec_info ei;
 552       if ((e = ec_getinfo(&ei, argv[i])) != 0)
 553         fprintf(stderr, "bad curve spec `%s': %s", argv[i], e);
 554       else {
 555         e = ec_checkinfo(&ei, gr);
 556         ec_freeinfo(&ei);
 557         if (!e)
 558           printf("OK %s\n", argv[i]);
 559         else {
 560           printf("BAD %s: %s\n", argv[i], e);
 561           ok = 0;
 562         }
 563       }
 564     }
 565   } else {
 566     fputs("checking standard curves:", stdout);
 567     fflush(stdout);
 568     for (ee = ectab; ee->name; ee++) {
 569       ec_info ei;
 570       ec_infofromdata(&ei, ee->data);
 571       e = ec_checkinfo(&ei, gr);
 572       ec_freeinfo(&ei);
 573       if (e) {
 574         printf("  [%s fails: %s]", ee->name, e);
 575         ok = 0;
 576       } else
 577         printf(" %s", ee->name);
 578       fflush(stdout);
 579     }
 580     fputs(ok ? " ok\n" : " failed\n", stdout);
 581   }
 582   gr->ops->destroy(gr);
 583   return (!ok);
 584 }
 585
 586 #endif
 587
 588 /*----- That's all, folks -------------------------------------------------*/