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

   1 /* -*-c-*-
   2  *
   3  * $Id: ec-info.c,v 1.3 2004/04/01 21:28:41 mdw Exp $
   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 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: ec-info.c,v $
  33  * Revision 1.3  2004/04/01 21:28:41  mdw
  34  * Normal basis support (translates to poly basis internally).  Rewrite
  35  * EC and prime group table generators in awk, so that they can reuse data
  36  * for repeated constants.
  37  *
  38  * Revision 1.2  2004/04/01 12:50:09  mdw
  39  * Add cyclic group abstraction, with test code.  Separate off exponentation
  40  * functions for better static linking.  Fix a buttload of bugs on the way.
  41  * Generally ensure that negative exponents do inversion correctly.  Add
  42  * table of standard prime-field subgroups.  (Binary field subgroups are
  43  * currently unimplemented but easy to add if anyone ever finds a good one.)
  44  *
  45  * Revision 1.1  2004/03/27 17:54:11  mdw
  46  * Standard curves and curve checking.
  47  *
  48  */
  49
  50 /*----- Header files ------------------------------------------------------*/
  51
  52 #include "ec.h"
  53 #include "ectab.h"
  54 #include "gf.h"
  55 #include "pgen.h"
  56 #include "mprand.h"
  57 #include "rabin.h"
  58
  59 /*----- Main code ---------------------------------------------------------*/
  60
  61 /* --- @ec_curveparse@ --- *
  62  *
  63  * Arguments:   @qd_parse *qd@ = parser context
  64  *
  65  * Returns:     Elliptic curve pointer if OK, or null.
  66  *
  67  * Use:         Parses an elliptic curve description, which has the form
  68  *
  69  *                * a field description
  70  *                * an optional `/'
  71  *                * `prime', `primeproj', `bin', or `binproj'
  72  *                * an optional `:'
  73  *                * the %$a$% parameter
  74  *                * an optional `,'
  75  *                * the %$b$% parameter
  76  */
  77
  78 ec_curve *ec_curveparse(qd_parse *qd)
  79 {
  80   mp *a = MP_NEW, *b = MP_NEW;
  81   ec_curve *c;
  82   field *f;
  83
  84   if ((f = field_parse(qd)) == 0) goto fail;
  85   qd_delim(qd, '/');
  86   switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
  87     case 0:
  88       if (F_TYPE(f) != FTY_PRIME) {
  89         qd->e = "field not prime";
  90         goto fail;
  91       }
  92       qd_delim(qd, ':');
  93       if ((a = qd_getmp(qd)) == 0) goto fail;
  94       qd_delim(qd, ',');
  95       if ((b = qd_getmp(qd)) == 0) goto fail;
  96       c = ec_prime(f, a, b);
  97       break;
  98     case 1:
  99       if (F_TYPE(f) != FTY_PRIME) {
 100         qd->e = "field not prime";
 101         goto fail;
 102       }
 103       qd_delim(qd, ':');
 104       if ((a = qd_getmp(qd)) == 0) goto fail;
 105       qd_delim(qd, ',');
 106       if ((b = qd_getmp(qd)) == 0) goto fail;
 107       c = ec_primeproj(f, a, b);
 108       break;
 109     case 2:
 110       if (F_TYPE(f) != FTY_BINARY) {
 111         qd->e = "field not binary";
 112         goto fail;
 113       }
 114       qd_delim(qd, ':');
 115       if ((a = qd_getmp(qd)) == 0) goto fail;
 116       qd_delim(qd, ',');
 117       if ((b = qd_getmp(qd)) == 0) goto fail;
 118       c = ec_bin(f, a, b);
 119       break;
 120     case 3:
 121       if (F_TYPE(f) != FTY_BINARY) {
 122         qd->e = "field not binary";
 123         goto fail;
 124       }
 125       qd_delim(qd, ':');
 126       if ((a = qd_getmp(qd)) == 0) goto fail;
 127       qd_delim(qd, ',');
 128       if ((b = qd_getmp(qd)) == 0) goto fail;
 129       c = ec_binproj(f, a, b);
 130       break;
 131     default:
 132       goto fail;
 133   }
 134   if (a) MP_DROP(a);
 135   if (b) MP_DROP(b);
 136   return (c);
 137
 138 fail:
 139   if (f) F_DESTROY(f);
 140   if (a) MP_DROP(a);
 141   if (b) MP_DROP(b);
 142   return (0);
 143 }
 144
 145 /* --- @ec_ptparse@ --- *
 146  *
 147  * Arguments:   @qd_parse *qd@ = parser context
 148  *              @ec *p@ = where to put the point
 149  *
 150  * Returns:     The point address, or null.
 151  *
 152  * Use:         Parses an elliptic curve point.  This has the form
 153  *
 154  *                * %$x$%-coordinate
 155  *                * optional `,'
 156  *                * %$y$%-coordinate
 157  */
 158
 159 ec *ec_ptparse(qd_parse *qd, ec *p)
 160 {
 161   mp *x = MP_NEW, *y = MP_NEW;
 162
 163   if (qd_enum(qd, "inf") >= 0) {
 164     EC_SETINF(p);
 165     return (p);
 166   }
 167   if ((x = qd_getmp(qd)) == 0) goto fail;
 168   qd_delim(qd, ',');
 169   if ((y = qd_getmp(qd)) == 0) goto fail;
 170   EC_DESTROY(p);
 171   p->x = x;
 172   p->y = y;
 173   p->z = 0;
 174   return (p);
 175
 176 fail:
 177   if (x) MP_DROP(x);
 178   if (y) MP_DROP(y);
 179   return (0);
 180 }
 181
 182 /* --- @getinfo@ --- *
 183  *
 184  * Arguments:   @ec_info *ei@ = where to write the information
 185  *              @ecdata *ed@ = raw data
 186  *
 187  * Returns:     ---
 188  *
 189  * Use:         Loads elliptic curve information about one of the standard
 190  *              curves.
 191  */
 192
 193 static void getinfo(ec_info *ei, ecdata *ed)
 194 {
 195   field *f;
 196
 197   switch (ed->ftag) {
 198     case FTAG_PRIME:
 199       f = field_prime(&ed->p);
 200       ei->c = ec_primeproj(f, &ed->a, &ed->b);
 201       break;
 202     case FTAG_NICEPRIME:
 203       f = field_niceprime(&ed->p);
 204       ei->c = ec_primeproj(f, &ed->a, &ed->b);
 205       break;
 206     case FTAG_BINPOLY:
 207       f = field_binpoly(&ed->p);
 208       ei->c = ec_binproj(f, &ed->a, &ed->b);
 209       break;
 210     case FTAG_BINNORM:
 211       f = field_binnorm(&ed->p, &ed->beta);
 212       ei->c = ec_binproj(f, &ed->a, &ed->b);
 213       break;
 214     default:
 215       abort();
 216   }
 217
 218   EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0;
 219   ei->r = &ed->r; ei->h = &ed->h;
 220 }
 221
 222 /* --- @ec_infoparse@ --- *
 223  *
 224  * Arguments:   @qd_parse *qd@ = parser context
 225  *              @ec_info *ei@ = curve information block, currently
 226  *                      uninitialized
 227  *
 228  * Returns:     Zero on success, nonzero on failure.
 229  *
 230  * Use:         Parses an elliptic curve information string, and stores the
 231  *              information in @ei@.  This is either the name of a standard
 232  *              curve, or it has the form
 233  *
 234  *                * elliptic curve description
 235  *                * optional `/'
 236  *                * common point
 237  *                * optional `:'
 238  *                * group order
 239  *                * optional `*'
 240  *                * cofactor
 241  */
 242
 243 int ec_infoparse(qd_parse *qd, ec_info *ei)
 244 {
 245   ec_curve *c = 0;
 246   field *f;
 247   ec g = EC_INIT;
 248   const ecentry *ee;
 249   mp *r = MP_NEW, *h = MP_NEW;
 250
 251   for (ee = ectab; ee->name; ee++) {
 252     if (qd_enum(qd, ee->name) >= 0) {
 253       getinfo(ei, ee->data);
 254       goto found;
 255     }
 256   }
 257   if ((c = ec_curveparse(qd)) == 0) goto fail;
 258   qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail;
 259   qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail;
 260   qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail;
 261   ei->c = c; ei->g = g; ei->r = r; ei->h = h;
 262
 263 found:
 264   return (0);
 265
 266 fail:
 267   EC_DESTROY(&g);
 268   if (r) MP_DROP(r);
 269   if (h) MP_DROP(h);
 270   if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); }
 271   return (-1);
 272 }
 273
 274 /* --- @ec_getinfo@ --- *
 275  *
 276  * Arguments:   @ec_info *ei@ = where to write the information
 277  *              @const char *p@ = string describing a curve
 278  *
 279  * Returns:     Null on success, or a pointer to an error message.
 280  *
 281  * Use:         Parses out information about a curve.  The string is either a
 282  *              standard curve name, or a curve info string.
 283  */
 284
 285 const char *ec_getinfo(ec_info *ei, const char *p)
 286 {
 287   qd_parse qd;
 288
 289   qd.p = p;
 290   qd.e = 0;
 291   if (ec_infoparse(&qd, ei))
 292     return (qd.e);
 293   if (!qd_eofp(&qd)) {
 294     ec_freeinfo(ei);
 295     return ("junk found at end of string");
 296   }
 297   return (0);
 298 }
 299
 300 /* --- @ec_sameinfop@ --- *
 301  *
 302  * Arguments:   @ec_info *ei, *ej@ = two elliptic curve parameter sets
 303  *
 304  * Returns:     Nonzero if the curves are identical (not just isomorphic).
 305  *
 306  * Use:         Checks for sameness of curve parameters.
 307  */
 308
 309 int ec_sameinfop(ec_info *ei, ec_info *ej)
 310 {
 311   return (ec_samep(ei->c, ej->c) &&
 312           MP_EQ(ei->r, ej->r) && MP_EQ(ei->h, ej->h) &&
 313           EC_EQ(&ei->g, &ej->g));
 314 }
 315
 316 /* --- @ec_freeinfo@ --- *
 317  *
 318  * Arguments:   @ec_info *ei@ = elliptic curve information block to free
 319  *
 320  * Returns:     ---
 321  *
 322  * Use:         Frees the information block.
 323  */
 324
 325 void ec_freeinfo(ec_info *ei)
 326 {
 327   field *f;
 328
 329   EC_DESTROY(&ei->g);
 330   MP_DROP(ei->r);
 331   MP_DROP(ei->h);
 332   f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f);
 333 }
 334
 335 /* --- @ec_checkinfo@ --- *
 336  *
 337  * Arguments:   @const ec_info *ei@ = elliptic curve information block
 338  *
 339  * Returns:     Null if OK, or pointer to error message.
 340  *
 341  * Use:         Checks an elliptic curve according to the rules in SEC1.
 342  */
 343
 344 static int primeeltp(mp *x, field *f)
 345 {
 346   return (!MP_ISNEG(x) && MP_CMP(x, <, f->m));
 347 }
 348
 349 static const char *primecheck(const ec_info *ei, grand *gr)
 350 {
 351   ec_curve *c = ei->c;
 352   field *f = c->f;
 353   int i;
 354   mp *x, *y;
 355   ec p;
 356   int rc;
 357
 358   /* --- Check %$p$% is an odd prime --- */
 359
 360   if (!pgen_primep(f->m, gr)) return ("p not prime");
 361
 362   /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
 363
 364   if (!primeeltp(c->a, f)) return ("a out of range");
 365   if (!primeeltp(c->b, f)) return ("b out of range");
 366   if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
 367   if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
 368
 369   /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
 370
 371   x = F_SQR(f, MP_NEW, c->a);
 372   x = F_MUL(f, x, x, c->a);
 373   x = F_QDL(f, x, x);
 374   y = F_SQR(f, MP_NEW, c->b);
 375   y = F_TPL(f, y, y);
 376   y = F_TPL(f, y, y);
 377   y = F_TPL(f, y, y);
 378   x = F_ADD(f, x, x, y);
 379   rc = F_ZEROP(f, x);
 380   MP_DROP(x);
 381   MP_DROP(y);
 382   if (rc) return ("not an elliptic curve");
 383
 384   /* --- Check %$G \in E$% --- */
 385
 386   if (EC_ATINF(&ei->g)) return ("generator at infinity");
 387   if (ec_check(c, &ei->g)) return ("generator not on curve");
 388
 389   /* --- Check %$r$% is prime --- */
 390
 391   if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
 392
 393   /* --- Check %$0 < h \le 4$% --- */
 394
 395   if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
 396     return ("cofactor out of range");
 397
 398   /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
 399    *
 400    * This seems to work with the approximate-sqrt in the library, but might
 401    * not be so good in some cases.  Throw in some extra significate figures
 402    * for good measure.
 403    */
 404
 405   x = mp_lsl(MP_NEW, f->m, 128);
 406   x = mp_sqrt(x, x);
 407   y = mp_lsl(MP_NEW, MP_ONE, 64);
 408   x = mp_add(x, x, y);
 409   x = mp_sqr(x, x);
 410   mp_div(&x, 0, x, ei->r);
 411   x = mp_lsr(x, x, 128);
 412   rc = MP_EQ(x, ei->h);
 413   MP_DROP(x);
 414   MP_DROP(y);
 415   if (!rc) return ("incorrect cofactor");
 416
 417   /* --- Check %$n G = O$% --- */
 418
 419   EC_CREATE(&p);
 420   ec_mul(c, &p, &ei->g, ei->r);
 421   rc = EC_ATINF(&p);
 422   EC_DESTROY(&p);
 423   if (!rc) return ("incorrect group order");
 424
 425   /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
 426    *
 427    * The spec says %$q$%, not %$p$%, but I think that's a misprint.
 428    */
 429
 430   x = MP_NEW;
 431   mp_div(0, &x, f->m, ei->r);
 432   i = 20;
 433   while (i) {
 434     if (MP_EQ(x, MP_ONE)) break;
 435     x = mp_mul(x, x, f->m);
 436     mp_div(0, &x, x, ei->r);
 437     i--;
 438   }
 439   MP_DROP(x);
 440   if (i) return ("curve is weak");
 441
 442   /* --- Done --- */
 443
 444   return (0);
 445 }
 446
 447 static const char *bincheck(const ec_info *ei, grand *gr)
 448 {
 449   ec_curve *c = ei->c;
 450   field *f = c->f;
 451   int i;
 452   mp *x, *y;
 453   ec p;
 454   int rc;
 455
 456   /* --- Check that %$p$% is irreducible --- */
 457
 458   if (!gf_irreduciblep(f->m)) return ("p not irreducible");
 459
 460   /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
 461
 462   if (mp_bits(c->a) > f->nbits) return ("a out of range");
 463   if (mp_bits(c->b) > f->nbits) return ("a out of range");
 464   if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
 465   if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
 466
 467   /* --- Check that %$b \ne 0$% --- */
 468
 469   if (F_ZEROP(f, c->b)) return ("b is zero");
 470
 471   /* --- Check that %$G \in E$% --- */
 472
 473   if (EC_ATINF(&ei->g)) return ("generator at infinity");
 474   if (ec_check(c, &ei->g)) return ("generator not on curve");
 475
 476   /* --- Check %$r$% is prime --- */
 477
 478   if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
 479
 480   /* --- Check %$0 < h \le 4$% --- */
 481
 482   if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
 483     return ("cofactor out of range");
 484
 485   /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
 486    *
 487    * This seems to work with the approximate-sqrt in the library, but might
 488    * not be so good in some cases.  Throw in some extra significate figures
 489    * for good measure.
 490    */
 491
 492   x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
 493   x = mp_sqrt(x, x);
 494   y = mp_lsl(MP_NEW, MP_ONE, 64);
 495   x = mp_add(x, x, y);
 496   x = mp_sqr(x, x);
 497   mp_div(&x, 0, x, ei->r);
 498   x = mp_lsr(x, x, 128);
 499   rc = MP_EQ(x, ei->h);
 500   MP_DROP(x);
 501   MP_DROP(y);
 502   if (!rc) return ("incorrect cofactor");
 503
 504   /* --- Check %$n G = O$% --- */
 505
 506   EC_CREATE(&p);
 507   ec_mul(c, &p, &ei->g, ei->r);
 508   rc = EC_ATINF(&p);
 509   EC_DESTROY(&p);
 510   if (!rc) return ("incorrect group order");
 511
 512   /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
 513
 514   x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
 515   mp_div(0, &x, x, ei->r);
 516   i = 20;
 517   while (i) {
 518     if (MP_EQ(x, MP_ONE)) break;
 519     x = mp_mul(x, x, f->m);
 520     mp_div(0, &x, x, ei->r);
 521     i--;
 522   }
 523   MP_DROP(x);
 524   if (i) return ("curve is weak");
 525
 526   /* --- Done --- */
 527
 528   return (0);
 529 }
 530
 531 const char *ec_checkinfo(const ec_info *ei, grand *gr)
 532 {
 533   switch (F_TYPE(ei->c->f)) {
 534     case FTY_PRIME: return (primecheck(ei, gr)); break;
 535     case FTY_BINARY: return (bincheck(ei, gr)); break;
 536   }
 537   return ("unknown curve type");
 538 }
 539
 540 /*----- Test rig ----------------------------------------------------------*/
 541
 542 #ifdef TEST_RIG
 543
 544 #include "fibrand.h"
 545
 546 int main(void)
 547 {
 548   const ecentry *ee;
 549   const char *e;
 550   int ok = 1;
 551   grand *gr;
 552
 553   gr = fibrand_create(0);
 554   fputs("checking standard curves: ", stdout);
 555   for (ee = ectab; ee->name; ee++) {
 556     ec_info ei;
 557     getinfo(&ei, ee->data);
 558     e = ec_checkinfo(&ei, gr);
 559     ec_freeinfo(&ei);
 560     if (e) {
 561       fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e);
 562       ok = 0;
 563     }
 564     putchar('.');
 565     fflush(stdout);
 566   }
 567   gr->ops->destroy(gr);
 568   fputs(ok ? " ok\n" : " failed\n", stdout);
 569   return (!ok);
 570 }
 571
 572 #endif
 573
 574 /*----- That's all, folks -------------------------------------------------*/