[u/mdw/catacomb] / ec-info.c

/* -*-c-*-
 *
 * $Id: ec-info.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
 *
 * Elliptic curve information management
 *
 * (c) 2004 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 * 
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 * 
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

/*----- Header files ------------------------------------------------------*/

#include "ec.h"
#include "ectab.h"
#include "gf.h"
#include "pgen.h"
#include "mprand.h"
#include "rabin.h"

/*----- Main code ---------------------------------------------------------*/

/* --- @ec_curveparse@ --- *
 *
 * Arguments:	@qd_parse *qd@ = parser context
 *
 * Returns:	Elliptic curve pointer if OK, or null.
 *
 * Use:		Parses an elliptic curve description, which has the form
 *
 *		  * a field description
 *		  * an optional `/'
 *		  * `prime', `primeproj', `bin', or `binproj'
 *		  * an optional `:'
 *		  * the %$a$% parameter
 *		  * an optional `,'
 *		  * the %$b$% parameter
 */

ec_curve *ec_curveparse(qd_parse *qd)
{
  mp *a = MP_NEW, *b = MP_NEW;
  ec_curve *c;
  field *f;

  if ((f = field_parse(qd)) == 0) goto fail;
  qd_delim(qd, '/');
  switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
    case 0:
      if (F_TYPE(f) != FTY_PRIME) {
	qd->e = "field not prime";
	goto fail;
      }
      qd_delim(qd, ':');
      if ((a = qd_getmp(qd)) == 0) goto fail;
      qd_delim(qd, ',');
      if ((b = qd_getmp(qd)) == 0) goto fail;
      c = ec_prime(f, a, b);
      break;
    case 1:
      if (F_TYPE(f) != FTY_PRIME) {
	qd->e = "field not prime";
	goto fail;
      }
      qd_delim(qd, ':');
      if ((a = qd_getmp(qd)) == 0) goto fail;
      qd_delim(qd, ',');
      if ((b = qd_getmp(qd)) == 0) goto fail;
      c = ec_primeproj(f, a, b);
      break;
    case 2:
      if (F_TYPE(f) != FTY_BINARY) {
	qd->e = "field not binary";
	goto fail;
      }
      qd_delim(qd, ':');
      if ((a = qd_getmp(qd)) == 0) goto fail;
      qd_delim(qd, ',');
      if ((b = qd_getmp(qd)) == 0) goto fail;
      c = ec_bin(f, a, b);
      break;
    case 3:
      if (F_TYPE(f) != FTY_BINARY) {
	qd->e = "field not binary";
	goto fail;
      }
      qd_delim(qd, ':');
      if ((a = qd_getmp(qd)) == 0) goto fail;
      qd_delim(qd, ',');
      if ((b = qd_getmp(qd)) == 0) goto fail;
      c = ec_binproj(f, a, b);
      break;
    default:
      goto fail;
  }
  if (!c) {
    qd->e = "bad curve parameters";
    goto fail;
  }
  if (a) MP_DROP(a);
  if (b) MP_DROP(b);
  return (c);

fail:
  if (f) F_DESTROY(f);
  if (a) MP_DROP(a);
  if (b) MP_DROP(b);
  return (0);
}

/* --- @ec_ptparse@ --- *
 *
 * Arguments:	@qd_parse *qd@ = parser context
 *		@ec *p@ = where to put the point
 *
 * Returns:	The point address, or null.
 *
 * Use:		Parses an elliptic curve point.  This has the form
 *
 *		  * %$x$%-coordinate
 *		  * optional `,'
 *		  * %$y$%-coordinate
 */

ec *ec_ptparse(qd_parse *qd, ec *p)
{
  mp *x = MP_NEW, *y = MP_NEW;

  if (qd_enum(qd, "inf") >= 0) {
    EC_SETINF(p);
    return (p);
  }
  if ((x = qd_getmp(qd)) == 0) goto fail;
  qd_delim(qd, ',');
  if ((y = qd_getmp(qd)) == 0) goto fail;
  EC_DESTROY(p);
  p->x = x;
  p->y = y;
  p->z = 0;
  return (p);

fail:
  if (x) MP_DROP(x);
  if (y) MP_DROP(y);
  return (0);
}

/* --- @getinfo@ --- *
 *
 * Arguments:	@ec_info *ei@ = where to write the information
 *		@ecdata *ed@ = raw data
 *
 * Returns:	---
 *
 * Use:		Loads elliptic curve information about one of the standard
 *		curves.
 */

static void getinfo(ec_info *ei, ecdata *ed)
{
  field *f;

  switch (ed->ftag) {
    case FTAG_PRIME:
      f = field_prime(&ed->p);
      ei->c = ec_primeproj(f, &ed->a, &ed->b);
      break;
    case FTAG_NICEPRIME:
      f = field_niceprime(&ed->p);
      ei->c = ec_primeproj(f, &ed->a, &ed->b);
      break;
    case FTAG_BINPOLY:
      f = field_binpoly(&ed->p);
      ei->c = ec_binproj(f, &ed->a, &ed->b);
      break;
    case FTAG_BINNORM:
      f = field_binnorm(&ed->p, &ed->beta);
      ei->c = ec_binproj(f, &ed->a, &ed->b);
      break;
    default:
      abort();
  }

  assert(f); assert(ei->c);
  EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0;
  ei->r = &ed->r; ei->h = &ed->h;
}

/* --- @ec_infoparse@ --- *
 *
 * Arguments:	@qd_parse *qd@ = parser context
 *		@ec_info *ei@ = curve information block, currently
 *			uninitialized
 *
 * Returns:	Zero on success, nonzero on failure.
 *
 * Use:		Parses an elliptic curve information string, and stores the
 *		information in @ei@.  This is either the name of a standard
 *		curve, or it has the form
 *
 *		  * elliptic curve description
 *		  * optional `/'
 *		  * common point
 *		  * optional `:'
 *		  * group order
 *		  * optional `*'
 *		  * cofactor
 */

int ec_infoparse(qd_parse *qd, ec_info *ei)
{
  ec_curve *c = 0;
  field *f;
  ec g = EC_INIT;
  const ecentry *ee;
  mp *r = MP_NEW, *h = MP_NEW;

  for (ee = ectab; ee->name; ee++)
    if (qd_enum(qd, ee->name) >= 0) { getinfo(ei, ee->data); goto found; }

  if ((c = ec_curveparse(qd)) == 0) goto fail;
  qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail;
  qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail;
  qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail;
  ei->c = c; ei->g = g; ei->r = r; ei->h = h;

found:
  return (0);

fail:
  EC_DESTROY(&g);
  if (r) MP_DROP(r);
  if (h) MP_DROP(h);
  if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); }
  return (-1);
}

/* --- @ec_getinfo@ --- *
 *
 * Arguments:	@ec_info *ei@ = where to write the information
 *		@const char *p@ = string describing a curve
 *
 * Returns:	Null on success, or a pointer to an error message.
 *
 * Use:		Parses out information about a curve.  The string is either a
 *		standard curve name, or a curve info string.
 */

const char *ec_getinfo(ec_info *ei, const char *p)
{
  qd_parse qd;

  qd.p = p;
  qd.e = 0;
  if (ec_infoparse(&qd, ei))
    return (qd.e);
  if (!qd_eofp(&qd)) {
    ec_freeinfo(ei);
    return ("junk found at end of string");
  }
  return (0);
}

/* --- @ec_sameinfop@ --- *
 *
 * Arguments:	@ec_info *ei, *ej@ = two elliptic curve parameter sets
 *
 * Returns:	Nonzero if the curves are identical (not just isomorphic).
 *
 * Use:		Checks for sameness of curve parameters.
 */

int ec_sameinfop(ec_info *ei, ec_info *ej)
{
  return (ec_samep(ei->c, ej->c) &&
	  MP_EQ(ei->r, ej->r) && MP_EQ(ei->h, ej->h) &&
	  EC_EQ(&ei->g, &ej->g));
}

/* --- @ec_freeinfo@ --- *
 *
 * Arguments:	@ec_info *ei@ = elliptic curve information block to free
 *
 * Returns:	---
 *
 * Use:		Frees the information block.
 */

void ec_freeinfo(ec_info *ei)
{
  field *f;

  EC_DESTROY(&ei->g);
  MP_DROP(ei->r);
  MP_DROP(ei->h);
  f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f);
}

/* --- @ec_checkinfo@ --- *
 *
 * Arguments:	@const ec_info *ei@ = elliptic curve information block
 *
 * Returns:	Null if OK, or pointer to error message.
 *
 * Use:		Checks an elliptic curve according to the rules in SEC1.
 */

static int primeeltp(mp *x, field *f)
{
  return (!MP_ISNEG(x) && MP_CMP(x, <, f->m));
}

static const char *primecheck(const ec_info *ei, grand *gr)
{
  ec_curve *c = ei->c;
  field *f = c->f;
  int i;
  mp *x, *y;
  ec p;
  int rc;

  /* --- Check %$p$% is an odd prime --- */

  if (!pgen_primep(f->m, gr)) return ("p not prime");

  /* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */

  if (!primeeltp(c->a, f)) return ("a out of range");
  if (!primeeltp(c->b, f)) return ("b out of range");
  if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
  if (!primeeltp(ei->g.x, f)) return ("G_y out of range");

  /* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */

  x = F_SQR(f, MP_NEW, c->a);
  x = F_MUL(f, x, x, c->a);
  x = F_QDL(f, x, x);
  y = F_SQR(f, MP_NEW, c->b);
  y = F_TPL(f, y, y);
  y = F_TPL(f, y, y);
  y = F_TPL(f, y, y);
  x = F_ADD(f, x, x, y);
  rc = F_ZEROP(f, x);
  MP_DROP(x);
  MP_DROP(y);
  if (rc) return ("not an elliptic curve");

  /* --- Check %$G \in E$% --- */

  if (EC_ATINF(&ei->g)) return ("generator at infinity");
  if (ec_check(c, &ei->g)) return ("generator not on curve");

  /* --- Check %$r$% is prime --- */

  if (!pgen_primep(ei->r, gr)) return ("generator order not prime");

  /* --- Check %$0 < h \le 4$% --- */

  if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
    return ("cofactor out of range");

  /* --- Check %$h = \lfloor (\sqrt{p} + 1)^2/r \rlfoor$% --- *
   *
   * This seems to work with the approximate-sqrt in the library, but might
   * not be so good in some cases.  Throw in some extra significate figures
   * for good measure.
   */

  x = mp_lsl(MP_NEW, f->m, 128);
  x = mp_sqrt(x, x);
  y = mp_lsl(MP_NEW, MP_ONE, 64);
  x = mp_add(x, x, y);
  x = mp_sqr(x, x);
  mp_div(&x, 0, x, ei->r);
  x = mp_lsr(x, x, 128);
  rc = MP_EQ(x, ei->h);
  MP_DROP(x);
  MP_DROP(y);
  if (!rc) return ("incorrect cofactor");

  /* --- Check %$n G = O$% --- */

  EC_CREATE(&p);
  ec_mul(c, &p, &ei->g, ei->r);
  rc = EC_ATINF(&p);
  EC_DESTROY(&p);
  if (!rc) return ("incorrect group order");

  /* --- Check that %$p^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
   *
   * The spec says %$q$%, not %$p$%, but I think that's a misprint.
   */

  x = MP_NEW;
  mp_div(0, &x, f->m, ei->r);
  i = 20;
  while (i) {
    if (MP_EQ(x, MP_ONE)) break;
    x = mp_mul(x, x, f->m);
    mp_div(0, &x, x, ei->r);
    i--;
  }
  MP_DROP(x);
  if (i) return ("curve is weak");

  /* --- Done --- */

  return (0);
}

static const char *bincheck(const ec_info *ei, grand *gr)
{
  ec_curve *c = ei->c;
  field *f = c->f;
  int i;
  mp *x, *y;
  ec p;
  int rc;

  /* --- Check that %$p$% is irreducible --- */

  if (!gf_irreduciblep(f->m)) return ("p not irreducible");

  /* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */

  if (mp_bits(c->a) > f->nbits) return ("a out of range");
  if (mp_bits(c->b) > f->nbits) return ("a out of range");
  if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
  if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");

  /* --- Check that %$b \ne 0$% --- */

  if (F_ZEROP(f, c->b)) return ("b is zero");

  /* --- Check that %$G \in E$% --- */

  if (EC_ATINF(&ei->g)) return ("generator at infinity");
  if (ec_check(c, &ei->g)) return ("generator not on curve");

  /* --- Check %$r$% is prime --- */

  if (!pgen_primep(ei->r, gr)) return ("generator order not prime");

  /* --- Check %$0 < h \le 4$% --- */

  if (MP_CMP(ei->h, <, MP_ONE) || MP_CMP(ei->h, >, MP_FOUR))
    return ("cofactor out of range");

  /* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
   *
   * This seems to work with the approximate-sqrt in the library, but might
   * not be so good in some cases.  Throw in some extra significate figures
   * for good measure.
   */     

  x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
  x = mp_sqrt(x, x);
  y = mp_lsl(MP_NEW, MP_ONE, 64);
  x = mp_add(x, x, y);
  x = mp_sqr(x, x);
  mp_div(&x, 0, x, ei->r);
  x = mp_lsr(x, x, 128);
  rc = MP_EQ(x, ei->h);
  MP_DROP(x);
  MP_DROP(y);
  if (!rc) return ("incorrect cofactor");

  /* --- Check %$n G = O$% --- */

  EC_CREATE(&p);
  ec_mul(c, &p, &ei->g, ei->r);
  rc = EC_ATINF(&p);
  EC_DESTROY(&p);
  if (!rc) return ("incorrect group order");

  /* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */

  x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
  mp_div(0, &x, x, ei->r);
  i = 20;
  while (i) {
    if (MP_EQ(x, MP_ONE)) break;
    x = mp_mul(x, x, f->m);
    mp_div(0, &x, x, ei->r);
    i--;
  }
  MP_DROP(x);
  if (i) return ("curve is weak");

  /* --- Done --- */

  return (0);
}

const char *ec_checkinfo(const ec_info *ei, grand *gr)
{
  switch (F_TYPE(ei->c->f)) {
    case FTY_PRIME: return (primecheck(ei, gr)); break;
    case FTY_BINARY: return (bincheck(ei, gr)); break;
  }
  return ("unknown curve type");
}

/*----- Test rig ----------------------------------------------------------*/

#ifdef TEST_RIG

#include "fibrand.h"

int main(void)
{
  const ecentry *ee;
  const char *e;
  int ok = 1;
  grand *gr;

  gr = fibrand_create(0);
  fputs("checking standard curves: ", stdout);
  for (ee = ectab; ee->name; ee++) {
    ec_info ei;
    getinfo(&ei, ee->data);
    e = ec_checkinfo(&ei, gr);
    ec_freeinfo(&ei);
    if (e) {
      fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e);
      ok = 0;
    }
    putchar('.');
    fflush(stdout);
  }
  gr->ops->destroy(gr);
  fputs(ok ? " ok\n" : " failed\n", stdout);
  return (!ok);
}

#endif

/*----- That's all, folks -------------------------------------------------*/
Commit	Line	Data
432c4e18	1	/* --c--
432c4e18	2	*
b817bfc6	3	* $Id: ec-info.c,v 1.5 2004/04/08 01:36:15 mdw Exp $
432c4e18	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
432c4e18	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 "rabin.h"
	38
	39	/----- Main code ---------------------------------------------------------/
	40
	41	/* --- @ec_curveparse@ --- *
	42	*
	43	* Arguments: @qd_parse *qd@ = parser context
	44	*
	45	* Returns: Elliptic curve pointer if OK, or null.
	46	*
	47	* Use: Parses an elliptic curve description, which has the form
	48	*
	49	* * a field description
	50	* * an optional `/'
	51	* * `prime', `primeproj', `bin', or `binproj'
	52	* * an optional `:'
	53	* * the %$a$% parameter
	54	* * an optional `,'
	55	* * the %$b$% parameter
	56	*/
	57
	58	ec_curve ec_curveparse(qd_parse qd)
	59	{
	60	mp a = MP_NEW, b = MP_NEW;
	61	ec_curve *c;
	62	field *f;
	63
	64	if ((f = field_parse(qd)) == 0) goto fail;
	65	qd_delim(qd, '/');
	66	switch (qd_enum(qd, "prime,primeproj,bin,binproj")) {
	67	case 0:
	68	if (F_TYPE(f) != FTY_PRIME) {
	69	qd->e = "field not prime";
	70	goto fail;
	71	}
	72	qd_delim(qd, ':');
	73	if ((a = qd_getmp(qd)) == 0) goto fail;
	74	qd_delim(qd, ',');
	75	if ((b = qd_getmp(qd)) == 0) goto fail;
	76	c = ec_prime(f, a, b);
	77	break;
	78	case 1:
	79	if (F_TYPE(f) != FTY_PRIME) {
	80	qd->e = "field not prime";
	81	goto fail;
	82	}
	83	qd_delim(qd, ':');
	84	if ((a = qd_getmp(qd)) == 0) goto fail;
	85	qd_delim(qd, ',');
	86	if ((b = qd_getmp(qd)) == 0) goto fail;
	87	c = ec_primeproj(f, a, b);
	88	break;
	89	case 2:
	90	if (F_TYPE(f) != FTY_BINARY) {
	91	qd->e = "field not binary";
	92	goto fail;
	93	}
94	qd_delim(qd, ':');
95	if ((a = qd_getmp(qd)) == 0) goto fail;
96	qd_delim(qd, ',');
97	if ((b = qd_getmp(qd)) == 0) goto fail;
98	c = ec_bin(f, a, b);
99	break;
100	case 3:
101	if (F_TYPE(f) != FTY_BINARY) {
102	qd->e = "field not binary";
103	goto fail;
104	}
105	qd_delim(qd, ':');
106	if ((a = qd_getmp(qd)) == 0) goto fail;
107	qd_delim(qd, ',');
108	if ((b = qd_getmp(qd)) == 0) goto fail;
109	c = ec_binproj(f, a, b);
110	break;
111	default:
112	goto fail;
113	}
02d7884d	114	if (!c) {
	115	qd->e = "bad curve parameters";
	116	goto fail;
	117	}
432c4e18	118	if (a) MP_DROP(a);
	119	if (b) MP_DROP(b);
	120	return (c);
	121
	122	fail:
	123	if (f) F_DESTROY(f);
	124	if (a) MP_DROP(a);
	125	if (b) MP_DROP(b);
	126	return (0);
	127	}
	128
	129	/* --- @ec_ptparse@ --- *
	130	*
	131	* Arguments: @qd_parse *qd@ = parser context
	132	* @ec *p@ = where to put the point
	133	*
	134	* Returns: The point address, or null.
	135	*
	136	* Use: Parses an elliptic curve point. This has the form
	137	*
	138	* * %$x$%-coordinate
	139	* * optional `,'
	140	* * %$y$%-coordinate
	141	*/
	142
	143	ec ec_ptparse(qd_parse qd, ec *p)
	144	{
	145	mp x = MP_NEW, y = MP_NEW;
	146
	147	if (qd_enum(qd, "inf") >= 0) {
	148	EC_SETINF(p);
	149	return (p);
	150	}
	151	if ((x = qd_getmp(qd)) == 0) goto fail;
	152	qd_delim(qd, ',');
	153	if ((y = qd_getmp(qd)) == 0) goto fail;
	154	EC_DESTROY(p);
	155	p->x = x;
	156	p->y = y;
	157	p->z = 0;
	158	return (p);
	159
	160	fail:
	161	if (x) MP_DROP(x);
	162	if (y) MP_DROP(y);
	163	return (0);
	164	}
	165
34e4f738	166	/* --- @getinfo@ --- *
	167	*
	168	* Arguments: @ec_info *ei@ = where to write the information
	169	* @ecdata *ed@ = raw data
	170	*
	171	* Returns: ---
	172	*
	173	* Use: Loads elliptic curve information about one of the standard
	174	* curves.
	175	*/
	176
	177	static void getinfo(ec_info ei, ecdata ed)
	178	{
	179	field *f;
	180
	181	switch (ed->ftag) {
	182	case FTAG_PRIME:
	183	f = field_prime(&ed->p);
	184	ei->c = ec_primeproj(f, &ed->a, &ed->b);
	185	break;
	186	case FTAG_NICEPRIME:
	187	f = field_niceprime(&ed->p);
	188	ei->c = ec_primeproj(f, &ed->a, &ed->b);
	189	break;
	190	case FTAG_BINPOLY:
	191	f = field_binpoly(&ed->p);
	192	ei->c = ec_binproj(f, &ed->a, &ed->b);
	193	break;
4edc47b8	194	case FTAG_BINNORM:
	195	f = field_binnorm(&ed->p, &ed->beta);
	196	ei->c = ec_binproj(f, &ed->a, &ed->b);
	197	break;
34e4f738	198	default:
	199	abort();
	200	}
	201
02d7884d	202	assert(f); assert(ei->c);
34e4f738	203	EC_CREATE(&ei->g); ei->g.x = &ed->gx; ei->g.y = &ed->gy; ei->g.z = 0;
	204	ei->r = &ed->r; ei->h = &ed->h;
	205	}
	206
432c4e18	207	/* --- @ec_infoparse@ --- *
	208	*
	209	* Arguments: @qd_parse *qd@ = parser context
	210	* @ec_info *ei@ = curve information block, currently
	211	* uninitialized
	212	*
	213	* Returns: Zero on success, nonzero on failure.
	214	*
	215	* Use: Parses an elliptic curve information string, and stores the
34e4f738	216	* information in @ei@. This is either the name of a standard
34e4f738	217	* curve, or it has the form
432c4e18	218	*
	219	* * elliptic curve description
	220	* * optional `/'
	221	* * common point
	222	* * optional `:'
	223	* * group order
	224	* * optional `*'
	225	* * cofactor
	226	*/
	227
	228	int ec_infoparse(qd_parse qd, ec_info ei)
	229	{
	230	ec_curve *c = 0;
	231	field *f;
	232	ec g = EC_INIT;
34e4f738	233	const ecentry *ee;
432c4e18	234	mp r = MP_NEW, h = MP_NEW;
432c4e18	235
02d7884d	236	for (ee = ectab; ee->name; ee++)
	237	if (qd_enum(qd, ee->name) >= 0) { getinfo(ei, ee->data); goto found; }
	238
432c4e18	239	if ((c = ec_curveparse(qd)) == 0) goto fail;
	240	qd_delim(qd, '/'); if (!ec_ptparse(qd, &g)) goto fail;
	241	qd_delim(qd, ':'); if ((r = qd_getmp(qd)) == 0) goto fail;
	242	qd_delim(qd, '*'); if ((h = qd_getmp(qd)) == 0) goto fail;
432c4e18	243	ei->c = c; ei->g = g; ei->r = r; ei->h = h;
34e4f738	244
34e4f738	245	found:
432c4e18	246	return (0);
	247
	248	fail:
	249	EC_DESTROY(&g);
	250	if (r) MP_DROP(r);
	251	if (h) MP_DROP(h);
	252	if (c) { f = c->f; ec_destroycurve(c); F_DESTROY(f); }
	253	return (-1);
	254	}
	255
432c4e18	256	/* --- @ec_getinfo@ --- *
	257	*
	258	* Arguments: @ec_info *ei@ = where to write the information
	259	* @const char *p@ = string describing a curve
	260	*
	261	* Returns: Null on success, or a pointer to an error message.
	262	*
	263	* Use: Parses out information about a curve. The string is either a
	264	* standard curve name, or a curve info string.
	265	*/
	266
	267	const char ec_getinfo(ec_info ei, const char *p)
	268	{
	269	qd_parse qd;
432c4e18	270
	271	qd.p = p;
	272	qd.e = 0;
432c4e18	273	if (ec_infoparse(&qd, ei))
432c4e18	274	return (qd.e);
432c4e18	275	if (!qd_eofp(&qd)) {
	276	ec_freeinfo(ei);
	277	return ("junk found at end of string");
	278	}
	279	return (0);
	280	}
	281
34e4f738	282	/* --- @ec_sameinfop@ --- *
	283	*
	284	* Arguments: @ec_info ei, ej@ = two elliptic curve parameter sets
	285	*
	286	* Returns: Nonzero if the curves are identical (not just isomorphic).
	287	*
	288	* Use: Checks for sameness of curve parameters.
	289	*/
	290
	291	int ec_sameinfop(ec_info ei, ec_info ej)
	292	{
	293	return (ec_samep(ei->c, ej->c) &&
	294	MP_EQ(ei->r, ej->r) && MP_EQ(ei->h, ej->h) &&
	295	EC_EQ(&ei->g, &ej->g));
	296	}
	297
432c4e18	298	/* --- @ec_freeinfo@ --- *
	299	*
	300	* Arguments: @ec_info *ei@ = elliptic curve information block to free
	301	*
	302	* Returns: ---
	303	*
	304	* Use: Frees the information block.
	305	*/
	306
	307	void ec_freeinfo(ec_info *ei)
	308	{
	309	field *f;
	310
	311	EC_DESTROY(&ei->g);
	312	MP_DROP(ei->r);
	313	MP_DROP(ei->h);
	314	f = ei->c->f; ec_destroycurve(ei->c); F_DESTROY(f);
	315	}
	316
	317	/* --- @ec_checkinfo@ --- *
	318	*
	319	* Arguments: @const ec_info *ei@ = elliptic curve information block
	320	*
	321	* Returns: Null if OK, or pointer to error message.
	322	*
	323	* Use: Checks an elliptic curve according to the rules in SEC1.
	324	*/
	325
432c4e18	326	static int primeeltp(mp x, field f)
	327	{
	328	return (!MP_ISNEG(x) && MP_CMP(x, <, f->m));
	329	}
	330
	331	static const char primecheck(const ec_info ei, grand *gr)
	332	{
	333	ec_curve *c = ei->c;
	334	field *f = c->f;
	335	int i;
	336	mp x, y;
	337	ec p;
	338	int rc;
	339
	340	/* --- Check %$p$% is an odd prime --- */
	341
34e4f738	342	if (!pgen_primep(f->m, gr)) return ("p not prime");
432c4e18	343
	344	/* --- Check %$a$%, %$b$%, %$G_x$% and %$G_y$% are in %$[0, p)$% --- */
	345
	346	if (!primeeltp(c->a, f)) return ("a out of range");
	347	if (!primeeltp(c->b, f)) return ("b out of range");
	348	if (!primeeltp(ei->g.x, f)) return ("G_x out of range");
	349	if (!primeeltp(ei->g.x, f)) return ("G_y out of range");
	350
	351	/* --- Check %$4 a^3 + 27 b^2 \not\equiv 0 \pmod{p}$% --- */
	352
	353	x = F_SQR(f, MP_NEW, c->a);
	354	x = F_MUL(f, x, x, c->a);
	355	x = F_QDL(f, x, x);
	356	y = F_SQR(f, MP_NEW, c->b);
	357	y = F_TPL(f, y, y);
	358	y = F_TPL(f, y, y);
	359	y = F_TPL(f, y, y);
	360	x = F_ADD(f, x, x, y);
	361	rc = F_ZEROP(f, x);
	362	MP_DROP(x);
	363	MP_DROP(y);
	364	if (rc) return ("not an elliptic curve");
	365
	366	/* --- Check %$G \in E$% --- */
	367
	368	if (EC_ATINF(&ei->g)) return ("generator at infinity");
	369	if (ec_check(c, &ei->g)) return ("generator not on curve");
	370
	371	/* --- Check %$r$% is prime --- */
	372
34e4f738	373	if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
432c4e18	374
	375	/* --- Check %$0 < h \le 4$% --- */
	376
	377	if (MP_CMP(ei->h, <, MP_ONE) \|\| MP_CMP(ei->h, >, MP_FOUR))
	378	return ("cofactor out of range");
	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	/* --- Done --- */
	425
	426	return (0);
	427	}
	428
	429	static const char bincheck(const ec_info ei, grand *gr)
	430	{
	431	ec_curve *c = ei->c;
	432	field *f = c->f;
	433	int i;
	434	mp x, y;
	435	ec p;
	436	int rc;
	437
438	/* --- Check that %$p$% is irreducible --- */
439
440	if (!gf_irreduciblep(f->m)) return ("p not irreducible");
441
442	/* --- Check that %$a, b, G_x, G_y$% have degree less than %$p$% --- */
443
444	if (mp_bits(c->a) > f->nbits) return ("a out of range");
445	if (mp_bits(c->b) > f->nbits) return ("a out of range");
446	if (mp_bits(ei->g.x) > f->nbits) return ("G_x out of range");
447	if (mp_bits(ei->g.y) > f->nbits) return ("G_y out of range");
448
449	/* --- Check that %$b \ne 0$% --- */
450
451	if (F_ZEROP(f, c->b)) return ("b is zero");
452
453	/* --- Check that %$G \in E$% --- */
454
455	if (EC_ATINF(&ei->g)) return ("generator at infinity");
456	if (ec_check(c, &ei->g)) return ("generator not on curve");
457
458	/* --- Check %$r$% is prime --- */
459
34e4f738	460	if (!pgen_primep(ei->r, gr)) return ("generator order not prime");
432c4e18	461
	462	/* --- Check %$0 < h \le 4$% --- */
	463
	464	if (MP_CMP(ei->h, <, MP_ONE) \|\| MP_CMP(ei->h, >, MP_FOUR))
	465	return ("cofactor out of range");
	466
	467	/* --- Check %$h = \lfloor (\sqrt{2^m} + 1)^2/r \rlfoor$% --- *
	468	*
	469	* This seems to work with the approximate-sqrt in the library, but might
	470	* not be so good in some cases. Throw in some extra significate figures
	471	* for good measure.
	472	*/
	473
	474	x = mp_lsl(MP_NEW, MP_ONE, f->nbits + 128);
	475	x = mp_sqrt(x, x);
	476	y = mp_lsl(MP_NEW, MP_ONE, 64);
	477	x = mp_add(x, x, y);
	478	x = mp_sqr(x, x);
	479	mp_div(&x, 0, x, ei->r);
	480	x = mp_lsr(x, x, 128);
	481	rc = MP_EQ(x, ei->h);
	482	MP_DROP(x);
	483	MP_DROP(y);
	484	if (!rc) return ("incorrect cofactor");
	485
	486	/* --- Check %$n G = O$% --- */
	487
	488	EC_CREATE(&p);
	489	ec_mul(c, &p, &ei->g, ei->r);
	490	rc = EC_ATINF(&p);
	491	EC_DESTROY(&p);
	492	if (!rc) return ("incorrect group order");
	493
	494	/* --- Check %$2^{m B} \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- */
	495
	496	x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
	497	mp_div(0, &x, x, ei->r);
	498	i = 20;
	499	while (i) {
	500	if (MP_EQ(x, MP_ONE)) break;
	501	x = mp_mul(x, x, f->m);
	502	mp_div(0, &x, x, ei->r);
	503	i--;
	504	}
	505	MP_DROP(x);
	506	if (i) return ("curve is weak");
	507
	508	/* --- Done --- */
	509
	510	return (0);
	511	}
	512
	513	const char ec_checkinfo(const ec_info ei, grand *gr)
	514	{
	515	switch (F_TYPE(ei->c->f)) {
	516	case FTY_PRIME: return (primecheck(ei, gr)); break;
	517	case FTY_BINARY: return (bincheck(ei, gr)); break;
	518	}
	519	return ("unknown curve type");
	520	}
	521
	522	/----- Test rig ----------------------------------------------------------/
	523
	524	#ifdef TEST_RIG
525
526	#include "fibrand.h"
527
528	int main(void)
529	{
530	const ecentry *ee;
531	const char *e;
532	int ok = 1;
533	grand *gr;
534
535	gr = fibrand_create(0);
536	fputs("checking standard curves: ", stdout);
537	for (ee = ectab; ee->name; ee++) {
538	ec_info ei;
539	getinfo(&ei, ee->data);
540	e = ec_checkinfo(&ei, gr);
541	ec_freeinfo(&ei);
542	if (e) {
543	fprintf(stderr, "\n*** curve %s fails: %s\n", ee->name, e);
544	ok = 0;
545	}
546	putchar('.');
547	fflush(stdout);
548	}
549	gr->ops->destroy(gr);
550	fputs(ok ? " ok\n" : " failed\n", stdout);
551	return (!ok);
552	}
553
554	#endif
555
556	/----- That's all, folks -------------------------------------------------/