primeiter: New functions for iterating over small primes.

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

/* -*-c-*-
 *
 * $Id$
 *
 * 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 "mpint.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);
}

/* --- @ec_infofromdata@ --- *
 *
 * 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.
 */

void ec_infofromdata(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) {
      ec_infofromdata(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 const char *gencheck(const ec_info *ei, grand *gr, mp *q)
{
  ec_curve *c = ei->c;
  field *f = c->f;
  int i, j, n;
  mp *qq;
  mp *nn;
  mp *x, *y;
  ec p;
  int rc;

  /* --- 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 that the cofactor is correct --- *
   *
   * Let %$q$% be the size of the field, and let %$n = h r = \#E(\gf{q})$% be
   * the number of %$\gf{q}$%-rational points on our curve.  Hasse's theorem
   * tells us that
   *
   *   %$|q + 1 - n| \le 2\sqrt{q}$%
   *
   * or, if we square both sides,
   *
   *   %$(q + 1 - n)^2 \le 4 q$%.
   *
   * We'd like the cofactor to be uniquely determined by this equation, which
   * is possible as long as it's not too big.  (If it is, we have to mess
   * about with Weil pairings, which is no fun.)  For this, we need the
   * following inequalities:
   *
   *   * %$A = (q + 1 - n)^2 \le 4 q$% (both lower and upper bounds from
   *	 Hasse's theorem);
   *
   *   * %$B = (q + 1 - n - r)^2 > 4 q$% (check %$h - 1$% isn't possible);
   *	 and
   *
   *   * %$C = (q + 1 - n + r)^2 > 4 q$% (check %$h + 1$% isn't possible).
   */

  rc = 1;
  qq = mp_add(MP_NEW, q, MP_ONE);
  nn = mp_mul(MP_NEW, ei->r, ei->h);
  nn = mp_sub(nn, qq, nn);
  qq = mp_lsl(qq, q, 2);

  y = mp_sqr(MP_NEW, nn);
  if (MP_CMP(y, >, qq)) rc = 0;

  x = mp_sub(MP_NEW, nn, ei->r);
  y = mp_sqr(y, x);
  if (MP_CMP(y, <=, qq)) rc = 0;

  x = mp_add(x, nn, ei->r);
  y = mp_sqr(y, x);
  if (MP_CMP(y, <=, qq)) rc = 0;

  MP_DROP(x);
  MP_DROP(y);
  MP_DROP(nn);
  MP_DROP(qq);
  if (!rc) return ("incorrect or ambiguous 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 %$q^B \not\equiv 1 \pmod{r}$% for %$1 \le B < 20$% --- *
   *
   * Actually, give up if %$q^B \ge 2^{2000}$% because that's probably
   * good enough for jazz.
   */

  x = MP_NEW;
  mp_div(0, &x, q, ei->r);
  n = mp_bits(ei->r) - 1;
  for (i = 0, j = n; i < 20; i++, j += n) {
    if (j >= 2000)
      break;
    if (MP_EQ(x, MP_ONE)) {
      MP_DROP(x);
      return("curve embedding degree too low");
    }
    x = mp_mul(x, x, f->m);
    mp_div(0, &x, x, ei->r);
  }
  MP_DROP(x);

  /* --- Done --- */

  return (0);
}

static int primeeltp(mp *x, field *f)
  { return (!MP_NEGP(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;
  mp *x, *y;
  int rc;
  const char *err;

  /* --- 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");

  /* --- Now do the general checks --- */

  err = gencheck(ei, gr, f->m);
  return (err);
}

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

  /* --- Check that %$m$% is prime --- */

  x = mp_fromuint(MP_NEW, f->nbits);
  rc = pfilt_smallfactor(x);
  mp_drop(x);
  if (rc != PGEN_DONE) return ("degree not prime");

  /* --- 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");

  /* --- Now do the general checks --- */

  x = mp_lsl(MP_NEW, MP_ONE, f->nbits);
  err = gencheck(ei, gr, x);
  mp_drop(x);
  return (err);
}

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(int argc, char *argv[])
{
  const ecentry *ee;
  const char *e;
  int ok = 1;
  int i;
  grand *gr;

  gr = fibrand_create(0);
  if (argc > 1) {
    for (i = 1; i < argc; i++) {
      ec_info ei;
      if ((e = ec_getinfo(&ei, argv[i])) != 0)
	fprintf(stderr, "bad curve spec `%s': %s", argv[i], e);
      else {
	e = ec_checkinfo(&ei, gr);
	ec_freeinfo(&ei);
	if (!e)
	  printf("OK %s\n", argv[i]);
	else {
	  printf("BAD %s: %s\n", argv[i], e);
	  ok = 0;
	}
      }
      assert(mparena_count(MPARENA_GLOBAL) == 0);
    }
  } else {
    fputs("checking standard curves:", stdout);
    fflush(stdout);
    for (ee = ectab; ee->name; ee++) {
      ec_info ei;
      ec_infofromdata(&ei, ee->data);
      e = ec_checkinfo(&ei, gr);
      ec_freeinfo(&ei);
      if (e) {
	printf(" [%s fails: %s]", ee->name, e);
	ok = 0;
      } else
	printf(" %s", ee->name);
      fflush(stdout);
      assert(mparena_count(MPARENA_GLOBAL) == 0);
    }
    fputs(ok ? " ok\n" : " failed\n", stdout);
  }
  gr->ops->destroy(gr);
  return (!ok);
}

#endif

/*----- That's all, folks -------------------------------------------------*/