Simple (non-projective) curves over prime fields now seem to work.

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

/* -*-c-*-
 *
 * $Id: ec-prime.c,v 1.3.4.1 2003/06/10 13:43:53 mdw Exp $
 *
 * Elliptic curves over prime fields
 *
 * (c) 2001 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.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: ec-prime.c,v $
 * Revision 1.3.4.1  2003/06/10 13:43:53  mdw
 * Simple (non-projective) curves over prime fields now seem to work.
 *
 * Revision 1.3  2003/05/15 23:25:59  mdw
 * Make elliptic curve stuff build.
 *
 * Revision 1.2  2002/01/13 13:48:44  mdw
 * Further progress.
 *
 * Revision 1.1  2001/04/29 18:12:33  mdw
 * Prototype version.
 *
 */

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

#include <mLib/sub.h>

#include "ec.h"

/*----- Data structures ---------------------------------------------------*/

typedef struct ecctx {
  ec_curve c;
  mp *a, *b;
} ecctx;

/*----- Simple prime curves -----------------------------------------------*/

static const ec_ops ec_primeops;

static ec *ecneg(ec_curve *c, ec *d, const ec *p)
{
  EC_COPY(d, p);
  d->y = F_NEG(c->f, d->y, d->y);
  return (d);
}

static ec *ecdbl(ec_curve *c, ec *d, const ec *a)
{
  if (EC_ATINF(a))
    EC_SETINF(d);
  else if (!MP_LEN(a->y))
    EC_COPY(d, a);
  else {
    field *f = c->f;
    ecctx *cc = (ecctx *)c;
    mp *lambda;
    mp *dy, *dx;

    dx = F_SQR(f, MP_NEW, a->x);
    dy = F_DBL(f, MP_NEW, a->y);
    dx = F_TPL(f, dx, dx);
    dx = F_ADD(f, dx, dx, cc->a);
    dy = F_INV(f, dy, dy);
    lambda = F_MUL(f, MP_NEW, dx, dy);

    dx = F_SQR(f, dx, lambda);
    dy = F_DBL(f, dy, a->x);
    dx = F_SUB(f, dx, dx, dy);
    dy = F_SUB(f, dy, a->x, dx);
    dy = F_MUL(f, dy, lambda, dy);
    dy = F_SUB(f, dy, dy, a->y);

    EC_DESTROY(d);
    d->x = dx;
    d->y = dy;
    d->z = 0;
    MP_DROP(lambda);
  }
  return (d);
}

static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b)
{
  if (a == b)
    ecdbl(c, d, a);
  else if (EC_ATINF(a))
    EC_COPY(d, b);
  else if (EC_ATINF(b))
    EC_COPY(d, a);
  else {
    field *f = c->f;
    mp *lambda;
    mp *dy, *dx;

    if (!MP_EQ(a->x, b->x)) {
      dy = F_SUB(f, MP_NEW, a->y, b->y);
      dx = F_SUB(f, MP_NEW, a->x, b->x);
      dx = F_INV(f, dx, dx);
      lambda = F_MUL(f, MP_NEW, dy, dx);
    } else if (!MP_LEN(a->y) || !MP_EQ(a->y, b->y)) {
      EC_SETINF(d);
      return (d);
    } else {
      ecctx *cc = (ecctx *)c;
      dx = F_SQR(f, MP_NEW, a->x);
      dx = F_TPL(f, dx, dx);
      dx = F_ADD(f, dx, dx, cc->a);
      dy = F_DBL(f, MP_NEW, a->y);
      dy = F_INV(f, dy, dy);
      lambda = F_MUL(f, MP_NEW, dx, dy);
    }

    dx = F_SQR(f, dx, lambda);
    dx = F_SUB(f, dx, dx, a->x);
    dx = F_SUB(f, dx, dx, b->x);
    dy = F_SUB(f, dy, b->x, dx);
    dy = F_MUL(f, dy, lambda, dy);
    dy = F_SUB(f, dy, dy, b->y);

    EC_DESTROY(d);
    d->x = dx;
    d->y = dy;
    d->z = 0;
    MP_DROP(lambda);
  }
  return (d);
}

static void ecdestroy(ec_curve *c)
{
  ecctx *cc = (ecctx *)c;
  MP_DROP(cc->a);
  MP_DROP(cc->b);
  DESTROY(cc);
}

/* --- @ec_prime@, @ec_primeproj@ --- *
 *
 * Arguments:	@field *f@ = the underlying field for this elliptic curve
 *		@mp *a, *b@ = the coefficients for this curve
 *
 * Returns:	A pointer to the curve.
 *
 * Use:		Creates a curve structure for an elliptic curve defined over
 *		a prime field.  The @primeproj@ variant uses projective
 *		coordinates, which can be a win.
 */

extern ec_curve *ec_prime(field *f, mp *a, mp *b)
{
  ecctx *cc = CREATE(ecctx);
  cc->c.ops = &ec_primeops;
  cc->c.f = f;
  cc->a = F_IN(f, MP_NEW, a);
  cc->b = F_IN(f, MP_NEW, b);
  return (&cc->c);
}

static const ec_ops ec_primeops = {
  ecdestroy, ec_idin, ec_idout, 0, ecneg, ecadd, ec_stdsub, ecdbl
};

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

#ifdef TEST_RIG

#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)

int main(void)
{
  field *f;
  ec_curve *c;
  ec g = EC_INIT, d = EC_INIT;
  mp *p, *a, *b, *r;

  printf("ec-prime: ");
  fflush(stdout);
  a = MP(-3);
  b = MP(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1);
  p = MP(6277101735386680763835789423207666416083908700390324961279);
  r = MP(6277101735386680763835789423176059013767194773182842284080);

  f = field_prime(p);
  c = ec_prime(f, a, b);
  
  g.x = MP(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012);
  g.y = MP(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811);

  ec_mul(c, &d, &g, r);
  if (EC_ATINF(&d)) {
    fprintf(stderr, "zero too early\n");
    return (1);
  }
  ec_add(c, &d, &d, &g);
  if (!EC_ATINF(&d)) {
    fprintf(stderr, "didn't reach zero\n");
    MP_EPRINT("d.x", d.x);
    MP_EPRINT("d.y", d.y);
    return (1);
  }

  ec_destroy(&d);
  ec_destroy(&g);
  ec_destroycurve(c);
  F_DESTROY(f);
  MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r);
  assert(!mparena_count(&mparena_global));
  printf("ok\n");
  return (0);
}

#endif

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