X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/ec.c

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-/* -*-c-*-
- *
- * $Id$
- *
- * Elliptic curve definitions
- *
- * (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.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "ec.h"
-
-/*----- Trivial wrappers --------------------------------------------------*/
-
-/* --- @ec_samep@ --- *
- *
- * Arguments:	@ec_curve *c, *d@ = two elliptic curves
- *
- * Returns:	Nonzero if the curves are identical (not just isomorphic).
- *
- * Use:		Checks for sameness of curves.  This function does the full
- *		check, not just the curve-type-specific check done by the
- *		@sampep@ field operation.
- */
-
-int ec_samep(ec_curve *c, ec_curve *d)
-{
-  return (c == d || (field_samep(c->f, d->f) &&
-		     c->ops == d->ops && EC_SAMEP(c, d)));
-}
-
-/* --- @ec_create@ --- *
- *
- * Arguments:	@ec *p@ = pointer to an elliptic-curve point
- *
- * Returns:	The argument @p@.
- *
- * Use:		Initializes a new point.  The initial value is the additive
- *		identity (which is universal for all curves).
- */
-
-ec *ec_create(ec *p) { EC_CREATE(p); return (p); }
-
-/* --- @ec_destroy@ --- *
- *
- * Arguments:	@ec *p@ = pointer to an elliptic-curve point
- *
- * Returns:	---
- *
- * Use:		Destroys a point, making it invalid.
- */
-
-void ec_destroy(ec *p) { EC_DESTROY(p); }
-
-/* --- @ec_atinf@ --- *
- *
- * Arguments:	@const ec *p@ = pointer to a point
- *
- * Returns:	Nonzero if %$p = O$% is the point at infinity, zero
- *		otherwise.
- */
-
-int ec_atinf(const ec *p) { return (EC_ATINF(p)); }
-
-/* --- @ec_setinf@ --- *
- *
- * Arguments:	@ec *p@ = pointer to a point
- *
- * Returns:	The argument @p@.
- *
- * Use:		Sets the given point to be the point %$O$% at infinity.
- */
-
-ec *ec_setinf(ec *p) { EC_SETINF(p); return (p); }
-
-/* --- @ec_copy@ --- *
- *
- * Arguments:	@ec *d@ = pointer to destination point
- *		@const ec *p@ = pointer to source point
- *
- * Returns:	The destination @d@.
- *
- * Use:		Creates a copy of an elliptic curve point.
- */
-
-ec *ec_copy(ec *d, const ec *p) { EC_COPY(d, p); return (d); }
-
-/* --- @ec_eq@ --- *
- *
- * Arguments:	@const ec *p, *q@ = two points
- *
- * Returns:	Nonzero if the points are equal.  Compares external-format
- *		points.
- */
-
-int ec_eq(const ec *p, const ec *q) { return (EC_EQ(p, q)); }
-
-/*----- Standard curve operations -----------------------------------------*/
-
-/* --- @ec_stdsamep@ --- *
- *
- * Arguments:	@ec_curve *c, *d@ = two elliptic curves
- *
- * Returns:	Nonzero if the curves are identical (not just isomorphic).
- *
- * Use:		Simple sameness check on @a@ and @b@ curve members.
- */
-
-int ec_stdsamep(ec_curve *c, ec_curve *d)
-  { return (MP_EQ(c->a, d->a) && MP_EQ(c->b, d->b)); }
-
-/* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination
- *		@const ec *p@ = pointer to a source point
- *
- * Returns:	The destination @d@.
- *
- * Use:		An identity operation if your curve has no internal
- *		representation.  (The field internal representation is still
- *		used.)
- */
-
-ec *ec_idin(ec_curve *c, ec *d, const ec *p)
-{
-  if (EC_ATINF(p))
-    EC_SETINF(d);
-  else {
-    field *f = c->f;
-    d->x = F_IN(f, d->x, p->x);
-    d->y = F_IN(f, d->y, p->y);
-    mp_drop(d->z); d->z = 0;
-  }
-  return (d);
-}
-
-ec *ec_idout(ec_curve *c, ec *d, const ec *p)
-{
-  if (EC_ATINF(p))
-    EC_SETINF(d);
-  else {
-    field *f = c->f;
-    d->x = F_OUT(f, d->x, p->x);
-    d->y = F_OUT(f, d->y, p->y);
-    mp_drop(d->z); d->z = 0;
-  }
-  return (d);
-}
-
-ec *ec_idfix(ec_curve *c, ec *d, const ec *p)
-  { EC_COPY(d, p); return (d); }
-
-/* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination
- *		@const ec *p@ = pointer to a source point
- *
- * Returns:	The destination @d@.
- *
- * Use:		Conversion functions if your curve operations use a
- *		projective representation.
- */
-
-ec *ec_projin(ec_curve *c, ec *d, const ec *p)
-{
-  if (EC_ATINF(p))
-    EC_SETINF(d);
-  else {
-    field *f = c->f;
-    d->x = F_IN(f, d->x, p->x);
-    d->y = F_IN(f, d->y, p->y);
-    mp_drop(d->z); d->z = MP_COPY(f->one);
-  }
-  return (d);
-}
-
-ec *ec_projout(ec_curve *c, ec *d, const ec *p)
-{
-  if (EC_ATINF(p))
-    EC_SETINF(d);
-  else {
-    mp *x, *y, *z, *zz;
-    field *f = c->f;
-    if (p->z == f->one) {
-      d->x = F_OUT(f, d->x, p->x);
-      d->y = F_OUT(f, d->y, p->y);
-    } else {
-      z = F_INV(f, MP_NEW, p->z);
-      zz = F_SQR(f, MP_NEW, z);
-      z = F_MUL(f, z, zz, z);
-      x = F_MUL(f, d->x, p->x, zz);
-      y = F_MUL(f, d->y, p->y, z);
-      mp_drop(z);
-      mp_drop(zz);
-      d->x = F_OUT(f, x, x);
-      d->y = F_OUT(f, y, y);
-    }
-    mp_drop(d->z);
-    d->z = 0;
-  }
-  return (d);
-}
-
-ec *ec_projfix(ec_curve *c, ec *d, const ec *p)
-{
-  if (EC_ATINF(p))
-    EC_SETINF(d);
-  else if (p->z == c->f->one)
-    EC_COPY(d, p);
-  else {
-    mp *z, *zz;
-    field *f = c->f;
-    z = F_INV(f, MP_NEW, p->z);
-    zz = F_SQR(f, MP_NEW, z);
-    z = F_MUL(f, z, zz, z);
-    d->x = F_MUL(f, d->x, p->x, zz);
-    d->y = F_MUL(f, d->y, p->y, z);
-    mp_drop(z);
-    mp_drop(zz);
-    mp_drop(d->z);
-    d->z = MP_COPY(f->one);
-  }
-  return (d);
-}
-
-/* --- @ec_stdsub@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination
- *		@const ec *p, *q@ = the operand points
- *
- * Returns:	The destination @d@.
- *
- * Use:		Standard point subtraction operation, in terms of negation
- *		and addition.  This isn't as efficient as a ready-made
- *		subtraction operator.
- */
-
-ec *ec_stdsub(ec_curve *c, ec *d, const ec *p, const ec *q)
-{
-  ec t = EC_INIT;
-  EC_NEG(c, &t, q);
-  EC_FIX(c, &t, &t);
-  EC_ADD(c, d, p, &t);
-  EC_DESTROY(&t);
-  return (d);
-}
-
-/*----- Creating curves ---------------------------------------------------*/
-
-/* --- @ec_destroycurve@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an ellptic curve
- *
- * Returns:	---
- *
- * Use:		Destroys a description of an elliptic curve.
- */
-
-void ec_destroycurve(ec_curve *c) { c->ops->destroy(c); }
-
-/*----- Real arithmetic ---------------------------------------------------*/
-
-/* --- @ec_find@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@mp *x@ = a possible x-coordinate
- *
- * Returns:	Zero if OK, nonzero if there isn't a point there.
- *
- * Use:		Finds a point on an elliptic curve with a given x-coordinate.
- */
-
-ec *ec_find(ec_curve *c, ec *d, mp *x)
-{
-  x = F_IN(c->f, MP_NEW, x);
-  if ((d = EC_FIND(c, d, x)) != 0)
-    EC_OUT(c, d, d);
-  MP_DROP(x);
-  return (d);
-}
-
-/* --- @ec_neg@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@const ec *p@ = pointer to the operand point
- *
- * Returns:	The destination point.
- *
- * Use:		Computes the negation of the given point.
- */
-
-ec *ec_neg(ec_curve *c, ec *d, const ec *p)
-  { EC_IN(c, d, p); EC_NEG(c, d, d); return (EC_OUT(c, d, d)); }
-
-/* --- @ec_add@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@const ec *p, *q@ = pointers to the operand points
- *
- * Returns:	---
- *
- * Use:		Adds two points on an elliptic curve.
- */
-
-ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
-{
-  ec pp = EC_INIT, qq = EC_INIT;
-  EC_IN(c, &pp, p);
-  EC_IN(c, &qq, q);
-  EC_ADD(c, d, &pp, &qq);
-  EC_OUT(c, d, d);
-  EC_DESTROY(&pp);
-  EC_DESTROY(&qq);
-  return (d);
-}
-
-/* --- @ec_sub@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@const ec *p, *q@ = pointers to the operand points
- *
- * Returns:	The destination @d@.
- *
- * Use:		Subtracts one point from another on an elliptic curve.
- */
-
-ec *ec_sub(ec_curve *c, ec *d, const ec *p, const ec *q)
-{
-  ec pp = EC_INIT, qq = EC_INIT;
-  EC_IN(c, &pp, p);
-  EC_IN(c, &qq, q);
-  EC_SUB(c, d, &pp, &qq);
-  EC_OUT(c, d, d);
-  EC_DESTROY(&pp);
-  EC_DESTROY(&qq);
-  return (d);
-}
-
-/* --- @ec_dbl@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@const ec *p@ = pointer to the operand point
- *
- * Returns:	---
- *
- * Use:		Doubles a point on an elliptic curve.
- */
-
-ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
-  { EC_IN(c, d, p); EC_DBL(c, d, d); return (EC_OUT(c, d, d)); }
-
-/* --- @ec_check@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@const ec *p@ = pointer to the point
- *
- * Returns:	Zero if OK, nonzero if this is an invalid point.
- *
- * Use:		Checks that a point is actually on an elliptic curve.
- */
-
-int ec_check(ec_curve *c, const ec *p)
-{
-  ec t = EC_INIT;
-  int rc;
-
-  if (EC_ATINF(p))
-    return (0);
-  EC_IN(c, &t, p);
-  rc = EC_CHECK(c, &t);
-  EC_DESTROY(&t);
-  return (rc);
-}
-
-/* --- @ec_rand@ --- *
- *
- * Arguments:	@ec_curve *c@ = pointer to an elliptic curve
- *		@ec *d@ = pointer to the destination point
- *		@grand *r@ = random number source
- *
- * Returns:	The destination @d@.
- *
- * Use:		Finds a random point on the given curve.
- */
-
-ec *ec_rand(ec_curve *c, ec *d, grand *r)
-{
-  mp *x = MP_NEW;
-  do x = F_RAND(c->f, x, r); while (!EC_FIND(c, d, x));
-  mp_drop(x);
-  if (grand_range(r, 2)) EC_NEG(c, d, d);
-  return (EC_OUT(c, d, d));
-}
-
-/*----- That's all, folks -------------------------------------------------*/