+++ /dev/null
-/* -*-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 -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff