/* -*-c-*-
*
- * $Id: ec.c,v 1.1 2001/04/29 18:12:33 mdw Exp $
+ * $Id: ec.c,v 1.2 2001/05/07 17:29:44 mdw Exp $
*
* Elliptic curve definitions
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec.c,v $
+ * Revision 1.2 2001/05/07 17:29:44 mdw
+ * Treat projective coordinates as an internal representation. Various
+ * minor interface changes.
+ *
* Revision 1.1 2001/04/29 18:12:33 mdw
* Prototype version.
*
void ec_copy(ec *d, const ec *p) { EC_COPY(d, p); }
-/*----- Real arithmetic ---------------------------------------------------*/
+/*----- Standard curve operations -----------------------------------------*/
-/* --- @ec_denorm@ --- *
+/* --- @ec_idin@, @ec_idout@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
- * @ec *d@ = pointer to the destination point
- * @const ec *p@ = pointer to the source point
+ * @ec *d@ = pointer to the destination
+ * @const ec *p@ = pointer to a source point
*
- * Returns: ---
+ * Returns: The destination @d@.
*
- * Use: Denormalizes the given point, converting to internal
- * representations and setting the denominator to 1.
+ * Use: An identity operation if your curve has no internal
+ * representation. (The field internal representation is still
+ * used.)
*/
-void ec_denorm(ec_curve *c, ec *d, const ec *p)
+ec *ec_idin(ec_curve *c, ec *d, const ec *p)
{
if (EC_ATINF(p))
EC_SETINF(d);
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);
+ 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_norm@ --- *
+/* --- @ec_projin@, @ec_projout@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
- * @ec *d@ = pointer to the destination point
- * @const ec *p@ = pointer to the source point
+ * @ec *d@ = pointer to the destination
+ * @const ec *p@ = pointer to a source point
*
- * Returns: ---
+ * Returns: The destination @d@.
*
- * Use: Normalizes the given point, by dividing through by the
- * denominator and returning to external representation.
+ * Use: Conversion functions if your curve operations use a
+ * projective representation.
*/
-void ec_norm(ec_curve *c, ec *d, const ec *p)
+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);
d->y = F_OUT(f, y, y);
d->z = 0;
}
+ return (d);
}
+/*----- Real arithmetic ---------------------------------------------------*/
+
/* --- @ec_find@ --- *
*
* Arguments: @ec_curve *c@ = pointer to an elliptic curve
* Use: Finds a point on an elliptic curve with a given x-coordinate.
*/
-void ec_find(ec_curve *c, ec *d, mp *x)
+ec *ec_find(ec_curve *c, ec *d, mp *x)
{
- int rc;
x = F_IN(c->f, MP_NEW, x);
- if ((rc = EC_FIND(c, d, x)) == 0)
- ec_norm(c, d, d);
+ if ((d = EC_FIND(c, d, x)) != 0)
+ EC_OUT(c, d, d);
mp_drop(x);
- return (rc);
+ return (d);
}
/* --- @ec_add@ --- *
* Use: Adds two points on an elliptic curve.
*/
-void ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
+ec *ec_add(ec_curve *c, ec *d, const ec *p, const ec *q)
{
ec pp = EC_INIT, qq = EC_INIT;
- ec_denorm(c, &pp, p);
- ec_denorm(c, &qq, q);
+ EC_IN(c, &pp, p);
+ EC_IN(c, &qq, q);
EC_ADD(c, d, &pp, &qq);
- ec_norm(c, d, d);
+ EC_OUT(c, d, d);
EC_DESTROY(&pp);
EC_DESTROY(&qq);
+ return (d);
}
/* --- @ec_dbl@ --- *
* Use: Doubles a point on an elliptic curve.
*/
-void ec_dbl(ec_curve *c, ec *d, const ec *p)
+ec *ec_dbl(ec_curve *c, ec *d, const ec *p)
{
- ec_denorm(c, d, p);
+ EC_IN(c, d, p);
EC_DBL(c, d, d);
- ec_norm(c, d, d);
+ return (EC_OUT(c, d, d));
}
/* --- @ec_mul@ --- *
* Use: Multiplies a point by a scalar, returning %$n p$%.
*/
-void ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
+ec *ec_mul(ec_curve *c, ec *d, const ec *p, mp *n)
{
mpscan sc;
ec g = EC_INIT;
while (!MP_RBIT(&sc))
MP_RSTEP(&sc);
- ec_denorm(c, &g, p);
+ EC_IN(c, &g, p);
if ((n->f & MP_BURN) && !(g.x->f & MP_BURN))
MP_DEST(g.x, 0, MP_BURN);
if ((n->f & MP_BURN) && !(g.y->f & MP_BURN))
EC_DESTROY(&g);
exit:
- ec_norm(c, d, d);
+ return (EC_OUT(c, d, d));
}
/*----- That's all, folks -------------------------------------------------*/
/* -*-c-*-
*
- * $Id: ec.h,v 1.1 2001/04/29 18:12:33 mdw Exp $
+ * $Id: ec.h,v 1.2 2001/05/07 17:29:44 mdw Exp $
*
* Elliptic curve definitions
*
/*----- Revision history --------------------------------------------------*
*
* $Log: ec.h,v $
+ * Revision 1.2 2001/05/07 17:29:44 mdw
+ * Treat projective coordinates as an internal representation. Various
+ * minor interface changes.
+ *
* Revision 1.1 2001/04/29 18:12:33 mdw
* Prototype version.
*
typedef struct ec_ops {
void (*destroy)(ec_curve */*c*/);
- int (*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/);
- void (*add)(ec_curve */*c*/, ec */*d*/, ec */*p*/, ec */*q*/);
- void (*dbl)(ec_curve */*c*/, ec */*d*/, ec */*p*/);
+ ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
+ ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
+ ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/);
+ ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/);
+ ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
} ec_ops;
#define EC_DESTROY(c) (c)->ops->destroy((c))
+#define EC_IN(c, d, p) (c)->ops->in((c), (d), (p))
+#define EC_OUT(c, d, p) (c)->ops->in((c), (d), (p))
+
#define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x))
#define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q))
#define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p))
*
* Arguments: @ec *p@ = pointer to an elliptic-curve point
*
- * Returns: ---
+ * Returns: The argument @p@.
*
* Use: Initializes a new point. The initial value is the additive
* identity (which is universal for all curves).
_p->x = _p->y = _p->z = MP_NEW; \
} while (0)
-extern void ec_create(ec */*p*/);
+extern ec *ec_create(ec */*p*/);
/* --- @ec_destroy@ --- *
*
*
* Arguments: @ec *p@ = pointer to a point
*
- * Returns: ---
+ * Returns: The argument @p@.
*
* Use: Sets the given point to be the point %$O$% at infinity.
*/
} \
} while (0)
-extern void ec_setinf(ec */*p*/);
+extern ec *ec_setinf(ec */*p*/);
/* --- @ec_copy@ --- *
*
* Arguments: @ec *d@ = pointer to destination point
* @const ec *p@ = pointer to source point
*
- * Returns: ---
+ * Returns: The destination @d@.
*
* Use: Creates a copy of an elliptic curve point.
*/
} \
} while (0)
-extern void ec_copy(ec */*d*/, const ec */*p*/);
+extern ec *ec_copy(ec */*d*/, const ec */*p*/);
/*----- Interesting arithmetic --------------------------------------------*/
* @ec *d@ = pointer to the destination point
* @const ec *p, *q@ = pointers to the operand points
*
- * Returns: ---
+ * Returns: The destination @d@.
*
* Use: Adds two points on an elliptic curve.
*/
-extern void ec_add(ec_curve */*c*/, ec */*d*/,
- const ec */*p*/, const ec */*q*/);
+extern ec *ec_add(ec_curve */*c*/, ec */*d*/,
+ const ec */*p*/, const ec */*q*/);
/* --- @ec_dbl@ --- *
*
* @ec *d@ = pointer to the destination point
* @const ec *p@ = pointer to the operand point
*
- * Returns: ---
+ * Returns: The destination @d@.
*
* Use: Doubles a point on an elliptic curve.
*/
-extern void ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
+extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
/* --- @ec_mul@ --- *
*
* @const ec *p@ = pointer to the generator point
* @mp *n@ = integer multiplier
*
- * Returns: ---
+ * Returns: The destination @d@.
*
* Use: Multiplies a point by a scalar, returning %$n p$%.
*/
-extern void ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/);
+extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/);
+
+/*----- Standard curve operations -----------------------------------------*/
+
+/* --- @ec_idin@, @ec_idout@ --- *
+ *
+ * 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.)
+ */
+
+extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
+extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
+
+/* --- @ec_projin@, @ec_projout@ --- *
+ *
+ * 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.
+ */
+
+extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
+extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/);
/*----- Creating curves ---------------------------------------------------*/