Abstract

Elliptic curve cryptosystems, proposed by Koblitz ([11]) and Miller ([15]), can be constructed over a smaller field of definition than the ElGamal cryptosystems ([5]) or the RSA cryptosystems ([19]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate efficient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinates strategy, which significantly improves on the number of basic operations needed for elliptic curve exponentiation.

Citations