Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
- Cite this paper as:
- Cohen H., Miyaji A., Ono T. (1998) Efficient Elliptic Curve Exponentiation Using Mixed Coordinates. In: Ohta K., Pei D. (eds) Advances in Cryptology — ASIACRYPT’98. ASIACRYPT 1998. Lecture Notes in Computer Science, vol 1514. Springer, Berlin, Heidelberg
Elliptic curve cryptosystems, proposed by Koblitz () and Miller (), can be constructed over a smaller field of definition than the ElGamal cryptosystems () or the RSA cryptosystems (). 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.