Computing short Lucas chains for elliptic curve cryptosystems
Elliptic curves Em: By(2) = x(3) + Ax(2) + x are suitable for cryptographic use because fast addition operations can be defined over E-m. In elliptic curve cryptosystems, encryption/decryption involves multiplying a point P on E-m by a large integer n. In this paper, we propose a fast algorithm for computing such scalar multiplication over E-m. The new algorithm requires fewer operations than previously proposed algorithms. As a result, elliptic curve cryptosystems based on E-m can be speeded up by using the new algorithm.
lucas chains elliptic curves scalar multiplications addition chains