Improved Algorithm for Elliptic Curve Scalar MultiPlication using wMOF and Shamir Method

Since the inception of elliptic curve based cryptosystems, numerous amount of research has been done to increase the efficiency. ECC is accepted widely as a next generation cryptosystem and is more suitable for limited environments like cellular phones, PDA etc. Scalar multiplication is the most time consuming operation in elliptic curve based protocols. In this paper, we discuss the new canonical form called MOF (mutual opposite form) and propose a new method, which is an extended version of Shamir's method. It is found that our proposed method significantly improves the performance of the elliptic curve exponentiation.