Efficient Implementation of Arithmetic Operations in ECC over Binary Fields

In this paper the implementation of arithmetic operations in ECC is described.Elliptic curve cryptography is very useful in the field of the network security because of its small key size and its high strength of security.In this paper briefly describing general arithmetic operations we focus on scalar multiplication . We present two techniques: (i)reducing Hamming weight of scalars in binary representation and (ii) using sliding window , for obtatining scalar multiplication in a faster manner. Use of both the techniques is explained by suitable examples.