Implementation of Optimizing Point Multiplication in Elliptic Curve Cryptography Using Binary Method

Public key cryptography has become a mainstay for secure communications. They lay the foundation of secure transmission of documents, key management and digital signatures. Elliptic curve cryptography is an asymmetric key cryptographic tool that has gained a lot of attention in the industry. Elliptic Curve Cryptography provides greater security and more efficient performance than the first generation public key techniques now in use. The performance of elliptic curve cryptosystem heavily depends on an operation called point multiplication or scalar multiplication. The speed of scalar multiplication dominates the efficiency of the system. Fast multiplication is particularly more crucial for some environments such as central servers, where large numbers of key agreements or signature generations occur, and in handheld devices with low computational power. Because of such importance of speed of scalar multiplication, several methods have been developed. This paper describes implementations and test results of Elliptic Curve Cryptography (ECC) The paper deals with the problem of improving the performance of point multiplication using binary representation. This method reduces the point addition as well as the point doubling. This paper insists the application of Binary Method for point multiplication as it is faster than the widely used original method.