Optimal implementation of elliptic curve cryptography

The most time-consuming operation in the Elliptic Curve Cryptography (ECC) calculation is scalar multiplication. Scalar multiplication plays a major role in ECC. Currently, there are several optimization algorithms for point scalar multiplication which have either high computational complexity or additional storage requirement. They are all unsuitable for further applying. In this paper, we present a new compatible optimal algorithm which improves the efficiency by generating a special random number k as the scalar. The experimental results show that the processes of encryption and decryption have been speed up significantly in the same condition.