New scalar encoding method to accelerate point multiplication in elliptic curve cryptography

Abstract

The security of the wireless environment, especially for those which have limited resources like in the wireless sensor network, needs lightweight algorithms. Elliptic curve cryptography (ECC) is the unique algorithm which satisfies such property. It provides the high level of security with relatively small keys; therefore, it has been the core of many standards. The efficiency of ECC is depending mostly on the implementation of the scalar multiplication which is accomplished mainly by addition and doubling operations. In the add-double method, reducing the number of ones is considered the most likely way to diminish the total number of the entirety operations. In this chapter, we present the method for recoding this scalar such that decreasing the number of addition operations. We compared our method with the one's complement recoding method, and the simulation results showed that our proposed method produces mostly a better encoding. © 2012 Springer Science+Business.