Fast scalar multiplication on Elliptic Curve Cryptography in selected intervals suitable for Wireless Sensor Networks

Abstract

In Wireless Sensor Networks (WSNs), providing a robust security mechanism with limited energy resources is very challenging because of sensor node's limited resources. Symmetric-key can fulfill the requirement, but if the number of nodes is large, asymmetric-key cryptography is the best natural method because of its scalability. Asymmetric-key cryptography is power-hungry; nevertheless, Elliptic Curve Cryptosystems (ECC) are feasible and more flexible for sensor nodes. Scalar multiplication is the most widely used operation on ECC. Various methods for fast scalar multiplication are based on the binary/ternary representation of the scalar. In this paper, we present a novel technique to make fast scalar multiplication on ECC over prime field for light-weight embedded devices like sensor nodes. Our method significantly reduces the computation of scalar multiplication by an equivalent representation of points based on point order in a given interval. Since our technique can act as a support for most existing methods, after an analytical and efficiency analysis, we implement and evaluate its performance in different scenarios. © Springer International Publishing Switzerland 2013.