On the use of optimum curves in elliptic curve cryptography for wireless sensor networks

Abstract

Providing security in Wireless Sensor Networks (WSNs) is a considerable challenge due to the concomitant limitations in processing time, power, area and energy consumption in sensor nodes and the nature of wireless links. A variety of cryptographic methods are available for security establishment. Among them, Elliptic Curve Cryptography (ECC) is the best candidate to accomplish this challenge because it provides high security in spite of a smaller key size. In addition, ECC was subject to many recent studies to optimize the time needed for base point selection and point multiplication operations. In this paper, the points on elliptic curves are analyzed, and an efficient implementation of ECC base point selection is proposed. The proposed implementation can be utilized by extremely constrained devices. We prefer to utilize projective coordinate representations of field elements than to utilize affine coordinates over prime finite field Fp, whereas projective coordinates reduce computational complexity by eliminating the multiplicative inverse in point additions and point doubling. This paper further analyzes non-prime order elliptic curves.The analysis results show that the order of the elliptic curve plays a critical role in determining how fast a base point can be selected.