Smart Elliptic Curve Cryptography for Smart Dust

Abstract

Wireless ad-hoc and sensor networks play a vital role in an ever-growing number of applications ranging from environmental monitoring over vehicular communication to home automation. Security and privacy issues pose a big challenge for the widespread adoption of these networks, especially in the automotive domain. The two most essential security services needed to maintain the proper functioning of a wireless network are authentication and key establishment; both can be realized with Elliptic Curve Cryptography (ECC). In this paper, we introduce an efficient ECC implementation for resource-restricted devices such as sensor nodes. Our implementation uses a 160-bit Optimal Prime Field (OPF) over which a Gallant-Lambert-Vanstone (GLV) curve with good cryptographic properties can be defined. The combination of optimized field arithmetic with fast group arithmetic (thanks to an efficiently computable endomorphism) allows us to perform a scalar multiplication in about 5.5 ·106 clock cycles on an 8-bit ATmega128 processor, which is significantly faster than all previously-reported ECC implementations based on a 160-bit prime field.