Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform.

Utku Gulen,Selcuk Baktir

doi:10.3390/s20051507

Abstract

We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve scalar point multiplication. We take advantage of the fast Fourier transform for the first time in the literature to speed up the number theoretic transform for an efficient realization of elliptic curve cryptography. Our implementation achieves elliptic curve scalar point multiplication in only s and s for multiplication of fixed and random points, respectively, and has similar or better timing performance compared to previous works in the literature.

Highlights

Wireless sensor network (WSN) technology is a widespread and enabling technology that has been rapidly penetrating our daily lives
We show that number theoretic transform (NTT)-based finite field multiplication is feasible for small operand sizes and can be taken advantage of to speed up Elliptic curve cryptography (ECC) on WSN nodes
Our Main Contribution: We present a novel realization of ECC which uses Edwards curves for point arithmetic and the NTT for the underlying finite field multiplication and squaring operations

Summary

Introduction

Wireless sensor network (WSN) technology is a widespread and enabling technology that has been rapidly penetrating our daily lives. It has environmental applications such as temperature, humidity, pressure and fire monitoring [1,2], health applications such as patient monitoring [3], military applications such as enemy detection and reconnaissance [4], and applications to smart cities such as in smart grids [5]. Elements of the finite field GF ( pm ) are typically represented in the time domain as polynomials of degree m − 1 with coefficients in GF ( p) [55,56]. The complexity of polynomial multiplication can be reduced by performing this computation in the frequency domain

Methods

Results

Conclusion