A Polynomial-Based Key Distribution Approach for Wireless Sensor Networks

Abstract

Network coding is a novel concept for improving network capacity. This additional capacity may be used to increase throughput or reliability. Also in wireless networks, network coding has been proposed as a method for improving communication. The polynomial-based key predistribution scheme of Blom and Blundo et al. has been the basic ingredient for the key establishment for wireless sensor network (WSN). It is tempting to use many random and different instances of polynomial-based key predistribution scheme for various parts of the WSN to enhance the efficiency of WSN key establishment protocols. But it is not secure in general to use many instances of Blom-Blundo et al. polynomial-based key predistribution scheme in a WSN key establishment protocol. Thus the previously constructed group-based type WSN key predistribution schemes using polynomial-based key predistribution scheme are insecure. In this paper, a suitable error correction code is chosen based on codes of the type which are described as irreducible graded cyclic CCs which can algebraically be described by one-sided principal ideals in a noncommutative algebra $$A[x; \alpha ]$$ , where $$A \cong {\mathbb {F}}[x]/(x^n-1)$$ , $${\mathbb {F}}$$ is a finite field and n is the length of the code. This leads to the notion of a generator polynomial just like for cyclic block codes. Similarly, a parity check polynomial can be introduced by considering the right annihilator ideal. This way indicates that the big class of $$\sigma$$ -cyclic convolutional codes contains quite some good codes and deserves to be investigated further.