A Polynomial based Key Distribution Approach for Wireless Sensor Networks

Document Type : Regular Paper


Amirkabir University of Technology


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 secured 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, suitable error correction code is chosen
based on codes of the type which are described as irreducible graded
cyclic CC’s 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, therefore, deserves to be investigated further.


Main Subjects