Almost sure connectivity in secure wireless sensor network

Abstract

In this paper, our work is to focus on the almost sure connectivity properties of secure wireless sensor networks. We consider a wireless sensor network which is generated randomly using random key pre distribution scheme given by Eschenauer and Gligor under non-full visibilitys. Here, we consider a sensor network in 2-dimensional space, and a sequence Xn = {Xi, X2,...Xn}, with n sensor nodes distributed uniformly over a compact space C ⊂ R2 We focus on network cut to deal with connectivity issues in WSNs. We have given a strong relationship and derived a threshold for the proportion of key ring and key pool size, above which graph will have no cut in the network almost surely. We prove that if key pool size is n log n and key ring size of an arbitrary node is c log n and if c > 1/s(1-s/n) then there will be no cut in the network.