k-Connectivity in Secure Wireless Sensor Networks with Physical Link Constraints - The On/Off Channel Model

Random key predistribution scheme of Eschenauerand Gligor (EG) is a typical solution for ensuring secure commu-nications in a wireless sensor network (WSN). Connectivity of theWSNs under this scheme has received much interest over the lastdecade, and most of the existing work is based on the assumptionof unconstrained sensor-to-sensor communications. In this paper,we study the k-connectivity of WSNs under the EG schemewith physical link constraints; k-connectivity is defined as theproperty that the network remains connected despite the failureof any (k − 1) sensors. We use a simple communication model,where unreliable wireless links are modeled as independenton/off channels, and derive zero-one laws for the properties thati) the WSN is k-connected, and ii) each sensor is connectedto at least k other sensors. These zero-one laws improve theprevious results by Rybarczyk on the k-connectivity under a fullyconnected communication model. Moreover, under the on/offchannel model, we provide a stronger form of the zero-one lawfor the 1-connectivity as compared to that given by Yağan. Wealso discuss the applicability of our results in a different networkapplication, namely in a large-scale, distributed publish-subscribeservice for online social networks.