On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels

Abstract

The q-composite key predistribution scheme [1] is used prevalently for secure communications in large-scale wireless sensor networks (WSNs). Prior work [2]-[4] explores topological properties of WSNs employing the q-composite scheme for q = 1 with unreliable communication links modeled as independent on/off channels. In this paper, we investigate topological properties related to the node degree in WSNs operating under the q-composite scheme and the on/off channel model. Our results apply to general q and are stronger than those reported for the node degree in prior work even for the case of q being 1. Specifically, we show that the number of nodes with certain degree asymptotically converges in distribution to a Poisson random variable, present the asymptotic probability distribution for the minimum degree of the network, and establish the asymptotically exact probability for the property that the minimum degree is at least an arbitrary value. Numerical experiments confirm the validity of our analytical findings.

arXiv commentBest Student Paper Finalist in IEEE International Symposium on Information Theory (ISIT) 2014

References in corpus (7)

• Zero-one laws for connectivity in random key graphs
• Degree and clustering coefficient in sparse random intersection graphs
• Monotone properties of random geometric graphs have sharp thresholds
• Performance of the Eschenauer-Gligor key distribution scheme under an ON/OFF channel
• Assortativity and clustering of sparse random intersection graphs
• On the strengths of connectivity and robustness in general random intersection graphs
• Component Evolution in General Random Intersection Graphs

Cited by in corpus (7)

• Connectivity in Secure Wireless Sensor Networks under Transmission Constraints
• On the strengths of connectivity and robustness in general random intersection graphs
• Towards $k$-connectivity of the random graph induced by a pairwise key predistribution scheme with unreliable links
• Probabilistic key predistribution in mobile networks resilient to node-capture attacks
• On secure communication in sensor networks under q-composite key predistribution with unreliable links
• Analyzing resilience of interest-based social networks against node and link failures
• Secure Connectivity of Wireless Sensor Networks Under Key Predistribution with on/off Channels