Topological Properties of Wireless Sensor Networks Under the Q-Composite Key Predistribution Scheme With Unreliable Links (CMU-CyLab-14-002)

The seminal q-composite key predistribution scheme[3] (IEEE S&P; 2003) is used prevalently for secure communica-tions in large-scale wireless sensor networks (WSNs). Yağan [12](IEEE IT 2012) and we [15] (IEEE ISIT 2013) explore topologicalproperties of WSNs employing the q-composite scheme in thecase of q = 1 with unreliable communication links modeledas independent on/off channels. However, it is challenging toderive results for general q under such on/off channel model. Inthis paper, we resolve such challenge and investigate topologicalproperties related to node degree in WSNs operating under theq-composite scheme and the on/off channel model. Our resultsapply to general q, yet there has not been any work in theliterature reporting the corresponding results even for q = 1,which are stronger than those about node degree in [12], [15].Specifically, we show that the number of nodes with an arbitrarydegree asymptotically converges to a Poisson distribution, presentthe asymptotic probability distribution for the minimum nodedegree of the network, and establish the asymptotically exactprobability for the property that the minimum node degree isat least an arbitrary value. Numerical experiments confirm thevalidity our analytical findings.