Abstract

In wireless sensor networks, the qq-composite key predistribution scheme is a widely recognized way to secure communications. Although connectivity properties of secure sensor networks with the qq-composite scheme have been studied in the literature, few results address physical transmission constraints since it is challenging to analyze the network connectivity in consideration of both the qq-composite scheme and transmission constraints together. These transmission constraints reflect real-world implementations of sensor networks in which two sensors have to be within a certain distance from each other to communicate. In this paper, we rigorously derive conditions for connectivity in sensor networks employing the qq-composite scheme under transmission constraints. Furthermore, we extend the analysis to consider the unreliability of wireless links by modeling each link being independently active with some probability. Our results provide useful guidelines for designing securely and reliably connected sensor networks. We also present numerical experiments to confirm the analytical results.

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