Accurate Analysis of Connectivity and Resilience for a Class of Wireless Sensor Networks

Increasing attention is being devoted to network security with the extensive application of wireless sensor networks in various fields. Connectivity and resilience are the crucial metrics of network security. We establish precise formulas for obtaining the resilience of a Key predistribution scheme (KPS) obtained from an Orthogonal array (OA). We study the connectivity and resilience of the Broadcast-enhanced key predistribution scheme (BEKPS) based on OAs and improve the existing methods. We also present precise formulas for evaluating the resilience of these schemes based on any number of partitions, completely solving the problem regarding the resilience of this type of BEKPS. We obtain precise formulas for ensuring the connectivity of two partitions under the condition that each pair of trees from different partitions intersects at exactly one node. We present a general approximate formula for evaluating the connectivity of more than two partitions, providing a positive solution to the open problem in Kendall et al.'s paper in ACM Transactions on Sensor Networks (Vol.11, No.1, 2014). Thus, we can conclude that for this type of BEKPS, connectivity increases, whereas resilience remains unchanged as the number of partitions increases. A comparison of the obtained results and the previously reported results reveals the superior performance of the proposed BEKPSs.