We consider the network reliability problem in wireless sensor networks secured by the heterogeneous random key predistribution scheme. This scheme generalizes Eschenauer-Gligor scheme by considering the cases when the network comprises sensor nodes with varying level of resources; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted @math . We analyze the reliability of @math against random link failures. Namely, we consider @math formed by deleting each edge of @math independently with probability @math , and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on @math , @math , and @math such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We present numerical results to support these in the finite-node regime.
@cite_18: We investigate the secure connectivity of wireless sensor networks under the random key distribution scheme of Eschenauer and Gligor. Unlike recent work which was carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as on off channels. We present conditions on how to scale the model parameters so that the network: 1) has no secure node which is isolated and 2) is securely connected, both with high probability when the number of sensor nodes becomes large. The results are given in the form of full zero-one laws, and constitute the first complete analysis of the EG scheme under non-full visibility. Through simulations, these zero-one laws are shown to be valid also under a more realistic communication model (i.e., the disk model). The relations to the Gupta and Kumar's conjecture on the connectivity of geometric random graphs with randomly deleted edges are also discussed.
@cite_1: Distributed Sensor Networks (DSNs) are ad-hoc mobile networks that include sensor nodes with limited computation and communication capabilities. DSNs are dynamic in the sense that they allow addition and deletion of sensor nodes after deployment to grow the network or replace failing and unreliable nodes. DSNs may be deployed in hostile areas where communication is monitored and nodes are subject to capture and surreptitious use by an adversary. Hence DSNs require cryptographic protection of communications, sensor-capture detection, key revocation and sensor disabling. In this paper, we present a key-management scheme designed to satisfy both operational and security requirements of DSNs. The scheme includes selective distribution and revocation of keys to sensor nodes as well as node re-keying without substantial computation and communication capabilities. It relies on probabilistic key sharing among the nodes of a random graph and uses simple protocols for shared-key discovery and path-key establishment, and for key revocation, re-keying, and incremental addition of nodes. The security and network connectivity characteristics supported by the key-management scheme are discussed and simulation experiments presented.
The reliability of secure WSNs was also studied in @cite_18 , but under the Eschenauer-Gligor scheme @cite_1 where all sensors receive the same number of keys. However, when the network consists of sensors with varying level of resources (e.g., computational, memory, power) and or with varying level of security and connectivity requirements, it may no longer be sensible to assign the same number of keys to all sensors. Our work addresses this issue by generalizing @cite_18 to the cases where nodes can be assigned different number of keys. When @math , i.e., when all nodes belong to the same class and receive the same number of keys, our result recovers the main result in @cite_18 .