We introduce a new random key predistribution scheme for securing heterogeneous wireless sensor networks. Each of the @math sensors in the network is classified into @math classes according to some probability distribution @math . Before deployment, a class- @math sensor is assigned @math cryptographic keys that are selected uniformly at random from a common pool of @math keys. Once deployed, a pair of sensors can communicate securely if and only if they have a key in common. We model the communication topology of this network by a newly defined inhomogeneous random key graph. We establish scaling conditions on the parameters @math and @math so that this graph: 1) has no isolated nodes and 2) is connected, both with high probability. The results are given in the form of zero-one laws with the number of sensors @math growing unboundedly large; critical scalings are identified and shown to coincide for both graph properties. Our results are shown to complement and improve those given by and for the same model, therein referred to as the general random intersection graph.
In comparing Theorems , and , it is worth noting that @math -connectivity is a stronger property than connectivity, which in turn is stronger than absence of isolated nodes. However, although Theorems and consider strong graph properties, we now argue why the established results are not likely to be applicable for real-world sensor networks. First, Theorem focuses on the case where all possible key rings have a finite size that do not scale with @math . In addition, with @math fixed, it is clear that the scaling conditions ) and ) both require Unfortunately, it is often needed that key pool size @math be much larger than the network size @math @cite_15 @cite_10 as otherwise the network will be extremely vulnerable against node capture attacks. In fact, one can see that with ) in effect, an adversary can compromise a significant portion of the key pool (and, hence network communication) by capturing @math nodes.
@cite_15 @cite_10
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We give, for the first time, a precise mathematical analysis of the connectivity and security properties of sensor networks that make use of the random predistribution of keys. We also show how to set the parameters---pool and key ring size---in such a way that the network is not only connected with high probability via secure links but also provably resilient, in the following sense: We formally show that any adversary that captures sensors at random with the aim of compromising a constant fraction of the secure links must capture at least a constant fraction of the nodes of the network. In the context of wireless sensor networks where random predistribution of keys is employed, we are the first to provide a mathematically precise proof, with a clear indication of parameter choice, that two crucial properties---connectivity via secure links and resilience against malicious attacks---can be obtained simultaneously. We also show in a mathematically rigorous way that the network enjoys another strong security property. The adversary cannot partition the network into two linear size components, compromising all the links between them, unless it captures linearly many nodes. This implies that the network is also fault tolerant with respect to node failures. Our theoretical results are complemented by extensive simulations that reinforce our main conclusions. We introduce a new random key predistribution scheme for securing heterogeneous wireless sensor networks. Each of the @math sensors in the network is classified into @math classes according to some probability distribution @math . Before deployment, a class- @math sensor is assigned @math cryptographic keys that are selected uniformly at random from a common pool of @math keys. Once deployed, a pair of sensors can communicate securely if and only if they have a key in common. We model the communication topology of this network by a newly defined inhomogeneous random key graph. We establish scaling conditions on the parameters @math and @math so that this graph: 1) has no isolated nodes and 2) is connected, both with high probability. The results are given in the form of zero-one laws with the number of sensors @math growing unboundedly large; critical scalings are identified and shown to coincide for both graph properties. Our results are shown to complement and improve those given by and for the same model, therein referred to as the general random intersection graph. We investigate the connectivity of a wireless sensor network (WSN) secured by the heterogeneous key predistribution scheme under an independent on off channel model. The heterogeneous scheme induces an inhomogeneous random key graph, denoted by @math and the on off channel model induces an Erdős-Renyi graph, denoted by @math . Hence, the overall random graph modeling the WSN is obtained by the intersection of @math and @math . We present conditions on how to scale the parameters of the intersecting graph with respect to the network size @math such that the graph i) has no isolated nodes and ii) is connected, both with high probability (whp) as the number of nodes gets large. Our results are supported by a simulation study demonstrating that i) despite their asymptotic nature, our results can in fact be useful in designing finite -node WSNs so that they achieve secure connectivity whp; and ii) despite the simplicity of the on off communication model, the probability of connectivity in the resulting WSN approximates very well the case where the disk model is used. Despite much research on probabilistic key predistribution schemes for wireless sensor networks over the past decade, few formal analyses exist that define schemes’ resilience to node-capture attacks precisely and under realistic conditions. In this paper, we analyze the resilience of the @math -composite key predistribution scheme, which mitigates the node capture vulnerability of the Eschenauer-Gligor scheme in the neighbor discovery phase. We derive scheme parameters to have a desired level of resiliency, and obtain optimal parameters that defend against different adversaries as much as possible. We also show that this scheme can be easily enhanced to achieve the same “perfect resilience” property as in the random pairwise key predistribution for attacks launched after neighbor discovery. Despite considerable attention to this scheme, much prior work explicitly or implicitly uses an incorrect computation for the probability of link compromise under node-capture attacks and ignores the real-world transmission constraints of sensor nodes. Moreover, we derive the critical network parameters to ensure connectivity in both the absence and presence of node-capture attacks. We also investigate node replication attacks by analyzing the adversary’s optimal strategy.