Institute for Systems Research
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Item On the gradual deployment of random pairwise key distribution schemes(2010-07-31) Yagan, Osman; Makowski, Armand M.In the context of wireless sensor networks, the pairwise key distribution scheme of Chan et al. has several advantages over other key distribution schemes including the original scheme of Eschenauer and Gligor. However, this offline pairwise key distribution mechanism requires that the network size be set in advance, and involves all sensor nodes simultaneously. Here, we address this issue by describing an implementation of the pairwise scheme that supports the gradual deployment of sensor nodes in several consecutive phases. We discuss the key ring size needed to maintain the secure connectivity throughout all the deployment phases. In particular we show that the number of keys at each sensor node can be taken to be O(log n) in order to achieve secure connectivity (with high probability).Item On random graphs associated with a pairwise key distribution scheme for wireless sensor networks (Extended version)(2010-07) Yagan, Osman; Makowski, Armand M.The pairwise key distribution scheme of Chan et al. was proposed as an alternative to the key distribution scheme of Eschenauer and Gligor (EG) to enable network security in wireless sensor networks. In this paper we consider the random graph induced by this pairwise scheme under the assumption of full visibility. We first establish a zero-one law for graph connectivity. Then, we discuss the number of keys needed in the memory of each sensor in order to achieve secure connectivity (with high probability). For a network of n sensors the required number of keys is shown to be on the order of log n, a key ring size comparable to that of the EG scheme (in realistic scenarios).Item On random graphs associated with a pairwise key distribution scheme(2010-01-01) Yagan, Osman; Makowski, Armand M.The pairwise key distribution scheme of Chan et al. was proposed as an alternative to the key distribution scheme of Eschenauer and Gligor to enable network security in wireless sensor networks. We consider the random graph induced by this pairwise scheme under the assumption of full visibility, and show the existence of a zero-one law for graph connectivity.Item On the existence of triangles in random key graphs(2009-07-04) Yagan, Osman; Makowski, Armand M.The random key graph, also known as the uniform random intersection graph, is a random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We show the existence of a zero-one law for the appearance of triangles in random key graphs by applying the method of first and second moments to the number of triangles in the graph.Item On the random graph induced by a randomized predistribution scheme under full visibility (Extended version)(2008) Yagan, Osman; Makowski, Armand M.We consider the random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We show the existence of a zero-one law for the absence of isolated nodes, and complement it by a Poisson convergence for the number of isolated nodes. Leveraging earlier resu lts and analogies with Erd\H{o}s-Renyi graphs, we explore similar results for the property of graph connectivity. Implications for secure connectivity are discussed.