Browsing by Author "Yagan, Osman"
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Item Connectivity in random key graphs – Simple proofs for special cases(2009-01-14) Yagan, Osman; Makowski, ArmandWe consider the random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We report on recent results concerning a conjectured zero-one law for graph connectivity, and provide simple proofs for some special cases.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 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 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 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 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.Item On the resiliency of sensor networks under the pairwise key distribution scheme(2011-07) Yagan, Osman; Makowski, ArmandWe investigate the security of wireless sensor networks under the pairwise key distribution scheme of Chan et al. [2]. We present conditions on how to scale the model parameters so that the network is i) unassailable, and ii) unsplittable, both with high probability, as the number of sensor nodes becomes large. We show that the required number of secure keys to be stored in the memory of each sensors is order of magnitude smaller than what is required for the Eschenauer-Gligor scheme [5].Item RANDOM GRAPH MODELING OF KEY DISTRIBUTION SCHEMES IN WIRELESS SENSOR NETWORKS(2011) Yagan, Osman; Makowski, Armand M; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Wireless sensor networks (WSNs) are distributed collections of sensors with limited capabilities for computations and wireless communications. It is envisioned that such networks will be deployed in hostile environments where communications are monitored, and nodes are subject to capture and surreptitious use by an adversary. Thus, cryptographic protection will be needed to ensure secure communications, as well as to support sensor-capture detection, key revocation and sensor disabling. Recently, random key predistribution schemes have been introduced to address these issues, and they are by now a widely accepted solution for establishing security in WSNs. The main goal of the dissertation is to investigate and compare two popular random key predistribution schemes, namely the Eschenauer-Gligor (EG) scheme and the pairwise key distribution scheme of Chan, Perrig and Song. We investigate both schemes through their induced random graph models and develop scaling laws that corresponds to desirable network properties, e.g., absence of secure nodes that are isolated, secure connectivity, resiliency against attacks, scalability, and low memory load - We obtain conditions on the scheme parameters so that these properties occur with high probability as the number of nodes becomes large. We then compare these two schemes explaining their relative advantages and disadvantages, as well as their feasibility for several WSN applications. In the process, we first focus on the "full visibility" case, where sensors are all within communication range of each other. This assumption naturally leads to studying the random graph models induced by the aforementioned key distribution schemes, namely the random key graph and the random pairwise graph, respectively. In a second step, we remove the assumption of full visibility by integrating a wireless communication model with the random graph models induced under full visibility. We study the connectivity of WSNs under this new model and obtain conditions (for both schemes) that lead to the secure connectivity of theItem A zero-one law for the existence of triangles in random key graphs(2011) Yagan, Osman; Makowski, ArmandRandom key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the appearance of triangles, and identify the corresponding critical scaling. This is done by applying the method of first and second moments to the number of triangles in the graph.Item Zero-one laws for connectivity in random key graphs(2009-01-14) Yagan, Osman; Makowski, Armand;The random key graph is a random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We report on recent results concerning a conjectured zero-one law for graph connectivity.