On random graphs associated with a pairwise key distribution scheme for wireless sensor networks (Extended version) (original) (raw)
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2014 IEEE International Symposium on Information Theory, 2014
To be considered for an IEEE Jack Keil Wolf ISIT Student Paper Award. We study the secure and reliable connectivity of wireless sensor networks. Security is assumed to be ensured by the random pairwise key predistribution scheme of Chan, Perrig, and Song, and unreliable wireless links are represented by independent on/off channels. Modeling the network by an intersection of a random K-out graph and an Erdős-Rényi graph, we present scaling conditions (on the number of nodes, the scheme parameter K, and the probability of a wireless channel being on) such that the resulting graph contains no nodes with degree less than k with high probability, when the number of nodes gets large. Results are given in the form of zero-one laws and are shown to improve the previous results by Yagan and Makowski on the absence of isolated nodes (i.e., absence of nodes with degree zero). Via simulations, the established zero-one laws are shown to hold also for the property of k-connectivity; i.e., the property that graph remains connected despite the deletion of any k − 1 nodes or edges.
Connectivity results for sensor networks under a random pairwise key predistribution scheme
2012
We investigate the connectivity of wireless sensor networks under the random pairwise key predistribution scheme of Chan et al. Under the assumption of full visibility, this reduces to studying connectivity in the socalled random K-out graph H(n; K); here n is the number of nodes and K < n is an integer parameter affecting the number of keys stored at each node. We show that if K ≥ 2 (resp. K = 1), the probability that H(n; K) is a connected graph approaches 1 (resp. 0) as n goes to infinity. This is done by establishing an explicitly computable lower bound on the probability of connectivity. From this bound we conclude that with K ≥ 2, the connectivity of the network can already be guaranteed by a relatively small number of sensors with very high probability. This corrects an earlier analysis based on a heuristic transfer of classical connectivity results for Erdős-Rényi graphs.
On the Connectivity of Sensor Networks Under Random Pairwise Key Predistribution
IEEE Transactions on Information Theory, 2013
We investigate the connectivity of wireless sensor networks under the random pairwise key predistribution scheme of Chan et al. Under the assumption of full visibility, this reduces to studying the connectivity in the so-called random-out graph ; here, is the number of nodes and is an integer parameter affecting the number of keys stored at each node. We show that if (respectively,), the probability that is a connected graph approaches 1 (respectively, 0) as goes to infinity. For the one-law this is done by establishing an explicitly computable lower bound on the probability of connectivity. Using this bound, we see that with high probability, network connectivity can already be guaranteed (with) by a relatively small number of sensors. This corrects earlier predictions made on the basis of a heuristic transfer of connectivity results available for Erdős-Rényi graphs.
Designing secure and reliable wireless sensor networks under a pairwise key predistribution scheme
2015 IEEE International Conference on Communications (ICC), 2015
We investigate k-connectivity in secure wireless sensor networks under the random pairwise key predistribution scheme with unreliable links; a network is said to be k-connected if it remains connected despite the failure of any of its (k−1) nodes or links. With wireless communication links modeled as independent on-off channels, this amounts to analyzing a random graph model formed by intersecting a random K-out graph and an Erdős-Rényi graph. We present conditions on how to scale the parameters of this intersection model so that the resulting graph is k-connected with probability approaching to one (resp. zero) as the number of nodes gets large. The resulting zero-one law is shown to improve and sharpen the previous result on the 1-connectivity of the same model. We also provide numerical results to support our analysis and show that even in the finite node regime, our results can provide useful guidelines for designing sensor networks that are secure and reliable.
Connected Component in Secure Sensor NetworkInduced by a Random Key Pre-Distribution Scheme
International Journal of Machine Learning and Computing, 2011
Wireless sensor network (WSN) has a wide range of applications in various areas. Many time the environment in which these sensor were deployed are hostile in nature and sensors have continuous attacks from the adversary, in such environmental conditions we need a secure communication between the sensors. For secure communication, neighbors must posses a secret common key or there must exists a key-path among these nodes. In this paper, the object of study is a random graph induced by the random key pre-distribution scheme of Eschenauer and Gligor under the assumption of full visibility. Here we establish the threshold value of the parameters (Key pool size and key-ring of an individual node) for which the entire network is almost surely a single connected component. We prove that for a network having N nodes, is a single connected component almost surely, if size of the key-ring is m = √ 2 log N and the size of key pool is K = N log N.
Lecture Notes in Computer Science, 2010
We study the applicability of random graph theory in modeling secure connectivity of wireless sensor networks. Specifically, our work focuses on the highly influential random key predistribution scheme by Eschenauer and Gligor to examine the appropriateness of the modeling in finding system parameters for desired connectivity. We use extensive simulation and theoretical results to identify ranges of the parameters where i) random graph theory is not applicable, ii) random graph theory may lead to estimates with excessive errors, and iii) random graph theory gives very accurate results. We also investigate the similarities and dissimilarities in the structure of random graphs and key graphs (i.e., graphs describing key sharing information between sensor nodes). Our results provide insights into research relying on random graph modeling to examine behaviors of key graphs.
On the Connectivity of Key-Distribution Strategies in Wireless Sensor Networks
GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009
Wireless sensor networks (WSNs) are usually missioned to gather critical information in hostile and adversarial environments, which make them susceptible to compromise and revelation. Therefore, establishing secure communication in such networks is of great importance necessitating utilization of efficient key distribution schemes. In order to address such methods, several works using probabilistic, deterministic and hybrid approaches have been introduced in past few years. In this paper, we study the connectivity of key-distribution mechanisms in secured topologies of wireless sensor networks. We explore the effect of the radio range on the connectivity of the network and provide a lower bound on the radio range under which the cover time of the underlying topology decreases significantly. We also deduce that any broadcasting algorithm in such a network is performing only by a factor O(n β), where β ∈ (0, 1), worse than broadcasting algorithms in unsecured topologies. Our numerical results and simulation experiments validates the correctness and efficiency of our analysis.
A Combinatorial Approach for Key-Distribution in Wireless Sensor Networks
IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference, 2008
Sensor nodes are usually deployed in adversarial environments in which they are subject to compromise and revelation of critical information rendering the entire network useless. Therefore, secure communication of wireless sensor networks (WSNs) necessitates utilization of efficient key distribution schemes. Over the past few years, several works using probabilistic, deterministic and hybrid methods have been conducted to address key distribution among sensor nodes. In this paper we propose a novel method to deterministically distribute key-chains throughout a WSN utilizing expander graphs based on the ZigZag graph product. Given a set of constraints such as network size, amount of storage, radio range and key-chain length, we are able to efficiently construct a resilient yet scalable key distribution graph. The main advantage of the obtained method is providing a more user-adjustable and predictable framework compared to the previously proposed approaches. Simulation results demonstrate the efficiency of our proposed scheme and its general applicability to different network paradigms with diverse requirements.
IEEE ACM Transactions on Networking, 2016
We investigate the resiliency of wireless sensor networks against sensor capture attacks when the network uses the random pairwise key distribution scheme of Chan, Perrig and Song [3]. We present conditions on the model parameters so that the network is (i) unassailable, and (ii) unsplittable, both with high probability, as the number n of sensor nodes becomes large. Both notions are defined against an adversary who has unlimited computing resources and full knowledge of the network topology, but can only capture a negligible fraction o(n) of sensors. We also show that the number of cryptographic keys needed to ensure unassailability and unsplittability under the pairwise key predistribution scheme is an order of magnitude smaller than it is under the key predistribution scheme of Eschenauer and Gligor.