On the random graph induced by a random key predistribution scheme under full visibility

Yağan, Osman; Makowski, Armand M.

doi:10.1109/isit.2008.4595045

Cited by 22 publications

(21 citation statements)

References 16 publications

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“…sufficiently large, and the random key graph does not degenerate into a complete graph under a strongly admissible scaling. Finally, in Lemma 7.3 we show that (22) suffices to imply…”

Section: A Roadmap For the Proof Of Theorem 41mentioning

confidence: 76%

Zero–One Laws for Connectivity in Random Key Graphs

Yağan

Makowski

2012

IEEE Trans. Inform. Theory

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132

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The random key graph is a random graph naturally associated with the random key predistribution scheme introduced by Eschenauer and Gligor in the context of wireless sensor networks. For this class of random graphs we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large. The results reported here complement and strengthen recent work on this conjecture by Blackburn and Gerke. In particular, the results are given under conditions which are more realistic for applications to wireless sensor networks.

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“…sufficiently large, and the random key graph does not degenerate into a complete graph under a strongly admissible scaling. Finally, in Lemma 7.3 we show that (22) suffices to imply…”

Section: A Roadmap For the Proof Of Theorem 41mentioning

confidence: 76%

Zero–One Laws for Connectivity in Random Key Graphs

Yağan

Makowski

2012

IEEE Trans. Inform. Theory

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132

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“…When c > 1, we have lim n→∞ γ n = ∞ and Theorem III.1 gives the one-law (16), hence the one-law part of (23) holds. On the other hand, with 0 < c < 1, lim n→∞ γ n = −∞ and Theorem III.3 yields the zero-law (18), hence the zero-law part of (23), if the additional conditions (20) or (21) hold. We now show that this additional condition is superfluous for the zero-law to hold; this is a consequence of the Principle of Subsubsequences [9] -In what follows a subsequence k → n k is simply any non-decreasing mapping N 0 → N 0 : k → n k such that lim k→∞ n k = ∞:…”

Section: The Main Resultsmentioning

confidence: 99%

On the Eschenauer-Gligor key predistribution scheme under on-off communication channels: The absence of isolated nodes

Makowski

Yağan

2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key graph and an Erdős-Rényi (ER) graph. For this class of composite random graphs we give various improvements on a recent result by Yagan [17] concerning zero-one laws for the absence of isolated nodes.

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“…In [Liu and Ning 2003], the authors improve on the work in [Eschenauer and Gligor 2002] by taking advantage of node location information to improve key connectivity. Critical thresholds on connectivity of the random Deployment Aware Node Compromise Spread · 27 graph induced by the random key predistribution scheme are investigated by the authors in [Yagan and Makowski 2008]. In [Du et al 2004], the authors discuss a key management scheme based on node deployment knowledge.…”

Section: Related Workmentioning

confidence: 99%

Deployment-aware modeling of node compromise spread in wireless sensor networks using epidemic theory

Liu

Das

2009

ACM Trans. Sen. Netw.

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Motivated by recently surfacing viruses that can spread over the air interfaces, in this article, we investigate the potentially disastrous threat of node compromise spreading in wireless sensor networks. We assume such a compromise originating from a single infected node, can propagate to other sensor nodes via communication and pre-established mutual trust. We focus on the possible epidemic breakout of such propagations where the whole network may fall victim to the attack. Using epidemic theory, we model and analyze this spreading process and identify key factors determining potential outbreaks. In particular, we perform our study on random graphs precisely constructed according to the parameters of the network, such as distance, key sharing constrained communication and node recovery, thereby reflecting the true characteristics therein. Moreover, a comparative study of the epidemic propagation is performed based on the effects of two types of sensor deployment strategies, viz., uniform random and group-based deployment. The analytical results provide deep insights in designing potential defense strategies against this threat. Furthermore, through extensive simulations, we validate the model and perform investigations on the system dynamics. Our analysis and simulation results indicate that the uniform random deployment is more vulnerable to an epidemic outbreak than the group based deployment strategy.

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On the random graph induced by a random key predistribution scheme under full visibility

Cited by 22 publications

References 16 publications

Zero–One Laws for Connectivity in Random Key Graphs

Zero–One Laws for Connectivity in Random Key Graphs

On the Eschenauer-Gligor key predistribution scheme under on-off communication channels: The absence of isolated nodes

Deployment-aware modeling of node compromise spread in wireless sensor networks using epidemic theory

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