TY - JOUR

T1 - The effect of eavesdroppers on network connectivity

T2 - A secrecy graph approach

AU - Goel, Satashu

AU - Aggarwal, Vaneet

AU - Yener, Aylin

AU - Calderbank, A. Robert

N1 - Funding Information:
Manuscript received September 15, 2010; revised January 25, 2011; accepted April 11, 2011. Date of publication May 02, 2011; date of current version August 17, 2011. A preliminary version of part of this work was presented at the IEEE International Symposium on Information Theory, Austin, TX, Jun. 2010. The work of S. Goel and A. Yener was supported in part by the National Science Foundation under Grant CNS-0716325 and Grant CCF-0964362, and by the DARPA ITMANET program under Grant W911NF-07-11-0028. The work of V. Aggarwal and A. R. Calderbank was supported in part by the NSF under Grant DMS 0701226, by the ONR under Grant N00173-06-1-G006, and by the AFOSR under Grant FA 9550-09-1-0643. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Wade Trappe.

PY - 2011/9

Y1 - 2011/9

N2 - This paper investigates the effect of eavesdroppers on network connectivity, using a wiretap model and percolation theory. The wiretap model captures the effect of eavesdroppers on link security. A link exists between two nodes only if the secrecy capacity of that link is positive. Network connectivity is defined in a percolation sense, i.e., connectivity exists if an infinite connected component exists in the corresponding secrecy graph. We consider uncertainty in location of eavesdroppers, which is modeled directly at the network level as correlated failures in the secrecy graph. Our approach attempts to bridge the gap between physical layer security under uncertain channel state information and network level connectivity under secrecy constraints. For square and triangular lattice secrecy graphs, we obtain bounds on the percolation threshold, which is the critical value of the probability of occurrence of an eavesdropper, above which network connectivity does not exist. For Poisson secrecy graphs, degree distribution and mean value of upper and lower bounds on node degree are obtained. Further, inner and outer bounds on the achievable region for network connectivity are obtained. Both analytic and simulation results show that uncertainty in location of eavesdroppers has a dramatic effect on network connectivity in a secrecy graph.

AB - This paper investigates the effect of eavesdroppers on network connectivity, using a wiretap model and percolation theory. The wiretap model captures the effect of eavesdroppers on link security. A link exists between two nodes only if the secrecy capacity of that link is positive. Network connectivity is defined in a percolation sense, i.e., connectivity exists if an infinite connected component exists in the corresponding secrecy graph. We consider uncertainty in location of eavesdroppers, which is modeled directly at the network level as correlated failures in the secrecy graph. Our approach attempts to bridge the gap between physical layer security under uncertain channel state information and network level connectivity under secrecy constraints. For square and triangular lattice secrecy graphs, we obtain bounds on the percolation threshold, which is the critical value of the probability of occurrence of an eavesdropper, above which network connectivity does not exist. For Poisson secrecy graphs, degree distribution and mean value of upper and lower bounds on node degree are obtained. Further, inner and outer bounds on the achievable region for network connectivity are obtained. Both analytic and simulation results show that uncertainty in location of eavesdroppers has a dramatic effect on network connectivity in a secrecy graph.

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U2 - 10.1109/TIFS.2011.2148714

DO - 10.1109/TIFS.2011.2148714

M3 - Article

AN - SCOPUS:80051749394

VL - 6

SP - 712

EP - 724

JO - IEEE Transactions on Information Forensics and Security

JF - IEEE Transactions on Information Forensics and Security

SN - 1556-6013

IS - 3 PART 1

M1 - 5759739

ER -