Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#235999] of Robert Calderbank

Papers Published

  1. Goel, S; Aggarwal, V; Yener, A; Calderbank, AR, The effect of eavesdroppers on network connectivity: A secrecy graph approach, IEEE Transactions on Information Forensics and Security, vol. 6 no. 3 PART 1 (2011), pp. 712-724, ISSN 1556-6013 [doi]
    (last updated on 2018/10/23)

    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. © 2011 IEEE.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320