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Percolation and Connectivity in the Intrinsically Secure Communications Graph

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2 Author(s)
Pinto, P.C. ; Lab. for Inf. & Decision Syst., Massachusetts Inst. of Technol., Cambridge, MA, USA ; Win, M.Z.

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper aims to characterize the global properties of the iS-graph in terms of (1) percolation on the infinite plane, and (2) full connectivity on a finite region. First, for the Poisson iS-graph defined on the infinite plane, the existence of a phase transition is proven, whereby an unbounded component of connected nodes suddenly arises as the density of legitimate nodes is increased. This shows that long-range secure communication is still possible in the presence of eavesdroppers. Second, full connectivity on a finite region of the Poisson iS-graph is considered. The exact asymptotic behavior of full connectivity in the limit of a large density of legitimate nodes is characterized. Then, simple, explicit expressions are derived in order to closely approximate the probability of full connectivity for a finite density of legitimate nodes. These results help clarify how the presence of eavesdroppers can compromise long-range secure communication.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 3 )