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Abstract: The ability to exchange secret information is critical to many commercial,governmental, and military networks. The intrinsically secure communicationsgraph iS-graph is a random graph which describes the connections that can besecurely established over a large-scale network, by exploiting the physicalproperties of the wireless medium. This paper aims to characterize the globalproperties of the iS-graph in terms of: i percolation on the infinite plane,and ii full connectivity on a finite region. First, for the Poisson iS-graphdefined on the infinite plane, the existence of a phase transition is proven,whereby an unbounded component of connected nodes suddenly arises as thedensity of legitimate nodes is increased. This shows that long-range securecommunication is still possible in the presence of eavesdroppers. Second, fullconnectivity on a finite region of the Poisson iS-graph is considered. Theexact asymptotic behavior of full connectivity in the limit of a large densityof legitimate nodes is characterized. Then, simple, explicit expressions arederived in order to closely approximate the probability of full connectivityfor a finite density of legitimate nodes. The results help clarify how thepresence of eavesdroppers can compromise long-range secure communication.



Author: Pedro C. Pinto, Moe Z. Win

Source: https://arxiv.org/







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