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|a Pinto, Pedro C.
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|a Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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|a Pinto, Pedro C.
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|a Win, Moe Z.
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|a Win, Moe Z.
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|a Percolation and Connectivity in the Intrinsically Secure Communications Graph
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|b Institute of Electrical and Electronics Engineers (IEEE),
|c 2013-09-24T18:25:52Z.
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|u http://hdl.handle.net/1721.1/80910
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|a 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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|a Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies
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|a United States. Office of Naval Research (Presidential Early Career Award for Scientists and Engineers N00014-09-1-0435)
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|a National Science Foundation (U.S.) (Grant ECS-0636519)
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|a Article
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|t IEEE Transactions on Information Theory
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