Percolation and Connectivity in the Intrinsically Secure Communications Graph

• Main Authors: Pinto, Pedro C. (Contributor), Win, Moe Z. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Laboratory for Information and Decision Systems (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2013-09-24T18:25:52Z.
• Subjects: Article
• Online Access: Get fulltext

 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.