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Information theoretic secrecy is combined with cryptographic secrecy to create a secret-key exchange protocol for wireless networks. A network of transmitters, which already have cryptographically secured channels between them, cooperate to exchange a secret key with a new receiver at a random location, in the presence of passive eavesdroppers at unknown locations. Two spatial point processes: homogeneous Poisson process and independent uniformly distributed points are used for the spatial distributions of transmitters and eavesdroppers. The authors analyze the impact of the number of cooperating transmitters and the number of eavesdroppers on the area fraction where secure communication is possible. Upper bounds on the probability of existence of positive secrecy between the cooperating transmitters and the receiver are derived.
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