Private Message Transmission Using Disjoint Paths
We consider private message transmission (PMT) between two communicants, Alice and Bob, in the presence of an eavesdropper, Eve. Alice and Bob have no shared keys and Eve is computationally unbounded. There is a total of n communicating paths, but not all may be simultaneously accessible to the parties. We let t a , t b , and t e denote the number of paths that are accessible to Alice, Bob and Eve respectively. We allow the parties to change their accessed paths at certain points in time during the PMT protocol. We study perfect (P)-PMT protocol families that guarantee absolute privacy and reliability of message transmission. For the sake of transmission rate improvement, we also investigate asymptotically-perfect (AP)-PMT protocol families that provide negligible error and leakage and behave the same as P-PMT families when message length tends to infinity.
We derive the necessary and sufficient conditions under which P-PMT and AP-PMT are possible and introduce explicit PMT schemes. Our results show AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, AP-PMT may be possible even in poor conditions where t a = t b = 1 and t e = n − 1. We study applications of our results to private communication over the real-life scenarios of multiple-frequency links and multiple-route networks. We show practical examples of such scenarios that can be abstracted by the multipath setting: Our results prove the possibility of keyless information-theoretic private message transmission at rates 17% and 20% for the two example scenarios, respectively. We discuss open question and future work.
KeywordsDisjoint Path Message Transmission Secret Sharing Scheme Connectivity Condition Message Length
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