Multipath Private Communication: An Information Theoretic Approach

Sending private messages over communication environments under surveillance is a very important challenge in communication security and has attracted a lot of attention from cryptographers through time. We believe that resources other than cryptographic keys can be used to provide communication privacy. We consider private message transmission (PMT) in an abstract multipath communication setting between two communicants, Alice and Bob, in the presence of a third-party eavesdropper, Eve. Alice and Bob have no a priori shared keys and furthermore, Eve is computationally unbounded. There are a total of n paths, and the three parties can have simultaneous access to at most ta, tb, and te paths. The parties can reselect their accessed paths after every λ bits of communication over a path. We study two types of perfect (P)-PMT and asymptotically-perfect (AP)-PMT protocols. The former has zero tolerance of transmission error and leakage, whereas the latter allows for positive error and leakage, which tend to zero as the message length increases. We derive the necessary and sufficient conditions (based on the above parameters) under which P-PMT and AP-PMT are possible. We also introduce explicit P-PMT and APPMT protocol constructions. Our results show that AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, Alice and Bob can achieve AP-PMT even in unfortunate conditions that they have the least connectivity (ta = tb = 1) and Eve may access all but one paths (te = n − 1). It remains however an open question whether the derived rates can be improved by more sophisticated AP-PMT protocols. We study applications of our results to private communication over the real-life scenarios of multiplefrequency 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 problems and future work at the end.