Multipath Private Communication: An Information Theoretic Approach

Abstract: Sending private messages over communication environments under surveillance is an important challenge in communication security and has attracted attentions of cryptographers through time. We believe that resources other than cryptographic keys can be used for communication privacy. We consider private message transmission (PMT) in an abstract multipath communication model between two communicants, Alice and Bob, in the presence of an eavesdropper, Eve. Alice and Bob have pre-shared keys and Eve is computationally unbounded. There are a total of $n$ paths and the three parties can have simultaneous access to at most $t_a$, $t_b$, and $t_e$ paths. The parties can switch their paths after every $\lambda$ bits of communication. We study perfect (P)-PMT versus asymptotically-perfect (AP)-PMT protocols. The former has zero tolerance of transmission error and leakage, whereas the latter allows for positive error and leakage that tend to zero as the message length increases. We derive the necessary and sufficient conditions under which P-PMT and AP-PMT are possible. We also introduce explicit P-PMT and AP-PMT constructions. Our results show AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, AP-PMT is possible even in poorest condition where $t_a=t_b=1$ and $t_e=n-1$. 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 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 problems and future work at the end.