Private Message Transmission Using Disjoint Paths Hadi Ahmadi ⋆ and Reihaneh Safavi-Naini Department of Computer Science, University of Calgary, Canada ⋆⋆ {hahmadi,rei}@ucalgary.ca Abstract. 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 un- bounded. There is a total of n communicating paths, but not all may be simultaneously accessible to the parties. We let ta, t b , and te denote the number of paths that are accessible to Alice, Bob and Eve respec- tively. 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 mes- sage 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 re- sults show AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, AP-PMT may be possible even in poor con- ditions where ta = t b = 1 and te = 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 mes- sage transmission at rates 17% and 20% for the two example scenarios, respectively. We discuss open question and future work. 1 Introduction With the rapid growth of online communication, an increasing number of daily activities are moved to the online world and fall under prying eyes resulting in increasing loss of privacy. Personal data can be under surveillance by various entities. Hackers easily tap into WiFi connections to steal online communication data [9]. There are reported news on security agencies watching civilian com- munications through routers in the Internet [8]. Given massive computational resources accessible to the adversaries, na¨ ıve usage of traditional cryptographic ⋆ The author has moved to Nulli Identity Solution Inc., Canada (hahmadi@nulli.com). ⋆⋆ This work is in part supported by Alberta Innovates Technology Futures. I. Boureanu, P. Owesarski, and S. Vaudenay (Eds.): ACNS 2014, LNCS 8479, pp. 116–133, 2014. c  Springer International Publishing Switzerland 2014