The MAC Resolvability Region, Semantic Security and Its Operational Implications

Building upon previous work on the relation between secrecy and channel resolvability, we revisit a secrecy proof for the multiple-access channel (MAC) from the perspective of resolvability. In particular, we refine and extend the proof to obtain novel results on the second-order achievable rates. Then we characterize the resolvability region of the memoryless MAC by establishing a conceptually simple converse proof for resolvability that relies on the uniform continuity of Shannon's entropy with respect to the variational distance. We discuss the operational meaning of the information theoretic concept of semantic security from the viewpoint of Ahlswede's General Theory of Information Transfer and show interesting implications on the resilience against a large class of attacks even if no assumption can be made about the distributions of the transmitted messages. Finally we provide details on how the resolvability results can be used to construct a wiretap code that achieves semantic security.
Comment: Substantially extended version of arXiv:1707.04156 v2: Restructured and in part rephrased to improve readability, removed typos, added some details and figures