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. We then refine the approach in order to obtain some novel results on the second-order achievable rates. Establishing a conceptually simple converse proof for resolvability over the memoryless MAC, which relies on uniform continuity of Shannon’s entropy with respect to the variational distance, we characterize the resolvability region. In a discussion of the operational meaning of the information theoretic concept of semantic security from the point of view of Ahlswede’s General Theory of Information Transfer, we show some interesting implications on the resilience against a wide-ranging class of attacks even if no assumption can be made about the distributions of the transmitted messages. We then give details on how the resolvability results can be used to construct a wiretap code that achieves semantic security.