Secrecy capacity of the wiretap channel with noisy feedback

In this work, the role of noisy feedback In enhancing the secrecy capacity of the wiretap channel Is Investigated A model Is considered In which the feed-forward and feedback signals share the same noisy channel. More specifically, a discrete memoryless modulo - Additive channel with a full-duplex destina-tion node is considered first, and it is shown that a judicious use of feedback increases the perfect secrecy capacity to the capacity of the source-destination channel in the absence of the wiretappeR. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. Then a half-duplex system is considered, for which a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) Is proposed. These results hinge on the modulo - Additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source.