On the Continuity of the Secrecy Capacity of Compound and Arbitrarily Varying Wiretap Channels

摘要

The wiretap channel models secure communication between two users in thepresence of an eavesdropper who must be kept ignorant of transmitted messages.The performance of such a system is usually characterized by its secrecycapacity which determines the maximum transmission rate of securecommunication. In this paper, the issue of whether or not the secrecy capacityis a continuous function of the system parameters is examined. In particular,this is done for channel uncertainty modeled via compound channels andarbitrarily varying channels, in which the legitimate users know only that thetrue channel realization is from a pre-specified uncertainty set. In the formermodel, this realization remains constant for the entire duration oftransmission, while in the latter the realization varies from channel use tochannel use in an unknown and arbitrary manner. These models not only capturethe case of channel uncertainty, but are also suitable for modeling scenariosin which a malicious adversary jams or otherwise influence the legitimatetransmission. The secrecy capacity of the compound wiretap channel is shown tobe robust in the sense that it is a continuous function of the uncertainty set.Thus, small variations in the uncertainty set lead to small variations insecrecy capacity. On the other hand, the deterministic secrecy capacity of the\emph{arbitrarily varying wiretap channel} is shown to be discontinuous in theuncertainty set meaning that small variations can lead to dramatic losses incapacity.