Reliability and secrecy functions of the wiretap channel under cost constraint

Abstract

The wiretap channel has been devised and studied first by Wyner, and subsequently extended to the case with nondegraded general wiretap channels by Csiszár and Körner. Focusing mainly on the stationary memoryless channel with cost constraint, we newly introduce the notion of reliability and secrecy functions as a fundamental tool to analyze and/or design the performance of an efficient wiretap channel system, including binary symmetric wiretap channels, Poisson wiretap channels, and Gaussian wiretap channels. Compact formulas for those functions are explicitly given for stationary memoryless wiretap channels. It is also demonstrated that, based on such a pair of reliability and secrecy functions, we can control the tradeoff between reliability and secrecy (usually conflicting), both with exponentially decreasing rates as block length n becomes large. Four ways to do so are given on the basis of rate shifting, rate exchange, concatenation, and change of cost constraint. In addition, the notion of the δ secrecy capacity is defined and shown to attain the strongest secrecy standard among others. The maximized versus averaged secrecy measures is also discussed.