  The wiretap channel has been devised and studied first by Wyner, and
subsequently extended to the case with non-degraded general wiretap channels by
Csiszar and Korner. Focusing mainly on the Poisson wiretap channel with cost
constraint, we newly introduce the notion of reliability and security functions
as a fundamental tool to analyze and/or design the performance of an efficient
wiretap channel system. Compact formulae for those functions are explicitly
given for stationary memoryless wiretap channels. It is also demonstrated that,
based on such a pair of reliability and security functions, we can control the
tradeoff between reliability and security (usually conflicting), both with
exponentially decreasing rates as block length n becomes large. Two ways to do
so are given on the basis of concatenation and rate exchange. In this
framework, the notion of the {\delta} secrecy capacity is defined and shown to
attain the strongest security standard among others. The maximized vs. averaged
security measures is also discussed.
