  Several non-asymptotic formulas are established in channel resolvability and
identification capacity, and they are applied to wire-tap channel. By using
these formulas, the $\epsilon$ capacities of the above three problems are
considered in the most general setting, where no structural assumptions such as
the stationary memoryless property are made on a channel. As a result, we solve
an open problem proposed in Han & Verdu and Han. Moreover, we obtain lower
bounds of the exponents of error probability and the wire-tapper's information
in wire-tap channel.
