This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given block length. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second order coding rate for discrete memory less and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal trade off between reliability and secrecy in the finite block length regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.
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