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We consider privacy amplification against quantum side information by usingregular random binning as an effective extractor. For constant-type sources, weobtain error exponent and strong converse bounds in terms of the so-calledquantum Augustin information. Via type decomposition, we then recover the errorexponent for independent and identically distributed sources proved by Dupuis[arXiv:2105.05342]. As an application, we obtain an achievable secrecy exponentfor classical-quantum wiretap channel coding in terms of the Augustininformation, which solves an open problem in [IEEE Trans.~Inf.~Theory,65(12):7985, 2019]. Our approach is to establish an operational equivalencebetween privacy amplification and quantum soft covering; this may be ofindependent interest.

Privacy Amplification Against Quantum Side Information Via Regular Random Binning