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