  An arbitrarily varying wiretap channel (AVWTC) with a type constraint on the
allowed state sequences is considered, and a single-letter characterization of
its correlated-random (CR) assisted semantic-security (SS) capacity is derived.
The allowed state sequences are the ones in a typical set around a single
constraining type. SS is established by showing that the mutual information
between the message and the eavesdropper's observations is negligible even when
maximized over all message distributions, choices of state sequences and
realizations of the CR-code. Both the achievability and the converse proofs of
the type constrained coding theorem rely on stronger claims than actually
required. The direct part establishes a novel single-letter lower bound on the
CR-assisted SS-capacity of an AVWTC with state sequences constrained by any
convex and closed set of state probability mass functions. This bound achieves
the best known single-letter secrecy rates for a corresponding compound wiretap
channel over the same constraint set. In contrast to other single-letter
results in the AVWTC literature, this work does not assume the existence of a
best channel to the eavesdropper. Instead, SS follows by leveraging the
heterogeneous version of the stronger soft-covering lemma and a CR-code
reduction argument. Optimality is a consequence of an max-inf upper bound on
the CR-assisted SS-capacity of an AVWTC with state sequences constrained to any
collection of type-classes. When adjusted to the aforementioned compound WTC,
the upper bound simplifies to a max-min structure, thus strengthening the
previously best known single-letter upper bound by Liang et al. that has a
min-max form. The proof of the upper bound uses a novel distribution coupling
argument.
