  Secure communication in a potentially malicious environment becomes more and
more important. The arbitrarily varying wiretap channel (AVWC) provides
information theoretical bounds on how much information can be exchanged even in
the presence of an active attacker. If the active attacker has non-causal side
information, situations in which a legitimate communication system has been
hacked, can be modeled. We investigate the AVWC with non-causal side
information at the jammer for the case that there exists a best channel to the
eavesdropper. Non-causal side information means that the transmitted codeword
is known to an active adversary before it is transmitted. By considering the
maximum error criterion, we allow also messages to be known at the jammer
before the corresponding codeword is transmitted. A single letter formula for
the common randomness secrecy capacity is derived. Additionally, we provide a
single letter formula for the common randomness secrecy capacity, for the cases
that the channel to the eavesdropper is strongly degraded, strongly noisier, or
strongly less capable with respect to the main channel. Furthermore, we compare
our results to the random code secrecy capacity for the cases of maximum error
criterion but without non-causal side information at the jammer, maximum error
criterion with non-causal side information of the messages at the jammer, and
the case of average error criterion without non-causal side information at the
jammer.
