  We define the common randomness assisted capacity of an arbitrarily varying
channel (AVWC) when the Eavesdropper is kept ignorant about the common
randomness. We prove a multi-letter capacity formula for this model. We prove
that, if enough common randomness is used, the capacity formula can be given a
single-shot form again. We then consider the opposite extremal case, where no
common randomness is available. It is known that the capacity of the system can
be discontinuous under these circumstances. We prove here that it is still
stable in the sense that it is continuous around its positivity points. We
further prove that discontinuities can only arise if the legal link is
symmetrizable and characterize the points where it is positive. These results
shed new light on the design principles of communication systems with embedded
security features. At last we investigate the effect of super-activation of the
message transmission capacity of AVWCs under the average error criterion. We
give a complete characterization of those AVWCs that may be super-activated.
The effect is thereby also related to the (conjectured) super-activation of the
common randomness assisted capacity of AVWCs with an eavesdropper that gets to
know the common randomness. Super-activation is based on the idea of "wasting"
a few bits of non-secret messages in order to enable provably secret
transmission of a large bulk of data, a concept that may prove to be of further
importance in the design of communication systems. In this work we provide
further insight into this phenomenon by providing a class of codes that is
capacity-achieving and does not convey any information to the Eavesdropper.
