  In this paper we present methods for attacking and defending $k$-gram
statistical analysis techniques that are used, for example, in network traffic
analysis and covert channel detection. The main new result is our demonstration
of how to use a behavior's or process' $k$-order statistics to build a
stochastic process that has those same $k$-order stationary statistics but
possesses different, deliberately designed, $(k+1)$-order statistics if
desired. Such a model realizes a "complexification" of the process or behavior
which a defender can use to monitor whether an attacker is shaping the
behavior. By deliberately introducing designed $(k+1)$-order behaviors, the
defender can check to see if those behaviors are present in the data. We also
develop constructs for source codes that respect the $k$-order statistics of a
process while encoding covert information. One fundamental consequence of these
results is that certain types of behavior analyses techniques come down to an
{\em arms race} in the sense that the advantage goes to the party that has more
computing resources applied to the problem.

Machine Learning