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 behaviors 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.
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