  Since 2009, Moving Target Defense (MTD) has become a new paradigm of
defensive mechanism that frequently changes the state of the target system to
confuse the attacker. This frequent change is costly and leads to a trade-off
between misleading the attacker and disrupting the quality of service.
Optimizing the MTD activation frequency is necessary to develop this defense
mechanism when facing realistic, multi-step attack scenarios. Attack modeling
formalisms based on DAG are prominently used to specify these scenarios. Our
contribution is a new DAG-based formalism for MTDs and its translation into a
Price Timed Markov Decision Process to find the best activation frequencies
against the attacker's time/cost-optimal strategies. For the first time, MTD
activation frequencies are analyzed in a state-of-the-art DAG-based
representation. Moreover, this is the first paper that considers the
specificity of MTDs in the automatic analysis of attack modeling formalisms.
Finally, we present some experimental results using Uppaal Stratego to
demonstrate its applicability and relevance.
