Progressively intricate cyber infiltration mechanisms have made conventional means of defense, such as firewalls and malware detectors, incompetent. These sophisticated infiltration mechanisms can study the defenders behavior, identify security caveats, and modify their actions adaptively. To tackle these security challenges, cyber-infrastructures require active defense techniques that incorporate cyber deception, in which the defender (deceiver) implements a strategy to mislead the infiltrator. To this end, we use a two-player partially observable stochastic game (POSG) framework, wherein the deceiver has full observability over the states of the POSG, and the infiltrator has partial observability. Then, the deception problem is to compute a strategy for the deceiver that minimizes the expected cost of deception against all strategies of the infiltrator. We first show that the underlying problem is a robust mixed-integer linear program, which is intractable to solve in general. Towards a scalable approach, we compute optimal finite-memory strategies for the infiltrator by a reduction to a series of synthesis problems for parametric Markov decision processes. We use these infiltration strategies to find robust strategies for the deceiver using mixed-integer linear programming. We illustrate the performance of our technique on a POSG model for network security. Our experiments demonstrate that the proposed approach handles scenarios considerably larger than those of the state-of-the-art methods.
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