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We study the maximum information gain that an adversary may obtain throughhacking without being detected. Consider a dynamical process observed by asensor that transmits a local estimate of the system state to a remoteestimator according to some reference transmission policy across apacket-dropping wireless channel equipped with acknowledgments (ACK). Anadversary overhears the transmissions and proactively hijacks the sensor toreprogram its transmission policy. We define perfect secrecy as keeping theaveraged expected error covariance bounded at the legitimate estimator andunbounded at the adversary. By analyzing the stationary distribution of theexpected error covariance, we show that perfect secrecy can be attained forunstable systems only if the ACK channel has no packet dropouts. In othersituations, we prove that independent of the reference policy and the detectionmethods, perfect secrecy is not attainable. For this scenario, we formulate aconstrained Markov decision process to derive the optimal transmission policythat the adversary should implement at the sensor, and devise a Stackelberggame to derive the optimal reference policy for the legitimate estimator.

Stealthy hacking and secrecy of controlled state estimation systems with random dropouts