Under the radar attacks in dynamical systems: Adversarial privacy utility tradeoffs

Cyber physical systems which integrate physical system dynamics with digital cyber infrastructure are envisioned to transform our core infrastructural frameworks such as the smart electricity grid, transportation networks and advanced manufacturing. This integration however exposes the physical system functioning to the security vulnerabilities of cyber communication. Both scientific studies and real world examples have demonstrated the impact of data injection attacks on state estimation mechanisms on the smart electricity grid. In this work, an abstract theoretical framework is proposed to study data injection/modification attacks on Markov modeled dynamical systems from the perspective of an adversary. Typical data injection attacks focus on one shot attacks by adversary and the non-detectability of such attacks under static assumptions. In this work we study dynamic data injection attacks where the adversary is capable of modifying a temporal sequence of data and the physical controller is equipped with prior statistical knowledge about the data arrival process to detect the presence of an adversary. The goal of the adversary is to modify the arrivals to minimize a utility function of the controller while minimizing the detectability of his presence as measured by the KL divergence between the prior and posterior distribution of the arriving data. Adversarial policies and tradeoffs between utility and detectability are characterized analytically using linearly solvable control optimization.