Towards a formal notion of impact metric for cyber-physical attacks

Industrial facilities and critical infrastructures are transforming into \u201csmart\u201d environments that dynamically adapt to external events. The result is an ecosystem of heterogeneous physical and cyber components integrated in cyber-physical systems which are more and more exposed to cyber-physical attacks, i.e., security breaches in cyberspace that adversely affect the physical processes at the core of the systems. We provide a formal compositional metric to estimate the impact of cyber-physical attacks targeting sensor devices of IoT systems formalised in a simple extension of Hennessy and Regan\u2019s Timed Process Language. Our impact metric relies on a discrete-time generalisation of Desharnais et al.\u2019s weak bisimulation metric for concurrent systems. We show the adequacy of our definition on two different attacks on a simple surveillance system