Nash Equilibrium Control Policy against Bus-off Attacks in CAN Networks

A bus-off attack is a denial-of-service (DoS) attack which exploits error handling in the controller area network (CAN) to induce an honest node to disconnect itself from the CAN bus. This paper develops a stochastic transmission policy as a countermeasure for the controller-transmitter pair against the bus-off attack. We model this as a non-zero-sum linear-quadratic-Gaussian game between the controller-transmitter pair and the attacker. We derive Nash equilibria of the game for two different information structures of the attacker. We show that the attacker has a dominant attack strategy under both information structures. Under the dominant attack strategy, we show that the optimal control policy is linear in the system state. We further identify a necessary and a sufficient conditions on the transmission policy to have bounded average cost. The theoretical results are complemented by a detailed case study of a bus-off attack on a vehicular adaptive cruise control model.