Optimal Encryption Scheduling Policy Against Eavesdropping Attacks in Cyber-Physical Systems

This article studies the optimal encryption scheduling for remote state estimation in cyber-physical systems (CPSs) against eavesdropping attacks. A smart sensor sends packets to a remote estimator based on an encrypted scheme, meanwhile, an eavesdropper overhears and decrypts the data transmitted with a certain probability. In this context, we formulate the optimal encryption problem as a Markov decision process (MDP) to minimize a convex combination of the expected estimation errors of the user and eavesdropper. A necessary and sufficient condition for the optimal encryption policy to be stationary is derived, and the double threshold structure is obtained. Furthermore, we derive the decay rate of the eavesdropper's estimation error with respect to the secret key leakage rate. To enhance the security of systems, a novel encryption approach with dynamic secret keys is proposed using the system dynamics and the feedback channel. Finally, some simulations are provided to illustrate theoretical analyzes.