Secure State Estimation for Cyber-Physical Systems Against Active Eavesdropping Attacks: A Stochastic Encryption-Based Method

This article is concerned with the problem of remote state estimation for cyber-physical systems (CPSs) in the presence of an active eavesdropper. To prevent information leakage, a novel stochastic encryption scheme is proposed to protect the data transmitted via packet loss channel. The scheme can guarantee the user's privacy and force the estimation error of the eavesdropper to diverge by using a predefined scheduling sequence to transmit raw data or an encrypted version randomly. In this case, two types of data are considered: raw measurements and local estimates. Aiming at these two transmission scenarios, the expected estimation error recursions with respect to encryption mechanisms, channel parameters, and the system dynamics are derived in the minimum mean error estimation sense. Further, we show the conditions that require the expected estimation error covariance of the user to be bounded, while the active eavesdropper's expected estimation error grows unbounded by mathematical induction and matrix theory methods. Finally, an application example is illustrated to verify the performance of the encryption scheme.