Linear Attacks Against Remote State Estimation: Performance Analysis Under an Encryption Scheme

This paper is concerned with the performance analysis of innovation-based remote state estimation with an encryption scheme under linear attacks. We investigate performances from the perspectives of both the system defender and the malicious attacker. For the system defender, we begin by detailing the design of an encryption mechanism that achieves an optimal trade-off between the estimation performance and the detection probability. Subsequently, we explore two scenarios where the attacker is aware of the existence of the proposed scheme. In these scenarios, we formulate the problems of seeking optimal linear attack strategies as convex optimization problems, and semi-definite programming (SDP) is employed to find their numerical solutions. In particular, a closed-form expression of the worst-case attacks is obtained when the attacker can observe the system state through its own sensor deployment. Moreover, we conduct a comparative analysis between these two scenarios and prove that the worst-case attack strategies have their respective advantages and disadvantages under different cases. Finally, some numerical examples are given to illustrate the theoretical results.