Optimal Deception Attacks in Remote State Estimation with Linear Encryption*

This paper investigates the vulnerability of a remote estimation system protected by linear encryption strategies. In a worst-case scenario, where attackers can intercept the encryption parameters while the secret key remains secure, it is demonstrated that adversaries can still execute stealthy false-data injection attacks using limited online information. These attacks can degrade estimation quality to its maximum extent while evading detection. The synthesis of optimal attacks comprises two steps: first, deriving the minimum mean-square error estimate of compromised prediction errors; and second, designing the attack vector through a linear transformation. By leveraging the structure of the optimization problem, explicit analytical forms of the attack parameters are derived, which can eliminate the need for numerical optimization. The effectiveness of the proposed approach is confirmed through numerical examples.