General Stealthy Attack Against Remote State Estimation with Encryption-Decryption Scheme

This paper is concerned with the design of general stealthy attacks on remote state estimation with encryption-decryption schemes. To ensure the stealthiness of general attacks under encryption-decryption schemes, we firstly redefine the stealthiness constraints of attacks from the perspectives of the alarm rate and the detection index's expectation. Then, under the constraint of the detection index's expectation, the analytical expression of the optimal general attack that maximizes estimation error is derived, and the corresponding detection rate is computed to assess the compliance with the alarm rate constraint. If the alarm rate constraint is not satisfied, we further derive an upper bound of the detection rate caused by general attacks, and obtain the analytical expression of a feasible general stealthy attack. Finally, a numerical example is presented to verify the effectiveness of theoretical results.