Secure Kalman Filter State Estimation by Partially Homomorphic Encryption

Recently, the security of state estimation has been attracting significant research attention due to the need for trustworthy situation awareness in emerging (e.g., industrial) cyber-physical systems. In this paper, we investigate secure estimation based on Kalman filtering (SEKF) using partially homomorphically encrypted data. The encryption will enhance the confidentiality not only of data transmitted in the communication network, but also key system information required by the estimator. We use a multiplicative homomorphic encryption scheme, but with a modified decryption algorithm. SEKF is able to conceal comprehensive information (i.e., system parameters, measurements, and state estimates) aggregated at the sink node of the estimator, while retaining the effectiveness of normal Kalman filtering. Therefore, even if an attacker has gained unauthorized access to the estimator and associated communication channels, he will not be able to obtain sufficient knowledge of the system state to guide the attack, e.g., ensure its stealthiness. We present an implementation structure of the SEKF to reduce the communication overhead compared with traditional secure multiparty computation (SMC) methods. Finally, we demonstrate the effectiveness of the SEKF on an IEEE 9-bus power system.