Secure State Estimation Using Hybrid Homomorphic Encryption Scheme

Recently, the security of state estimation has attracted significant research attention due to the need for trustworthy situation awareness in emerging cyber-physical systems. In this article, we design an encryption-based state estimation (ESE) using partially homomorphically encrypted data. The encryption will enhance the confidentiality not only of data transmitted in the communication network but also critical system information required by the estimator. We adopt a hybrid encryption scheme by jointly using the multiplicatively and additively homomorphic encryption methods. Armed with encryption, ESE is able to conceal comprehensive information (i.e., model parameters, measurements, and estimates) aggregated at the estimator while retaining the correctness of the normal state estimation. Therefore, even if an attacker has gained unauthorized access to the estimator and associated communication channels, he/she will not be able to obtain sufficient knowledge of the system state to guide the attack. Furthermore, due to the encryption-induced quantization error, we give a sufficient stability condition for ESE. Finally, we implement ESE with real-world hardware to illustrate its effectiveness and efficiency.