Secure Centralized Kalman Filter for Network Environments by Homomorphic Encryption

This paper presents a secure and private estimator in Cyber-Physical Systems (CPSs) where the estimator generates the state estimation without knowing the real inputs and outputs of the system. In particular, a secure and centralized Kalman filter is proposed by employing the Paillier encryption. Our proposed encrypted Kalman filter has less computational complexity in comparison to other investigated encrypted Kalman filters. In our structure, the encryption will improve the confidentiality of data transmitted through the communication network. Besides, the algebraic computations needed for the estimation are performed over the encrypted data. Therefore, calculating on encrypted signals improves the security and privacy of the estimation process. Accordingly, even if an adversary has obtained unauthorized entree to the estimator and associated transmission networks, he/she will not be able to gain enough information about the systems state to manage the attack. A numerical example is utilized to demonstrate the theoretical results.