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Encrypted control is a framework for the secure outsourcing of controllercomputation using homomorphic encryption that allows to perform arithmeticoperations on encrypted data without decryption. In a previous study, thesecurity level of encrypted control systems was quantified based on thedifficulty and computation time of system identification. This studyinvestigates an optimal design of encrypted control systems when facing anattack attempting to estimate a system parameter by the least squares methodfrom the perspective of the security level. This study proposes an optimal$H_2$ controller that maximizes the difficulty of estimation and an equation todetermine the minimum security parameter that guarantee the security of anencrypted control system as a solution to the design problem. The proposedcontroller and security parameter are beneficial for reducing the computationcosts of an encrypted control system, while achieving the desired securitylevel. Furthermore, the proposed design method enables the systematic design ofencrypted control systems.

Optimal Controller and Security Parameter for Encrypted Control Systems Under Least Squares Identification