Encrypted control is a framework for the secure outsourcing of controller computation using homomorphic encryption that allows to perform arithmetic operations on encrypted data without decryption. In a previous study, the security level of encrypted control systems was quantified based on the difficulty and computation time of system identification. This study investigates an optimal design of encrypted control systems when facing an attack attempting to estimate a system parameter by the least squares method from the perspective of the security level. This study proposes an optimal $H_2$ controller that maximizes the difficulty of estimation and an equation to determine the minimum security parameter that guarantee the security of an encrypted control system as a solution to the design problem. The proposed controller and security parameter are beneficial for reducing the computation costs of an encrypted control system, while achieving the desired security level. Furthermore, the proposed design method enables the systematic design of encrypted control systems.

翻译：加密控制是一种利用同态加密实现控制器计算安全外包的框架，其允许在不解密的情况下对加密数据执行算术运算。此前研究基于系统辨识的难度与计算时间对加密控制系统的安全等级进行了量化。本研究从安全等级视角出发，探讨了当攻击者试图通过最小二乘法估计系统参数时，加密控制系统的最优设计问题。本文提出了一种可最大化估计难度的最优$H_2$控制器，以及一个用于确定保证加密控制系统安全性的最小安全参数的方程，以此作为该设计问题的解决方案。所提出的控制器与安全参数有助于在达成预期安全等级的同时，降低加密控制系统的计算成本。此外，该设计方法能够实现加密控制系统的系统性设计。