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，该框架允许在不解密的情况下对加密数据进行算术运算。此前研究基于系统辨识的难度与计算时间量化了加密控制系统的安全等级。本研究从安全等级角度出发，探究面对试图通过最小二乘法估计系统参数的攻击时，加密控制系统的最优设计。本研究提出了一种能最大化估计难度的最优$H_2$控制器，以及一个确定保证加密控制系统安全的最小安全参数的方程，作为该设计问题的解答。所提出的控制器与安全参数有助于在实现期望安全等级的同时，降低加密控制系统的计算成本。此外，所提出的设计方法能够实现加密控制系统的系统性设计。