A sample identifying complexity and a sample deciphering time have been introduced in a previous study to capture an estimation error and a computation time of system identification by adversaries. The quantities play a crucial role in defining the security of encrypted control systems and designing a security parameter. This study proposes an optimal security parameter for an encrypted control system under a network eavesdropper and a malicious controller server who attempt to identify system parameters using a least squares method. The security parameter design is achieved based on a modification of conventional homomorphic encryption for improving a sample deciphering time and a novel sample identifying complexity, characterized by controllability Gramians and the variance ratio of identification input to system noise. The effectiveness of the proposed design method for a security parameter is demonstrated through numerical simulations.

翻译：先前研究中引入了样本识别复杂度与样本解密时间，用以刻画攻击者在系统辨识中的估计误差与计算耗时。这两个指标对定义加密控制系统的安全性及设计安全参数具有关键作用。本研究针对存在网络窃听者与恶意控制器服务器（试图通过最小二乘法辨识系统参数）的加密控制系统，提出一种最优安全参数设计方法。该安全参数设计基于对传统同态加密的改进，通过优化样本解密时间，并引入由可控性格拉姆矩阵与辨识输入-系统噪声方差比表征的新型样本识别复杂度来实现。数值仿真验证了所提安全参数设计方法的有效性。