Optimal security parameter for encrypted control systems against eavesdropper and malicious server

Abstract

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.

Keywords

• encrypted control
• homomorphic encryption
• cyber-physical system
• control systems security
• cryptography
• security parameter