Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time

TL;DR

This paper introduces a systematic approach to designing encrypted control systems by defining new notions of sample identifying complexity and deciphering time, enabling optimal key length and control law design for security and performance.

Contribution

It proposes the first control-theoretic framework linking cryptographic security with dynamical system properties, introducing novel measures and design methods.

Findings

The method effectively balances security and control performance.

Numerical simulations demonstrate improved security levels.

The approach offers a systematic way to prevent system identification.

Abstract

In the state-of-the-art literature on cryptography and control theory, there has been no systematic methodology of constructing cyber-physical systems that can achieve desired control performance while being protected against eavesdropping attacks. In this paper, we tackle this challenging problem. We first propose two novel notions referred to as sample identifying complexity and sample deciphering time in an encrypted-control framework. The former explicitly captures the relation between the dynamical characteristics of control systems and the level of identifiability of the systems while the latter shows the relation between the computation time for the identification and the key length of a cryptosystem. Based on these two tractable new notions, we propose a systematic method for designing the both of an optimal key length to prevent system identification with a given precision within a given life span of systems, and of an optimal controller to maximize both of the control performance and the difficulty of the identification. The efficiency of the proposed method in terms of security level and realtime-ness is investigated through numerical simulations. To the best of our knowledge, this paper first connect the relationship between the security of cryptography and dynamical systems from a control-theoretic perspective.