Homomorphic Encryption of Supervisory Control Systems Using Automata

Cyber-physical systems have been highly integrated into many contemporary infrastructures. As this integration deepens, the importance of protecting these systems from unauthorized access and data corruption increases. Nowadays, cyber-physical systems are not well protected against network attacks. One solution is to improve the security of a system by encrypting the transmitted data. In this paper, we consider the encryption of supervisors of discrete event systems modeled with deterministic finite-state automata. We propose an encryption framework of supervisory control systems based on the matrix notation of automata. The purpose of using matrix notation is to make it suitable for homomorphic encryption schemes over integers, which are emerging in the cryptography area. We calculate the entropy of the matrix notation and find that as the size of a system increases, it gets smaller and approaches zero. Owing to the low entropy of the matrix notation, we propose an algorithm to enhance its entropy. By applying the entropy-enhancing process, the distribution characteristics of entries in matrices or vectors can be hidden to avoid a brute force attack. Correspondingly, we propose an entropy restoration algorithm to ensure that the control action can be transmitted correctly.