Encrypted Control Systems Research Articles

Comprehensively enhancing the security of control with combined homomorphic encryption

Homomorphic encryption is an effective way to address the privacy and security issues of Networked Control Systems (NCSs). Since the control function needs to be redesigned according to the homomorphism to complete encrypted computing, the practical implementation of a perfectly secure and highly efficient NCS is challenging. Previously proposed NCSs based on homomorphic encryption are still subject to the risk of eavesdropping attacks. In this paper, a combined homomorphic encryption scheme is designed to build a secure environment for NCSs. This scheme comprehensively enhances the security of NCSs by eliminating potential security hazards. The risk of eavesdropping attacks on information in the controller and communication channel is avoided. More specifically, the entire control scheme is encrypted and privacy computing within the controller is performed on this basis. Data protection is provided for all transmission channels, including the transmission of the intermediate result and controller state. In particular, the computational efficiency of the encrypted control system is fast and feasible for real-time control. The performance and stability of the closed-loop system are maintained.

Controller Design Based on Closed-loop Data of an Encrypted Control System

Controller Design Based on Closed-loop Data of an Encrypted Control System

Detection and Cancellation of Multiplicative FDI Attack on Bilateral Encrypted Control System

Detection and Cancellation of Multiplicative FDI Attack on Bilateral Encrypted Control System

A Verifiable Computing Scheme for Encrypted Control Systems

A Verifiable Computing Scheme for Encrypted Control Systems

Experimental Validation of the Attack-Detection Capability of Encrypted Control Systems Using Man-in-the-Middle Attacks

Experimental Validation of the Attack-Detection Capability of Encrypted Control Systems Using Man-in-the-Middle Attacks

Towards Oblivious Guidance Systems for Autonomous Vehicles

We consider encrypted guidance systems for straight-line path following. With cloud-computing technology, we can outsource computations in guidance systems to third-party providers, increasing scalability and enabling guidance-as-a-service. However, by remotely hosting a conventional guidance system on third-party infrastructure, we leak information such as the path of the vehicle. Potential customers may consider these leaks a serious breach of confidentiality, which limits the practical use of such systems. Therefore, to make cloud-based guidance systems viable, we would like to design guidance systems that we can host remotely without revealing confidential information to the host. To this end, we show that we can construct guidance systems that operate on encrypted position measurements, encrypted waypoints, and the bearing between each waypoint by using homomorphic encryption, effectively preventing the cloud host from identifying the vehicle's position. We show that the proposed guidance laws are locally exponentially stable and that the induced computational latency is appropriate for the real-time guidance of autonomous vehicles. Through field experiments, we demonstrate that an encrypted guidance system is practical and allows an unmanned surface vehicle to follow an encrypted path. The originality of this work lies in conceptualizing, designing, and experimentally validating an encrypted guidance system, unlike other studies that considered encrypted control systems.

Nonminimality of the Realizations and Possessing State Matrices With Integer Elements in Linear Discrete-Time Controllers

It is known that discrete-time controllers, whose state matrices have no non-integer element, are beneficial in homomorphic based encrypted control systems. Nevertheless, it has been recently shown that possessing state matrices with integer elements usually yields unstable discrete-time controllers. In this note, we investigate the problem from a non-minimality perspective. It is shown that non-minimal realizations, in comparison to minimal ones, can theoretically provide a wider framework to obtain controllers having state matrices with integer elements. However, in the case of dealing with BIBO stable controllers, this framework cannot preserve internal stability. But, benefiting from the introduced framework, a class of unstable controllers is introduced which can be realized by state-space forms having state matrices with integer elements. Numerical examples are presented to verify the usefulness of the introduced framework in the realization of unstable controllers with integer state matrices.

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

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

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

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 the desired control performance while being protected against eavesdropping attacks. In this article, we tackle this challenging problem. We first propose two novel notions referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sample identifying complexity</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sample deciphering time</i> 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 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 article first connects the relationship between the security of cryptography and dynamical systems from a control-theoretic perspective.

Cybersecurity-Enhanced Encrypted Control System Using Keyed-Homomorphic Public Key Encryption

Encrypted control systems are secure control methods that use the cryptographic properties of a specific homomorphic encryption scheme. This study proposes a cyberattack-detectable encrypted control system and validates its effectiveness using a proportional integration derivative (PID) position-control system for an industrial motor. The proposed encrypted control system uses a keyed-homomorphic public-key encryption scheme for real-time detection of cyberattacks, such as signal and control parameter falsification. Additionally, a novel quantizer is presented to reduce the computation cost and quantization-error effects on control performance. The quantizer demonstrated a significant improvement, reducing the computation time by 47.3 % compared to using our previous quantizer, and decreasing the quantization-error effect by 30.6 % compared to a widely-used gain-multiplying quantizer. Moreover, this study establishes conditions through a theorem to avoid an overflow in the proposed control system. Experimental validation confirms that the proposed control system effectively conceals the control operation, and the presented theorem aids in designing the quantization gains to prevent overflows. Notably, the results of falsification attack tests highlight that the proposed control system enables real-time detection of attacked components within control parameters and signals, representing a significant advantage of this study.

Optimal Controller and Security Parameter for Encrypted Control Systems Under Least Squares Identification

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 H2 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.

Confidentiality attacks against encrypted control systems

ABSTRACT Encrypted control systems were introduced to enhance the security of cyber-physical systems, which outsource control action computations to a third-party platform. To protect the confidentiality of the transmitted data, homomorphic encryption schemes are particularly appealing for their capability of allowing computations on encrypted data. By considering the popular ElGamal and Paillier encryption schemes, this paper shows that encrypted control systems are vulnerable to attackers leveraging the inherently small domains of the plaintext data in control systems and the randomisation process required to make the utilised ciphers semantically secure. Finally, we present some countermeasures to defend against these attacks.

Detection of Cyber Attacks in Encrypted Control Systems

Recently a resilient homomorphic encryption (RHE) scheme has been proposed in <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , which allows not only to carry out the evaluation process of an output feedback controller in an encrypted environment but also can neutralize the effect of additive attacks injected into the ciphertexts. However, the resilience to additive attacks has its limits. In this letter, at first it will be shown that the resilience range of the RHE scheme to additive attacks is indeed much larger than shown in <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> . Then, a detection approach is proposed to give a twofold protection to control systems encrypted by the RHE scheme. A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">warning</i> signal is triggered as soon as an additive attack is injected into the ciphertexts transmitted over the network, while an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alarm</i> signal is triggered when the attack is outside of the resilience range. This is achieved by exploiting the symmetric property of the inner product. Therefore, the RHE scheme can be combined with the proposed detection approach to ensure the integrity of the signals obtained after decryption in case of additive attacks. A simulation example of the well-established quadruple-tank benchmark process is used to demonstrate the proposed detection approach for encrypted control systems.

ElGamal-type encryption for optimal dynamic quantizer in encrypted control systems

This study considers a quantizer design problem with controller encryption for minimizing performance degradation caused by encryption. It is difficult to design an optimal dynamic quantizer that c...

Stability‐guaranteed dynamic ElGamal cryptosystem for encrypted control systems

Despite the importance of cyber-security for networked control systems, no suitable cryptosystem exists for networked control systems that guarantees stability and has low computational complexity. This study proposes a novel dynamic ElGamal cryptosystem for encrypted control systems. The proposed cryptosystem is a multiplicative homomorphic cryptosystem, and it updates key pairs and ciphertexts by simple updating rules with modulo operations at every sampling period. Furthermore, the authors modify the proposed cryptosystem by using a dynamic encoder and decoder so that the asymptotic stability of the encrypted control systems is guaranteed. Numerical simulations demonstrate that the encrypted controller with the proposed cryptosystem achieves asymptotic stability while randomly updating key pairs and ciphertexts. The feasibility of the proposed encrypted control system is evaluated through regulation control with a positioning table testbed. The processing time of the proposed encrypted control system is on the order of milliseconds, indicating that the system achieves real-time control.

Development and Examination of Fog Computing-Based Encrypted Control System

This letter develops a fog computing-based encrypted control system in a practical industrial setting. The developed system conceals controller gains and signals over communication links using multiplicative homomorphic encryption to prevent eavesdropping attacks. Experimental validation confirms the feasibility of position servo control for the motor-driven stage with the developed system in terms of performance degradation, parameter variation, and processing time. The developed system inherits its stability regardless of whether plant parameters fluctuate or not even after the controller gains and signals are encrypted. Furthermore, although processing time becomes longer by increasing a key length of encryption, degradation of control performance is improved simultaneously.

Event-triggered Approach to Increasing Sampling Period of Encrypted Control Systems

Controller encryption is a cryptographic approach to enhancing the security of networked control systems. The method would be effective in reducing risks of eavesdropping attacks. However, encryption may cause high communication traffic and processing delays. This study proposes a redetermination method for a sampling period of a given encrypted control system to increase the sampling period. The proposed method can reduce the bit rate of communication between a plant and controller and improving the strength of ciphertexts. The validity of the proposed method is examined through numerical simulations. The simulation results demonstrate that the sampling period-redetermined encrypted control system achieves asymptotic stability and retains control performance of the original encrypted control system.

Control-theoretic Approach to Malleability Cancellation by Attacked Signal Normalization

In this study, we propose a novel attack for encrypted control systems along with a cancellation method for the attacks. The attacks assign the poles of closed-loop systems by utilizing the malleability of homomorphic encryption schemes used in encrypted control systems. Additionally, a condition of destabilization by the attacks is provided under the assumption that adversaries are aware of the homomorphic encryption scheme that is being used. The proposed method is applicable for encrypted control systems with partially or fully homomorphic encryption schemes, and completely removes influence of certain type of attacks with obfuscated controller gain, which is obtained by QR decomposition. The validity of the proposed method is examined through a numerical simulation. The results confirm that the proposed method is effective in canceling the malleability of encrypted control systems.

Encrypted control system with quantiser

This paper considers the design of encrypted control systems to secure data privacy when the control systems operate over a network. In particular, we propose to combine Paillier cryptosystem with a quantizer whose sensitivity changes with the evolution of the system. This allows the encrypted control system to balance between the cipher strength and processing time. Such an ability is essential for control systems that are expected to run real-time. It also allows the closed-loop system to achieve the asymptotic stability for linear systems. Extensions to event-triggered control and nonlinear control systems are also discussed.