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

Teranishi, Kaoru; Sadamoto, Tomonori; Chakrabortty, Aranya; Kogiso, Kiminao

doi:10.1109/tac.2022.3174691

Cited by 10 publications

(24 citation statements)

References 46 publications

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“…In [9], the authors examined the provable security of the systems and analyzed the connection between the security and a traditional cryptographic security definition. Another study [10] focused on quantifying the security level of encrypted control systems using the sample complexity and computation time of system identification, disclosing the parameters of a target system. The study also included a design for a controller that maximizes the sample complexity of the Bayes estimation for a system matrix of a closed-loop system with an encrypted controller.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that the sample complexity and computation time depend on the identification algorithm and encryption scheme used, respectively. The study [11] proposed another sample complexity for applying the approach to the least squares identification of the system and input matrices of a plant controlled by an encrypted controller.…”

Section: Introductionmentioning

confidence: 99%

“…This study proposes a systematic method for solving the security and performance trade-off by designing an optimal controller and security parameter for encrypted control systems based on the security definition in [10]. To this end, this study derives a novel sample complexity of the systems, which is a closed-loop version of the sample complexity in [11]. With the novel sample complexity, we reveal that the security level of the system is connected to the controllability Gramian of the target system.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed method contributes to the generalization of the design method in [10]. The previous method chose the minimum key length for a specific encryption scheme.…”

Section: Introductionmentioning

confidence: 99%

“…A security parameter is a common quantity for encryption schemes, and thus the proposed method can be applied to encrypted control systems with any homomorphic encryption. Moreover, the attack based on the least squares method considered in this study is easier for attackers to perform compared to the Bayesian estimation in [10] because the method does not require prior knowledge of a target system. Therefore, a broader class of encrypted control systems can be protected by preventing least squares identification attacks.…”

Section: Introductionmentioning

confidence: 99%

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

Teranishi¹,

Kogiso²

2023

Preprint

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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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The proposed method contributes to the generalization of the design method in [10]. The previous method chose the minimum key length for a specific encryption scheme.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Teranishi¹,

Kogiso²

2023

Preprint

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

Teranishi

Kogiso

2023

SICE Journal of Control, Measurement, and System Integration

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

et al. 2023

Self Cite

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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) positioncontrol 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 quantizationerror 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.

show abstract

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

Cited by 10 publications

References 46 publications

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

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

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

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

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