Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applied Sciences

Secure Control of Linear Controllers Using Fully Homomorphic Encryption

Jingshan Pan, Tongtong Sui, Wen Liu, Jizhi Wang, Lingrui Kong, Yue Zhao, Zhiqiang Wei

Published Dec 7, 2023• 3 citations
Publisher

Abstract

In actual operation, there are security risks to the data of the network control system, mainly in the form of possible eavesdropping of signals in the transmission channel and parameters in the controller leading to data leakage. In this paper, we propose a scheme for encrypting linear controllers using fully homomorphic encryption, which effectively removes these security risks and substantially improves the security of networked control systems. Meanwhile, this paper uses precomputation to handle data encryption, which eliminates the encryption time and solves the drawback of fully homomorphic encryption that it is difficult to apply due to the efficiency problem. Compared to previous schemes with precomputation, for the first time, we propose two methods to mitigate the problem of the slight security degradation caused by precomputation, which makes our scheme more secure. Finally, we provide numerical simulation results to support our scheme, and the data show that the encrypted controller achieves normal control and improves safety and efficiency.

DOI
10.3390/app132413071

Related papers

End-to-End Encryption for Cyber-Physical Systems Using Fully Homomorphic Encryption

Robert s Lois

Cyber-physical systems require reliable, safe, and secure control of critical infrastructure, combining computational and networking capabilities, which heighten the risk of cyber attacks. These attacks can disrupt the physical process, causing unforeseen consequences. One solution is the use of fully homomorphic encryption (FHE) to protect the control loop, allowing for secure computations and communications without compromising signal and control system privacy. The challenge with FHE, however, is its requirement for inputs to be integers. This presentation introduces a modified Learning With Errors (LWE) FHE approach that encodes control system dynamics and signals into integers. Our proposed scheme leverages a generalized LWE encoding function and modifies the Gentry-Sahai-Waters gadget decomposition tool to encrypt the control system. Using the modified LWE scheme, we formalize a fully encrypted control system, supported by simulated results.

•Sep 11, 2024•0 citations

Encrypted Control Using Modified Learning with Errors-based Schemes

Robert s Lois, Daniel G. Cole

Cyber-physical systems (CPSs) require reliable, safe, and secure control of critical infrastructure, combining computational and networking capabilities, which heighten the risk of cyberattacks. These attacks can disrupt the physical process, causing unforeseen consequences. One solution is using fully homomorphic encryption (FHE) to protect the control loop, allowing for secure computations and communications without compromising signal and control system privacy. One challenge with FHE, however, is its requirement for inputs to be integers. This paper introduces a modified FHE scheme based on the learning with errors (LWE) problem. Our proposed scheme leverages a generalized LWE encoding function and modifies the Gentry-Sahai-Waters (GSW) gadget decomposition tool to encrypt the control system. Using the modified LWE scheme, we formalize a fully encrypted control system, supported by simulated results.

IFAC-PapersOnLine•Jan 1, 2024•0 citations

Guidelines for Secure Process Control: Harnessing the Power of Homomorphic Encryption and State Feedback Control

Matúš Furka, Martin Kalúz, Miroslav Fikar +1 more

The paper presents applications of homomorphic cryptographic schemes in process control. Homomorphic encryption is a particular type of encryption that allows performing mathematical operations over encrypted data. Therefore the user can use third-party services as controllers without revealing any vulnerable information, like process data. Homomorphic properties make it possible to perform data aggregation or evaluate control actions without having any knowledge about the process data. Our paper explores two fully homomorphic cryptographic schemes, namely Brakerski/Fan-Vercauteren (BFV) and Cheon-Kim-Kim-Song (CKKS) cryptosystems. Each scheme is briefly described with its advantages and drawbacks, conditions, and applications. We present a case study involving hl linear-quadratic (LQ) control strategy implemented in an encrypted setup. This serves for comparison and a step-by-step guide for implementing encrypted process control.

IEEE Access•Jan 6, 2026•0 citations

Guidelines for Secure Process Control: Harnessing the Power of Homomorphic Encryption and State Feedback Control

Matúš Furka, Martin Kalúz, Miroslav Fikar +1 more

The paper presents applications of homomorphic cryptographic schemes in process control. Homomorphic encryption is a particular type of encryption that allows performing mathematical operations over encrypted data. Therefore the user can use third-party services as controllers without revealing any vulnerable information, like process data. Homomorphic properties make it possible to perform data aggregation or evaluate control actions without having any knowledge about the process data. Our paper explores two fully homomorphic cryptographic schemes, namely Brakerski/Fan-Vercauteren (BFV) and Cheon-Kim-Kim-Song (CKKS) cryptosystems. Each scheme is briefly described with its advantages and drawbacks, conditions, and applications. We present a case study involving linear-quadratic (LQ) control strategy implemented in an encrypted setup. This serves for comparison and a step-by-step guide for implementing encrypted process control.

IEEE Access•Jan 1, 2023•5 citations

Encrypted LQG using labeled homomorphic encryption

Andreea B. Alexandru, George J. Pappas

We consider the problem of implementing a Linear Quadratic Gaussian (LQG) controller on a distributed system, while maintaining the privacy of the measurements, state estimates, control inputs and system model. The component sub-systems and actuator outsource the LQG computation to a cloud controller and encrypt their signals and matrices. The encryption scheme used is Labeled Homomorphic Encryption, which supports the evaluation of degree-2 polynomials on encrypted data, by attaching a unique label to each piece of data and using the fact that the outsourced computation is known by the actuator. We write the state estimate update and control computation as multivariate polynomials in the encrypted data and propose an extension to the Labeled Homomorphic Encryption scheme that achieves the evaluation of low-degree polynomials on encrypted data, with degree larger than two. We showcase the numerical results of the proposed protocol for a temperature control application that indicates competitive online times.

ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS)•Apr 4, 2019•28 citations

Further Methods for Encrypted Linear Dynamic Controllers Utilizing Re-Encryption

Junsoo Kim

Homomorphic encryption (HE) applied to a networked controller enables secure operation, but in most cases it allows for addition and multiplication over integers only, because of computation efficiency. Several related results deal with such constraints by means of re-encrypted controller output, based on which the controller can be re-constructed and operate over integers. This paper presents two modified methods based on the output re-encryption, which will further reduce the required communication effort and computational burden, respectively.

arXiv:2307.16445•IEEE Transactions on Automatic Control•Apr 10, 2024•7 citations
In actual operation, there are security risks to the data of the network control system, mainly in the form of possible eavesdropping of signals in the transmission channel and parameters in the controller leading to data leakage. In this paper, we propose a scheme for encrypting linear controllers using fully homomorphic encryption, which effectively removes these security risks and substantially improves the security of networked control systems. Meanwhile, this paper uses precomputation to handle data encryption, which eliminates the encryption time and solves the drawback of fully homomorphic encryption that it is difficult to apply due to the efficiency problem. Compared to previous schemes with precomputation, for the first time, we propose two methods to mitigate the problem of the slight security degradation caused by precomputation, which makes our scheme more secure. Finally, we provide numerical simulation results to support our scheme, and the data show that the encrypted controller achieves normal control and improves safety and efficiency.
Cyber-physical systems require reliable, safe, and secure control of critical infrastructure, combining computational and networking capabilities, which heighten the risk of cyber attacks. These attacks can disrupt the physical process, causing unforeseen consequences. One solution is the use of fully homomorphic encryption (FHE) to protect the control loop, allowing for secure computations and communications without compromising signal and control system privacy. The challenge with FHE, however, is its requirement for inputs to be integers. This presentation introduces a modified Learning With Errors (LWE) FHE approach that encodes control system dynamics and signals into integers. Our proposed scheme leverages a generalized LWE encoding function and modifies the Gentry-Sahai-Waters gadget decomposition tool to encrypt the control system. Using the modified LWE scheme, we formalize a fully encrypted control system, supported by simulated results.
Cyber-physical systems (CPSs) require reliable, safe, and secure control of critical infrastructure, combining computational and networking capabilities, which heighten the risk of cyberattacks. These attacks can disrupt the physical process, causing unforeseen consequences. One solution is using fully homomorphic encryption (FHE) to protect the control loop, allowing for secure computations and communications without compromising signal and control system privacy. One challenge with FHE, however, is its requirement for inputs to be integers. This paper introduces a modified FHE scheme based on the learning with errors (LWE) problem. Our proposed scheme leverages a generalized LWE encoding function and modifies the Gentry-Sahai-Waters (GSW) gadget decomposition tool to encrypt the control system. Using the modified LWE scheme, we formalize a fully encrypted control system, supported by simulated results.
The paper presents applications of homomorphic cryptographic schemes in process control. Homomorphic encryption is a particular type of encryption that allows performing mathematical operations over encrypted data. Therefore the user can use third-party services as controllers without revealing any vulnerable information, like process data. Homomorphic properties make it possible to perform data aggregation or evaluate control actions without having any knowledge about the process data. Our paper explores two fully homomorphic cryptographic schemes, namely Brakerski/Fan-Vercauteren (BFV) and Cheon-Kim-Kim-Song (CKKS) cryptosystems. Each scheme is briefly described with its advantages and drawbacks, conditions, and applications. We present a case study involving hl linear-quadratic (LQ) control strategy implemented in an encrypted setup. This serves for comparison and a step-by-step guide for implementing encrypted process control.
The paper presents applications of homomorphic cryptographic schemes in process control. Homomorphic encryption is a particular type of encryption that allows performing mathematical operations over encrypted data. Therefore the user can use third-party services as controllers without revealing any vulnerable information, like process data. Homomorphic properties make it possible to perform data aggregation or evaluate control actions without having any knowledge about the process data. Our paper explores two fully homomorphic cryptographic schemes, namely Brakerski/Fan-Vercauteren (BFV) and Cheon-Kim-Kim-Song (CKKS) cryptosystems. Each scheme is briefly described with its advantages and drawbacks, conditions, and applications. We present a case study involving linear-quadratic (LQ) control strategy implemented in an encrypted setup. This serves for comparison and a step-by-step guide for implementing encrypted process control.
We consider the problem of implementing a Linear Quadratic Gaussian (LQG) controller on a distributed system, while maintaining the privacy of the measurements, state estimates, control inputs and system model. The component sub-systems and actuator outsource the LQG computation to a cloud controller and encrypt their signals and matrices. The encryption scheme used is Labeled Homomorphic Encryption, which supports the evaluation of degree-2 polynomials on encrypted data, by attaching a unique label to each piece of data and using the fact that the outsourced computation is known by the actuator. We write the state estimate update and control computation as multivariate polynomials in the encrypted data and propose an extension to the Labeled Homomorphic Encryption scheme that achieves the evaluation of low-degree polynomials on encrypted data, with degree larger than two. We showcase the numerical results of the proposed protocol for a temperature control application that indicates competitive online times.
Homomorphic encryption (HE) applied to a networked controller enables secure operation, but in most cases it allows for addition and multiplication over integers only, because of computation efficiency. Several related results deal with such constraints by means of re-encrypted controller output, based on which the controller can be re-constructed and operate over integers. This paper presents two modified methods based on the output re-encryption, which will further reduce the required communication effort and computational burden, respectively.