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Annual Reviews in Control

Comparison of encrypted control approaches and tutorial on dynamic systems using Learning With Errors-based homomorphic encryption

Junsoo Kim, Dongwoo Kim, Yongsoo Song, Hyungbo Shim, Henrik Sandberg, Karl Henrik Johansson

Published Jan 1, 2022• 34 citations
Publisher
DOI
10.1016/j.arcontrol.2022.10.002

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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 design of encrypted controllers, which perform control operation directly over encrypted signals via homomorphic cryptosystems, should consider both security of the control data and performance of the controller. Considering the use of Learning With Errors (LWE) based cryptosystem, in this paper, we present a design procedure for encrypted linear dynamic controllers. Providing a guideline for choosing the parameters of the cryptosystem as well as quantization, the procedure guarantees both the desired level of security and performance. Receiving the encrypted signals of the plant input as well as the output, the proposed controller is able to perform the dynamic operation over encrypted data for infinite time horizon, without the use of decryption or reset of the state. Thanks to additively and multiplicatively homomorphic property of the LWE-based cryptosystem, information of both control signals and gain matrices is protected by encryption.