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.
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.
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.
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 (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.
Summary Encrypted control enables confidential controller evaluations in cloud‐based or networked control systems. Roughly speaking, an encrypted controller is a modified control algorithms that is capable of computing encrypted control actions based on encrypted system states. Encrypted control has been realized using different tools from cryptography such as homomorphic encryption, secret sharing, and multiparty computation. However, the vast majority of existing encrypted controllers is linear or makes intensive use of encrypted linear operations. In this article, we present a novel and flexible method for the encrypted implementation of arbitrary polynomial controllers. Technically, our approach builds on tailored two‐party computation combined with secret sharing and additively homomorphic encryption.
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.
The cyber-security of multi-agent control systems has become vital in practice. To protect the communication process between the individual agents over TCP/IP networks, one must encrypt the messages to be sent, which is costly in a large-scale network when high-level security is demanded. To lessen the burden of heavy encryption and decryption processes, we introduce the Homomorphic Encryption to reduce the number of encryption/decryption terminals that are supposed to equip with every agent. The security is enhanced by the quantum key distribution technology, which can generate secret keys that are theoretically absolutely secure even against quantum computation. We proposed a hybrid method that make good use of the randomness of quantum keys, one-time pad and symmetric encryption to make sure the overall security of homomorphic encryption algorithms. Numerical simulations are provided to illustrate how our scheme.