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.
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.
Encrypted control systems allow to evaluate feedback laws on external servers without revealing private information about state and input data, the control law, or the plant. While there are a number of encrypted control schemes available for linear feedback laws, only few results exist for the evaluation of more general control laws. Recently, an approach to encrypted polynomial control was presented, relying on two-party secret sharing and an inter-server communication protocol using homomorphic encryption. As homomorphic encryptions are much more computationally demanding than secret sharing, they make up for a tremendous amount of the overall computational demand of this scheme. For this reason, in this paper, we investigate schemes for secure polynomial control based solely on secret sharing. We introduce a novel secure three-party control scheme based on three-party computation. Further, we propose a novel n-party control scheme to securely evaluate polynomial feedback laws of arbitrary degree without inter-server communication. The latter property makes it easier to realize the necessary requirement regarding non-collusion of the servers, with which perfect security can be guaranteed. Simulations suggest that the presented control schemes are many times less computationally demanding than the two-party scheme mentioned above.
Web-servers are a dominant medium of modern communication and thus process vast amounts of highly sensitive, private data. Social networks, online auctions, and all kinds of cloud services constitute popular examples of online services complying with this paradigm. Due to many alarming scandals regarding the misuse of private data, IT security solutions protecting this sensitive data (for example by hiding it through encryption) are indispensable. Ideally, web-servers should be able to compute on private data without seeing it - we refer to this as the "Secure Outsourcing of Computation". Most notably, the cryptographic primitive of Homomorphic Encryption (HE) enables the web-servers to process data in the encrypted domain, which thereby hides/protects all private data as it is never available in the clear. More precisely, HE is a type of encryption that allows for the computation of certain functionalities on encrypted data without knowledge of the decryption key. Depending on the HE scheme, various functionalities can be evaluated in the encrypted domain, ranging from additions or multiplications only (Group Homomorphic Encryption, GHE), to virtually any computable functionality (Fully Homomorphic Encryption, FHE). We provide a clean foundational framework for HE that permits security characterizations for a large class of HE schemes and shows strong similarities between GHE and FHE. We study these characterizations in order to assess the limits of HE, and show that GHE is obsolete in the quantum world, meaning that any GHE scheme can be broken by a quantum computer. Together with our newly constructed universal blueprint that encompasses virtually any GHE scheme, we know exactly how these schemes must be designed and what the underlying hardness assumptions must look like. To some extent, this rounds off the topic of GHE both in the standard and quantum model of computation. In the standard model (which is presently assumed to be the most realistic model of computation), GHE is still highly attractive as it provides very efficient solutions to a variety of practical problems. On the basis of our foundational framework, we construct new GHE schemes with unique features and show their employability in practical applications. Most importantly, we use the special features of one of these schemes and develop a novel technique to achieve a practically efficient solution to the problem of securely outsourcing computations. Our construction allows multiple users to send encryptions of their private data under their own keys to a distrusted web-server that can then, on behalf of the users, evaluate any dynamically chosen computable function on these inputs in the encrypted domain (even across encryptions under different public keys) without learning anything at all, and without interacting with the users.
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.
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.
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 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.