Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

This paper presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semi-homomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.Comment: Improved numerical exampl

Cloud-based Quadratic Optimization with Partially Homomorphic Encryption

The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a cloud-based protocol for a quadratic optimization problem involving multiple parties, each holding information it seeks to maintain private. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure multi-party computation techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy, i.e., there is no computationally efficient algorithm that any involved party can employ to obtain private information beyond what can be inferred from the party's inputs and outputs only. In order to reduce the communication complexity of the proposed protocol, we introduced a variant that achieves this objective at the expense of weaker privacy guarantees. We discuss in detail the computational and communication complexity properties of both algorithms theoretically and also through implementations. We conclude the paper with a discussion on computational privacy and other notions of privacy such as the non-unique retrieval of the private information from the protocol outputs

Secure Teleoperation Control Using Somewhat Homomorphic Encryption

Presented at 2022 Modeling, Estimation, and Control Conference (MECC) , October 2022The goal of this research is to establish control theoretic methods to enhance cyber security of networked motion control systems by utilizing somewhat homomorphic encryption. The proposed approach will encrypt the entire motion control schemes including: sensor signals, model parameters, feedback gains, and performs computation in the ciphertext space to generate motion commands to servo systems without a security hole. The paper will discuss implementation of encrypted bilateral teleoperation control schemes with nonlinear friction compensation. The paper will present (1) encrypted teleoperation control realization with somewhat homomorphic encryption and (2) simulation results.This work was supported in part by the National Science Foundation under Grant No. 2112793 and the Japan Society for the Promotion of Science KAKENHI Grant No. JP22H01509

Implementing Homomorphic Encryption Based Secure Feedback Control for Physical Systems

This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier's homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast

Cloud-Based Quadratic Optimization with Partially Homomorphic Encryption

This article develops a cloud-based protocol for a constrained quadratic optimization problem involving multiple parties, each holding private data. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure communication techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy. We show the implementation results of the protocol and discuss its computational and communication complexity. We conclude this article with a discussion on privacy notions