Encrypted Dynamic Control exploiting Limited Number of Multiplications and a Method using RLWE-based Cryptosystem

TL;DR

This paper introduces an encrypted dynamic control method that minimizes homomorphic multiplications and leverages RLWE-based cryptosystems to reduce computational and communication loads, ensuring long-term performance.

Contribution

It presents a novel encryption approach for dynamic controllers with limited multiplications and a RLWE-based customization that simplifies implementation without extra algorithms.

Findings

Effective encrypted control with limited multiplications

RLWE-based encryption reduces computation and communication

Simulation confirms practical viability

Abstract

In this paper, we present a method to encrypt dynamic controllers that can be implemented through most homomorphic encryption schemes, including somewhat, leveled fully, and fully homomorphic encryption. To this end, we represent the output of the given controller as a linear combination of a fixed number of previous inputs and outputs. As a result, the encrypted controller involves only a limited number of homomorphic multiplications on every encrypted data, assuming that the output is re-encrypted and transmitted back from the actuator. A guidance for parameter choice is also provided, ensuring that the encrypted controller achieves predefined performance for an infinite time horizon. Furthermore, we propose a customization of the method for Ring Learning With Errors (RLWE)-based cryptosystems, where a vector of messages can be encrypted into a single ciphertext and operated simultaneously, thus reducing computation and communication loads. Unlike previous results, the proposed customization does not require extra algorithms such as rotation, other than basic addition and multiplication. Simulation results demonstrate the effectiveness of the proposed method.