Comparison of encrypted control approaches and tutorial on dynamic systems using LWE-based homomorphic encryption

TL;DR

This paper reviews encrypted control methods, compares homomorphic encryption approaches, and introduces a new GSW-LWE cryptosystem enabling efficient recursive operations on encrypted dynamic systems.

Contribution

It provides a comprehensive comparison of encrypted control techniques and introduces the GSW-LWE cryptosystem for improved recursive encrypted system computations.

Findings

Homomorphic encryption approaches vary in complexity and operations.

The GSW-LWE cryptosystem enables recursive multiplication without bootstrapping.

Encrypted control methods are advancing towards practical dynamic system applications.

Abstract

Encrypted control has been introduced to protect controller data by encryption at the stage of computation and communication, by performing the computation directly on encrypted data. In this article, we first review and categorize recent relevant studies on encrypted control. Approaches based on homomorphic encryption, multi-party computation, and secret sharing are introduced, compared, and then discussed with respect to computational complexity, communication load, enabled operations, security, and research directions. We proceed to discuss a current challenge in the application of homomorphic encryption to dynamic systems, where arithmetic operations other than integer addition and multiplication are limited. We also introduce a homomorphic cryptosystem called ``GSW-LWE'' and discuss its benefits that allow for recursive multiplication of encrypted dynamic systems, without use of computationally expensive bootstrapping techniques.