An Online Approach to Physical Watermark Design

Hanxiao Liu,Karl H. ohansson,Yilin Mo,Lihua Xie,Jiaqi Yan

doi:10.1109/tac.2020.2971994

Abstract

This paper considers the problem of designing physical watermark signals in order to optimally detect possible replay attack in a linear time-invariant system, under the assumption that the system parameters are unknown and need to be identified online. We first provide a replay attack model, where an adversary replays the previous sensor data in order to fool the system. A physical watermarking scheme, which leverages a random control input as a watermark to detect the replay attack, is then introduced. The optimal watermark signal design problem is cast as an optimization problem, which aims to achieve the optimal trade-off between control performance and intrusion detection. An online watermarking design and system identification algorithm is provided to deal with systems with unknown parameters. We prove that the proposed algorithm converges to the optimal one and characterize the almost sure convergence rate. A numerical example and an industrial process example are provided to illustrate the effectiveness of the proposed strategy.

Highlights

C YBER-Physical Systems (CPSs) offer close integration of computational elements and physical processes [1]
The main differences between the current version of the paper and [26] are: 1) we prove that we can asymptotically identify the system parameters, and characterize the rate of the convergence; 2) we provide a procedure to automatically generate the Neyman-Pearson detector; 3) we add the simulation on an industrial process to verify the effectiveness of the proposed approach
2) We prove that the system parameters which are inferred via our proposed online algorithm converge to the true parameters almost surely even if the input signal asymptotically converges to a degenerate signal

Summary

Introduction

C YBER-Physical Systems (CPSs) offer close integration of computational elements and physical processes [1] They are defined as systems where “physical and software components are deeply intertwined, each operating on different spatial and temporal scales, exhibiting multiple and distinct behavioral modalities, and interacting with each other in a myriad of ways that change with context” [2]. Such systems play a critical role in large varieties of fields, such as manufacturing, health care, environment control, transportation, etc. This incident raised a great deal of attention to CPS security in recent years [7]

Objectives

Results

Conclusion