A Bernoulli-Gaussian Physical Watermark for Detecting Integrity Attacks in Control Systems

TL;DR

This paper introduces a combined Bernoulli-Gaussian watermarking approach for control systems that enhances detection of integrity attacks, especially in networks with packet drops, by optimizing watermark parameters.

Contribution

It proposes a novel joint Bernoulli-Gaussian watermark design and optimization framework for improved attack detection in control systems with packet drops.

Findings

Bernoulli packet drops can improve detection performance over pure Gaussian watermarks.

The joint design of Bernoulli-Gaussian watermarks enhances attack detectability.

Numerical results demonstrate the superiority of packet drop-based watermarks.

Abstract

We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the other hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.