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

2017/10/03 by Sean Weerakkody, Weerakkody, Sean, Omur Ozel +3
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Electrical engineering #Security in Wireless Sensor Networks #Smart Grid Security and Resilience #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1710.01105

openalex publication_date 2017/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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