Design of multiplicative watermarking against covert attacks

TL;DR

This paper proposes a multiplicative watermarking method for detecting covert cyberattacks, formulating an optimal yet non-convex design problem and providing a practical LMI-based solution to ensure attack detectability.

Contribution

It introduces a novel watermarking design framework based on output-to-output l2-gain, with an algorithm to design filters that bound the gain against covert attacks.

Findings

Watermarking makes the output-to-output l2-gain bounded under attack.

Without watermarking, the gain is unbounded, enabling covert attacks.

The proposed LMI-based algorithm provides a practical design approach.

Abstract

This paper addresses the design of an active cyberattack detection architecture based on multiplicative watermarking, allowing for detection of covert attacks. We propose an optimal design problem, relying on the so-called output-to-output l2-gain, which characterizes the maximum gain between the residual output of a detection scheme and some performance output. Although optimal, this control problem is non-convex. Hence, we propose an algorithm to design the watermarking filters by solving the problem suboptimally via LMIs. We show that, against covert attacks, the output-to-output l2-gain is unbounded without watermarking, and we provide a sufficient condition for boundedness in the presence of watermarks.