Fundamental Stealthiness-Distortion Tradeoffs in Dynamical Systems under Injection Attacks: A Power Spectral Analysis

TL;DR

This paper investigates the fundamental tradeoffs between stealthiness and distortion in linear Gaussian dynamical systems under injection attacks, using power spectral analysis and KL divergence to characterize worst-case attack strategies.

Contribution

It provides explicit formulas linking power spectra to stealthiness-distortion tradeoffs and reveals that attackers only need system input-output knowledge for worst-case attacks.

Findings

Explicit formulas for stealthiness-distortion tradeoffs

Worst-case attack properties characterized analytically

Attackers require only input-output behavior knowledge

Abstract

In this paper, we analyze the fundamental stealthiness-distortion tradeoffs of linear Gaussian dynamical systems under data injection attacks using a power spectral analysis, whereas the Kullback-Leibler (KL) divergence is employed as the stealthiness measure. Particularly, we obtain explicit formulas in terms of power spectra that characterize analytically the stealthiness-distortion tradeoffs as well as the properties of the worst-case attacks. Furthermore, it is seen in general that the attacker only needs to know the input-output behaviors of the systems in order to carry out the worst-case attacks.