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

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