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.

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