  In this paper, we study the fundamental limits of obfuscation in terms of
privacy-distortion tradeoffs for linear Gaussian dynamical systems via an
information-theoretic approach. Particularly, we obtain analytical formulas
that capture the fundamental privacy-distortion tradeoffs when privacy masks
are to be added to the outputs of the dynamical systems, while indicating
explicitly how to design the privacy masks in an optimal way: The privacy masks
should be colored Gaussian with power spectra shaped specifically based upon
the system and noise properties.
