Fundamental Limits of Obfuscation for Linear Gaussian Dynamical Systems: An Information-Theoretic Approach

TL;DR

This paper investigates the theoretical limits of privacy preservation in linear Gaussian dynamical systems using information theory, deriving formulas for optimal privacy masks that balance privacy and distortion.

Contribution

It provides analytical formulas for privacy-distortion tradeoffs and guides the design of optimal colored Gaussian privacy masks based on system properties.

Findings

Derived explicit formulas for privacy-distortion tradeoffs.

Optimal privacy masks are colored Gaussian with specific power spectra.

Guidelines for designing privacy masks tailored to system and noise characteristics.

Abstract

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.