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Channel Leakage Information-Theoretic Limitations of Obfuscation and Optimal Privacy Mask Design for Streaming Data

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Document pages: 31 pages

Abstract: In this paper, we first introduce the notion of channel leakage as theminimum mutual information between the channel input and channel output. As itsname indicates, channel leakage quantifies the minimum information leakage tothe malicious receiver. In a broad sense, it can be viewed as a dual concept ofchannel capacity, which characterizes the maximum information transmission tothe targeted receiver. We obtain explicit formulas of channel leakage for thewhite Gaussian case, the colored Gaussian case, and the fading case. We thenutilize this notion to investigate the fundamental limitations of obfuscationin terms of privacy-distortion tradeoffs (as well as privacy-power tradeoffs)for streaming data; particularly, we derive analytical tradeoff equations forthe stationary case, the non-stationary case, and the finite-time case. Ourresults also indicate explicitly how to design the privacy masks in an optimalway.

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