  In this paper, we first introduce the notion of channel leakage as the
minimum mutual information between the channel input and channel output. As its
name indicates, channel leakage quantifies the minimum information leakage to
the malicious receiver. In a broad sense, it can be viewed as a dual concept of
channel capacity, which characterizes the maximum information transmission to
the targeted receiver. We obtain explicit formulas of channel leakage for the
white Gaussian case, the colored Gaussian case, and the fading case. We then
utilize this notion to investigate the fundamental limitations of obfuscation
in terms of privacy-distortion tradeoffs (as well as privacy-power tradeoffs)
for streaming data; particularly, we derive analytical tradeoff equations for
the stationary case, the non-stationary case, and the finite-time case. Our
results also indicate explicitly how to design the privacy masks in an optimal
way.
