Robustness of Maximal $\alpha$-Leakage to Side Information

TL;DR

This paper introduces conditional maximal $ extalpha$-leakage to analyze how side information affects information leakage, showing it cannot increase leakage if the side info is conditionally independent of public data given private data.

Contribution

It defines conditional maximal $ extalpha$-leakage and proves its properties, including the impact of side information independence on leakage.

Findings

Conditional maximal $ extalpha$-leakage is the supremum of the conditional Arimoto channel capacity.

Side information independent of public data given private data does not increase leakage.

The measure interpolates between log-loss and probability of error based on $ extalpha$.

Abstract

Maximal $\alpha$-leakage is a tunable measure of information leakage based on the accuracy of guessing an arbitrary function of private data based on public data. The parameter $\alpha$ determines the loss function used to measure the accuracy of a belief, ranging from log-loss at $\alpha=1$ to the probability of error at $\alpha=\infty$. To study the effect of side information on this measure, we introduce and define conditional maximal $\alpha$-leakage. We show that, for a chosen mapping (channel) from the actual (viewed as private) data to the released (public) data and some side information, the conditional maximal $\alpha$-leakage is the supremum (over all side information) of the conditional Arimoto channel capacity where the conditioning is on the side information. We prove that if the side information is conditionally independent of the public data given the private data, the side information cannot increase the information leakage.