A Tunable Measure for Information Leakage

TL;DR

This paper introduces maximal α-leakage, a tunable information leakage measure that generalizes mutual information and maximal leakage, with properties useful for privacy analysis.

Contribution

The paper proposes a new flexible leakage measure called maximal α-leakage, unifying existing metrics and establishing its key theoretical properties.

Findings

Maximal α-leakage interpolates between mutual information and maximal leakage.

The measure is shown to be quasi-convex, satisfy data processing inequalities, and have a composition property.

It is characterized as the Arimoto channel capacity for intermediate α values.

Abstract

A tunable measure for information leakage called \textit{maximal $\alpha$-leakage} is introduced. This measure quantifies the maximal gain of an adversary in refining a tilted version of its prior belief of any (potentially random) function of a dataset conditioning on a disclosed dataset. The choice of $\alpha$ determines the specific adversarial action ranging from refining a belief for $\alpha =1$ to guessing the best posterior for $\alpha = \infty$, and for these extremal values this measure simplifies to mutual information (MI) and maximal leakage (MaxL), respectively. For all other $\alpha$ this measure is shown to be the Arimoto channel capacity. Several properties of this measure are proven including: (i) quasi-convexity in the mapping between the original and disclosed datasets; (ii) data processing inequalities; and (iii) a composition property.