An Alphabet of Leakage Measures

TL;DR

This paper introduces a comprehensive family of information leakage measures called maximal α,β-leakage, unifying various existing privacy metrics and providing a simple, computable expression with desirable properties.

Contribution

It formalizes a new family of leakage measures parameterized by α and β, connecting and generalizing several known privacy measures.

Findings

Provides a simple, computable expression for maximal α,β-leakage.

Establishes properties like monotonicity, non-negativity, and data processing inequalities.

Shows the measure bridges multiple existing leakage and privacy measures.

Abstract

We introduce a family of information leakage measures called maximal $\alpha,\beta$-leakage, parameterized by real numbers $\alpha$ and $\beta$. The measure is formalized via an operational definition involving an adversary guessing an unknown function of the data given the released data. We obtain a simple, computable expression for the measure and show that it satisfies several basic properties such as monotonicity in $\beta$ for a fixed $\alpha$, non-negativity, data processing inequalities, and additivity over independent releases. Finally, we highlight the relevance of this family by showing that it bridges several known leakage measures, including maximal $\alpha$-leakage $(\beta=1)$, maximal leakage $(\alpha=\infty,\beta=1)$, local differential privacy $(\alpha=\infty,\beta=\infty)$, and local Renyi differential privacy $(\alpha=\beta)$.