An Alphabet of Leakage 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 $(\alpha =\beta )$.