An Alphabet of Leakage Measures
Atefeh Gilani
Abstract:
We introduce a family of information leakage measures called emph{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 R'{enyi} differential privacy $(alpha=beta)$.