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We introduce a family of information leakage measures called maximal$(\alpha,\beta)$-leakage (M$\alpha$beL), parameterized by real numbers $\alpha$and $\beta$ greater than or equal to 1. The measure is formalized via anoperational definition involving an adversary guessing an unknown (randomized)function of the data given the released data. We obtain a simplified computableexpression for the measure and show that it satisfies several basic propertiessuch as monotonicity in $\beta$ for a fixed $\alpha$, non-negativity, dataprocessing inequalities, and additivity over independent releases. We highlightthe relevance of this family by showing that it bridges several known leakagemeasures, including maximal $\alpha$-leakage $(\beta=1)$, maximal leakage$(\alpha=\infty,\beta=1)$, local differential privacy (LDP)$(\alpha=\infty,\beta=\infty)$, and local Renyi differential privacy (LRDP)$(\alpha=\beta)$, thereby giving an operational interpretation to local Renyidifferential privacy. We also study a conditional version of M$\alpha$beL onleveraging which we recover differential privacy and Renyi differentialprivacy. A new variant of LRDP, which we call maximal Renyi leakage, appears asa special case of M$\alpha$beL for $\alpha=\infty$ that smoothly tunes betweenmaximal leakage ($\beta=1$) and LDP ($\beta=\infty$). Finally, we show that avector form of the maximal Renyi leakage relaxes differential privacy underGaussian and Laplacian mechanisms.

Unifying Privacy Measures via Maximal $(\alpha,\beta)$-Leakage (M$\alpha$beL)