An Alphabet of Leakage Measures

We introduce a family of information leakage measures called maximal ?, ?-leakage, parameterized by real numbers ? and ?. 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 ? for a fixed ?, 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 ?-leakage (? = 1), maximal leakage (? = ?, ? = 1), local differential privacy (? = ?, ? = ?), and local Renyi differential privacy (? = ?).