(α,β)-Leakage: A Unified Privacy Leakage Measure
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We introduce a family of information leakage measures called maximal (α,β)-leakage, parameterized by non-negative real numbers α and β. The measure is formalized via an operational definition involving an adversary guessing an unknown (randomized) function of the data given the released data. We obtain a simplified computable expression for the measure and show that it satisfies several basic properties such as monotonicity in β for a fixed α, non-negativity, data processing inequalities, and additivity over independent releases. We highlight the relevance of this family by showing that it bridges several known leakage measures, including maximal α-leakage (β=1), maximal leakage (α=∞,β=1), local differential privacy [LDP] (α=∞,β=∞), and local Renyi differential privacy [LRDP] (α=β), thereby giving an operational interpretation to local Renyi differential privacy. We also study a conditional version of maximal (α,β)-leakage on leveraging which we recover differential privacy and Renyi differential privacy. A new variant of LRDP, which we call maximal Renyi leakage, appears as a special case of maximal (α,β)-leakage for α=∞ that smoothly tunes between maximal leakage (β=1) and LDP (β=∞). Finally, we show that a vector form of the maximal Renyi leakage relaxes differential privacy under Gaussian and Laplacian mechanisms.
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