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arXiv · 1806.03332

A Tunable Measure for Information Leakage

Jiachun Liao·Oliver Kosut·Lalitha Sankar·Flavio P. Calmon
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Abstract

A tunable measure for information leakage called \textit{maximal $\alpha$-leakage} is introduced. This measure quantifies the maximal gain of an adversary in refining a tilted version of its prior belief of any (potentially random) function of a dataset conditioning on a disclosed dataset. The choice of $\alpha$ determines the specific adversarial action ranging from refining a belief for $\alpha =1$ to guessing the best posterior for $\alpha = \infty$, and for these extremal values this measure simplifies to mutual information (MI) and maximal leakage (MaxL), respectively. For all other $\alpha$ this measure is shown to be the Arimoto channel capacity. Several properties of this measure are proven including: (i) quasi-convexity in the mapping between the original and disclosed datasets; (ii) data processing inequalities; and (iii) a composition property.

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Jiachun Liao, Oliver Kosut, Lalitha Sankar, Flavio P. Calmon. 2018-06-08. A Tunable Measure for Information Leakage. https://arxiv.org/abs/1806.03332

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