A Generalized Leakage Interpretation of Alpha-Mutual Information

Abstract

This paper presents a unified interpretation of $\hat{I}\pm$-mutual information ($\hat{I}\pm$-MI) in terms of generalized $g$-leakage. Specifically, we present a novel interpretation of $\hat{I}\pm$-MI within an extended framework for quantitative information flow based on adversarial generalized decision problems. This framework employs the Kolmogorov-Nagumo mean and the $q$-logarithm to characterize adversarial gain. Furthermore, we demonstrate that, within this framework, the parameter $\hat{I}\pm$ can be interpreted as a measure of the adversary's risk aversion.