$\alpha$-leakage by Rényi Divergence and Sibson Mutual Information

Abstract

For $\tilde{f}(t)=\exp (\frac{\alpha -1}{\alpha }t)$, this paper proposes a $\tilde{f}$-mean information gain measure. Rényi divergence is shown to be the maximum $\tilde{f}$-mean information gain incurred at each elementary event $y$ of channel output $Y$ and Sibson mutual information is the $\tilde{f}$-mean of this $Y$-elementary information gain. Both are proposed as $\alpha$-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing $\alpha$-leakage by Arimoto mutual information can be expressed as $\tilde{f}$-mean measures by a scaled probability. Further, Sibson mutual information is interpreted as the maximum $\tilde{f}$-mean information gain over all estimation decisions applied to channel output.

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