$\alpha$-leakage by R\'{e}nyi Divergence and Sibson Mutual Information

Ni Ding; Mohammad Amin Zarrabian; Parastoo Sadeghi

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arXiv · 2405.00423

$\alpha$-leakage by R\'{e}nyi Divergence and Sibson Mutual Information

Ni Ding·Mohammad Amin Zarrabian·Parastoo Sadeghi

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Abstract

For $\tilde{f}(t) = \exp(\frac{\alpha-1}{\alpha}t)$, this paper proposes a $\tilde{f}$-mean information gain measure. R\'{e}nyi 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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Ni Ding, Mohammad Amin Zarrabian, Parastoo Sadeghi. 2024-05-01. $\alpha$-leakage by R\'{e}nyi Divergence and Sibson Mutual Information. https://arxiv.org/abs/2405.00423

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