$α$-leakage by Rényi Divergence and Sibson Mutual Information
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909240310890496 |
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| author | Ding, Ni Zarrabian, Mohammad Amin Sadeghi, Parastoo |
| author_facet | Ding, Ni Zarrabian, Mohammad Amin Sadeghi, Parastoo |
| contents | For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, 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 $α$-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing $α$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $α$-leakage by Rényi Divergence and Sibson Mutual Information Ding, Ni Zarrabian, Mohammad Amin Sadeghi, Parastoo Information Theory For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, 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 $α$-leakage measures, indicating the most information an adversary can obtain on sensitive data. It is shown that the existing $α$-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. |
| title | $α$-leakage by Rényi Divergence and Sibson Mutual Information |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.00423 |