$α$-leakage Interpretation of Rényi Capacity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915538787106816 |
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| author | Ding, Ni Farokhi, Farhad Guo, Tao Xu, Yinfei Zhang, Xiang |
| author_facet | Ding, Ni Farokhi, Farhad Guo, Tao Xu, Yinfei Zhang, Xiang |
| contents | For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, this paper shows that the Sibson mutual information is an $α$-leakage averaged over the adversary's $\tilde{f}$-mean relative information gain (on the secret) at elementary event of channel output $Y$ as well as the joint occurrence of elementary channel input $X$ and output $Y$. This interpretation is used to derive a sufficient condition that achieves a $δ$-approximation of $ε$-upper bounded $α$-leakage. A $Y$-elementary $α$-leakage is proposed, extending the existing pointwise maximal leakage to the overall Rényi order range $α\in [0,\infty)$. Maximizing this $Y$-elementary leakage over all attributes $U$ of channel input $X$ gives the Rényi divergence. Further, the Rényi capacity is interpreted as the maximal $\tilde{f}$-mean information leakage over both the adversary's malicious inference decision and the channel input $X$ (represents the adversary's prior belief). This suggests an alternating max-max implementation of the existing generalized Blahut-Arimoto method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_06622 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $α$-leakage Interpretation of Rényi Capacity Ding, Ni Farokhi, Farhad Guo, Tao Xu, Yinfei Zhang, Xiang Information Theory For $\tilde{f}(t) = \exp(\frac{α-1}αt)$, this paper shows that the Sibson mutual information is an $α$-leakage averaged over the adversary's $\tilde{f}$-mean relative information gain (on the secret) at elementary event of channel output $Y$ as well as the joint occurrence of elementary channel input $X$ and output $Y$. This interpretation is used to derive a sufficient condition that achieves a $δ$-approximation of $ε$-upper bounded $α$-leakage. A $Y$-elementary $α$-leakage is proposed, extending the existing pointwise maximal leakage to the overall Rényi order range $α\in [0,\infty)$. Maximizing this $Y$-elementary leakage over all attributes $U$ of channel input $X$ gives the Rényi divergence. Further, the Rényi capacity is interpreted as the maximal $\tilde{f}$-mean information leakage over both the adversary's malicious inference decision and the channel input $X$ (represents the adversary's prior belief). This suggests an alternating max-max implementation of the existing generalized Blahut-Arimoto method. |
| title | $α$-leakage Interpretation of Rényi Capacity |
| topic | Information Theory |
| url | https://arxiv.org/abs/2510.06622 |