Maximal Guesswork Leakage
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913341315743744 |
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| author | Kurri, Gowtham R. Managoli, Malhar Prabhakaran, Vinod M. |
| author_facet | Kurri, Gowtham R. Managoli, Malhar Prabhakaran, Vinod M. |
| contents | We introduce the study of information leakage through \emph{guesswork}, the minimum expected number of guesses required to guess a random variable. In particular, we define \emph{maximal guesswork leakage} as the multiplicative decrease, upon observing $Y$, of the guesswork of a randomized function of $X$, maximized over all such randomized functions. We also study a pointwise form of the leakage which captures the leakage due to the release of a single realization of $Y$. We also study these two notions of leakage with oblivious (or memoryless) guessing. We obtain closed-form expressions for all these leakage measures, with the exception of one. Specifically, we are able to obtain closed-form expression for maximal guesswork leakage for the binary erasure source only; deriving expressions for arbitrary sources appears challenging. Some of the consequences of our results are -- a connection between guesswork and differential privacy and a new operational interpretation to maximal $α$-leakage in terms of guesswork. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal Guesswork Leakage Kurri, Gowtham R. Managoli, Malhar Prabhakaran, Vinod M. Information Theory We introduce the study of information leakage through \emph{guesswork}, the minimum expected number of guesses required to guess a random variable. In particular, we define \emph{maximal guesswork leakage} as the multiplicative decrease, upon observing $Y$, of the guesswork of a randomized function of $X$, maximized over all such randomized functions. We also study a pointwise form of the leakage which captures the leakage due to the release of a single realization of $Y$. We also study these two notions of leakage with oblivious (or memoryless) guessing. We obtain closed-form expressions for all these leakage measures, with the exception of one. Specifically, we are able to obtain closed-form expression for maximal guesswork leakage for the binary erasure source only; deriving expressions for arbitrary sources appears challenging. Some of the consequences of our results are -- a connection between guesswork and differential privacy and a new operational interpretation to maximal $α$-leakage in terms of guesswork. |
| title | Maximal Guesswork Leakage |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.02585 |