Maximal Guesswork Leakage
<|reference_start|>Maximal Guesswork Leakage: 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 $\alpha$-leakage in terms of guesswork.<|reference_end|>
@article{kurri2024maximal,
    title={Maximal Guesswork Leakage},
    author={Gowtham R. Kurri, Malhar Managoli, Vinod M. Prabhakaran},
    journal={arXiv preprint arXiv:2405.02585},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.02585},
    primaryClass={cs.IT math.IT}
}