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.

翻译：我们提出通过*猜测*研究信息泄露，即猜测一个随机变量所需的最小期望猜测次数。具体来说，我们将*最大猜测信息泄露*定义为观察到$Y$后，$X$随机函数猜测的乘性减少量，并在所有此类随机函数上取最大值。我们还研究了一种点态形式的泄露，它捕获了由单个$Y$实现释放引起的泄露。此外，我们研究了具有无记忆（或无状态）猜测的这两种泄露概念。除一种情形外，我们获得了所有泄露测度的闭式表达式。具体而言，我们仅对二元擦除源得到了最大猜测信息泄露的闭式表达式；推导一般源的表达式似乎具有挑战性。我们结果的部分启示包括——猜测与差分隐私之间的联系，以及通过猜测对最大$\alpha$-泄露的一种新的操作解释。