Maximal Guesswork Leakage

TL;DR

This paper explores information leakage through guesswork, defining maximal guesswork leakage, deriving closed-form expressions for certain sources, and connecting these concepts to differential privacy and maximal α-leakage.

Contribution

It introduces the concept of maximal guesswork leakage, provides closed-form formulas for specific sources, and links guesswork-based leakage to differential privacy and α-leakage.

Findings

Closed-form expressions for guesswork leakage in binary erasure sources.

Maximal guesswork leakage quantifies information leakage via guesswork reduction.

Connections established between guesswork, differential privacy, and α-leakage.

Abstract

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.