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Maximal Guesswork Leakage

Gowtham R. Kurri, Malhar Managoli, Vinod M. Prabhakaran

TL;DR

The paper develops a guessing-based framework for information leakage, introducing maximal guesswork leakage and its pointwise and oblivious variants. By exploiting Rényi information measures, it derives closed-form expressions for several leakage notions, including a complete solution for the binary erasure source, and reveals a tight connection to differential privacy and maximal $\alpha$-leakage. It also establishes an operational interpretation of oblivious maximal $\rho$-guesswork leakage in terms of Arimoto information and channel capacity, while identifying sharp local bounds via the pointwise and pw-oblivious forms. The results bridge guessing frameworks with privacy notions, providing precise characterizations and guiding principles for leakage analysis in secure data releases and privacy-preserving systems.

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 $α$-leakage in terms of guesswork.

Maximal Guesswork Leakage

TL;DR

The paper develops a guessing-based framework for information leakage, introducing maximal guesswork leakage and its pointwise and oblivious variants. By exploiting Rényi information measures, it derives closed-form expressions for several leakage notions, including a complete solution for the binary erasure source, and reveals a tight connection to differential privacy and maximal -leakage. It also establishes an operational interpretation of oblivious maximal -guesswork leakage in terms of Arimoto information and channel capacity, while identifying sharp local bounds via the pointwise and pw-oblivious forms. The results bridge guessing frameworks with privacy notions, providing precise characterizations and guiding principles for leakage analysis in secure data releases and privacy-preserving systems.

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 , of the guesswork of a randomized function of , 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 . 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 -leakage in terms of guesswork.
Paper Structure (12 sections, 7 theorems, 79 equations)

This paper contains 12 sections, 7 theorems, 79 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Rényi Information Measures
  4. Guesswork
  5. Maximal Leakage
  6. Maximal Guesswork Leakage
  7. Oblivious Maximal $\rho$-Guesswork Leakage
  8. Acknowledgment
  9. Proof of Theorem \ref{['thm:pointwiseleakagewithh']}
  10. Proof of Theorem \ref{['theorem:BES']}
  11. Proof of Theorem \ref{['thm:obmgl']}
  12. Proof of Theorem \ref{['thm:pwrhoguesleak']}

Key Result

Theorem 1

For any joint probability distribution $P_{XY}$ on a finite alphabet $\mathcal{X}\times\mathcal{Y}$, the pointwise maximal guesswork leakage from $X$ to $y\in\emph{supp}(Y)$ is given by

Theorems & Definitions (28)

  • Definition 1: Rényi divergence renyi1961measures
  • Definition 2: Arimoto mutual information arimoto1977information
  • Definition 3: Guesswork massey1994guessingpliam1998disparity
  • Definition 4: Maximal leakageIssaWK20
  • Definition 5: Maximal guesswork leakage
  • Remark 1
  • Definition 6: Pointwise maximal guesswork leakage
  • Remark 2
  • Theorem 1: Pointwise maximal guesswork leakage
  • Theorem 2
  • ...and 18 more