Quantifying Information Leakage Through Guesswork

Core Concepts

This paper introduces the study of information leakage through guesswork, which is the minimum expected number of guesses required to accurately predict a random variable. The authors define and analyze two key leakage measures: maximal guesswork leakage and pointwise maximal guesswork leakage. They also explore these notions in the context of oblivious (or memoryless) guessing.

Abstract

The paper makes the following key contributions:

Pointwise maximal guesswork leakage is shown to be equal to the Rényi divergence of order infinity between the a priori distribution and the a posteriori distribution. This establishes a connection between guesswork and differential privacy.

A closed-form expression for maximal guesswork leakage is derived for the binary erasure source, though obtaining a general closed-form expression appears challenging.

Oblivious maximal ρ-guesswork leakage is shown to be proportional to the Arimoto channel capacity of order α = 1/(1+ρ), providing a new operational interpretation to maximal α-leakage in terms of guesswork.

Pointwise oblivious maximal ρ-guesswork leakage is shown to be equal to the Rényi divergence of order infinity between the a priori distribution and the a posteriori distribution, independent of the value of ρ.

The paper provides a comprehensive analysis of information leakage measures based on guesswork, with operational interpretations and connections to other information-theoretic quantities.

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Key Insights Distilled From

Maximal Guesswork Leakage

by Gowtham R. K... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02585.pdf

Deeper Inquiries

How can the insights from this work on guesswork-based leakage measures be extended to other operational interpretations of information leakage, such as those based on hypothesis testing or decision-making

The insights from this work on guesswork-based leakage measures can be extended to other operational interpretations of information leakage, such as those based on hypothesis testing or decision-making, by considering the fundamental principles underlying guesswork. Guesswork quantifies the minimum expected number of guesses required to predict a random variable, which can be analogous to the concept of error rates in hypothesis testing. In hypothesis testing, the goal is to make decisions based on observed data, and the error rates (Type I and Type II errors) can be seen as a form of "guesswork" in determining the true state of nature. By drawing parallels between guesswork and error rates, one can develop leakage measures based on the performance of decision-making processes in revealing sensitive information.
Furthermore, the optimization framework used in guesswork-based leakage measures can be adapted to decision-making scenarios. Just as the optimal guessing strategy minimizes the expected number of guesses, optimal decision-making strategies aim to minimize decision errors. By formulating decision-making processes as optimization problems similar to guesswork minimization, one can derive leakage measures that capture the information revealed through decisions made in various contexts.

What are the implications of the connection between guesswork and differential privacy established in this work, and how can it be leveraged in the design of privacy-preserving systems

The connection between guesswork and differential privacy established in this work has significant implications for the design of privacy-preserving systems. Differential privacy aims to protect individuals' data by adding noise to query responses to prevent the disclosure of sensitive information. The relationship between guesswork and differential privacy highlights a new perspective on privacy guarantees in terms of the expected number of guesses required to infer sensitive data.
By leveraging this connection, privacy-preserving systems can be designed to incorporate guesswork-based leakage measures as a metric for evaluating the effectiveness of privacy mechanisms. For example, the minimal expected number of guesses required to predict a random variable can be used as a measure of the system's resilience to inference attacks. Integrating guesswork-based leakage measures into the design and evaluation of differential privacy mechanisms can provide a more intuitive and operationally meaningful way to assess the level of privacy protection offered by these systems.
Additionally, the insights from this work can guide the development of privacy-preserving algorithms that optimize guesswork leakage while maintaining differential privacy guarantees. By balancing the trade-off between minimizing guesswork leakage and preserving differential privacy, system designers can enhance the overall privacy protection provided by their systems.

Can the techniques developed in this paper be applied to study information leakage in other settings, such as interactive protocols or continuous-time systems

The techniques developed in this paper can be applied to study information leakage in other settings, such as interactive protocols or continuous-time systems, by adapting the guesswork framework to suit the specific characteristics of these systems. In interactive protocols, where multiple parties exchange information and make decisions based on shared data, guesswork-based leakage measures can be used to quantify the information revealed at each step of the protocol.
For continuous-time systems, where data is continuously generated and processed over time, guesswork-based leakage measures can be extended to capture the dynamic nature of information disclosure. By modeling the evolution of guesswork over time in continuous-time systems, one can analyze the leakage of information as data streams through the system.
Furthermore, the concept of guesswork can be applied to study information leakage in scenarios involving feedback mechanisms, where the adversary's guesses are influenced by previous observations. By incorporating memory and feedback into the guesswork framework, researchers can develop leakage measures that account for the dynamic and iterative nature of information disclosure in these settings.