Evaluating Differential Privacy on Correlated Datasets Using Pointwise Maximal Leakage

TL;DR

This paper critically examines the limitations of differential privacy when applied to correlated datasets, using pointwise maximal leakage to quantify potential privacy risks and revealing that DP guarantees can be arbitrarily weak in such scenarios.

Contribution

It introduces a novel analysis of DP's effectiveness on correlated data using PML, demonstrating that DP can be nearly as weak as releasing data without perturbation.

Findings

DP guarantees can be arbitrarily weak for correlated datasets

Pure DP mechanisms can have PML levels close to unperturbed data release

Highlights the need for more robust privacy mechanisms for correlated data

Abstract

Data-driven advancements significantly contribute to societal progress, yet they also pose substantial risks to privacy. In this landscape, differential privacy (DP) has become a cornerstone in privacy preservation efforts. However, the adequacy of DP in scenarios involving correlated datasets has sometimes been questioned and multiple studies have hinted at potential vulnerabilities. In this work, we delve into the nuances of applying DP to correlated datasets by leveraging the concept of pointwise maximal leakage (PML) for a quantitative assessment of information leakage. Our investigation reveals that DP's guarantees can be arbitrarily weak for correlated databases when assessed through the lens of PML. More precisely, we prove the existence of a pure DP mechanism with PML levels arbitrarily close to that of a mechanism which releases individual entries from a database without any perturbation. By shedding light on the limitations of DP on correlated datasets, our work aims to foster a deeper understanding of subtle privacy risks and highlight the need for the development of more effective privacy-preserving mechanisms tailored to diverse scenarios.