Bounding data reconstruction attacks with the hypothesis testing interpretation of differential privacy

TL;DR

This paper establishes a connection between hypothesis testing differential privacy and Reconstruction Robustness, deriving explicit bounds for common DP mechanisms, enhancing understanding of privacy guarantees against data reconstruction attacks.

Contribution

It introduces a new analytical framework linking hypothesis testing DP to ReRo, providing closed-form bounds for Laplace and Gaussian mechanisms.

Findings

Derived ReRo bounds for Laplace and Gaussian mechanisms

Connected hypothesis testing DP with data reconstruction robustness

Provided explicit bounds for subsampled DP mechanisms

Abstract

We explore Reconstruction Robustness (ReRo), which was recently proposed as an upper bound on the success of data reconstruction attacks against machine learning models. Previous research has demonstrated that differential privacy (DP) mechanisms also provide ReRo, but so far, only asymptotic Monte Carlo estimates of a tight ReRo bound have been shown. Directly computable ReRo bounds for general DP mechanisms are thus desirable. In this work, we establish a connection between hypothesis testing DP and ReRo and derive closed-form, analytic or numerical ReRo bounds for the Laplace and Gaussian mechanisms and their subsampled variants.