Lower Bounds for R\'enyi Differential Privacy in a Black-Box Setting

TL;DR

This paper introduces a novel black-box approach to assess Renyi Differential Privacy by developing a divergence estimator and statistical lower bounds, applicable to various algorithms, with demonstrated effectiveness through experiments.

Contribution

It presents the first method to evaluate Renyi Differential Privacy in a black-box setting using a new divergence estimator and statistical lower bounds.

Findings

Effective divergence estimator for black-box privacy assessment

Applicable to a broad class of algorithms including privacy-enhancing methods

Validated through experiments on diverse algorithms

Abstract

We present new methods for assessing the privacy guarantees of an algorithm with regard to R\'enyi Differential Privacy. To the best of our knowledge, this work is the first to address this problem in a black-box scenario, where only algorithmic outputs are available. To quantify privacy leakage, we devise a new estimator for the R\'enyi divergence of a pair of output distributions. This estimator is transformed into a statistical lower bound that is proven to hold for large samples with high probability. Our method is applicable for a broad class of algorithms, including many well-known examples from the privacy literature. We demonstrate the effectiveness of our approach by experiments encompassing algorithms and privacy enhancing methods that have not been considered in related works.