Differential privacy for symmetric log-concave mechanisms

TL;DR

This paper extends the understanding of differential privacy by establishing necessary and sufficient conditions for symmetric log-concave noise distributions, enabling more efficient privacy-preserving mechanisms with lower error.

Contribution

It provides a comprehensive condition for $(psilon, elta)$-differential privacy applicable to all symmetric log-concave distributions, improving privacy-utility trade-offs.

Findings

Allows tailored noise distributions based on query dimensionality.

Achieves significantly lower mean squared errors than Laplace and Gaussian mechanisms.

Enhances privacy mechanisms with more efficient noise addition.

Abstract

Adding random noise to database query results is an important tool for achieving privacy. A challenge is to minimize this noise while still meeting privacy requirements. Recently, a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for Gaussian noise was published. This condition allows the computation of the minimum privacy-preserving scale for this distribution. We extend this work and provide a sufficient and necessary condition for $(\epsilon, \delta)$-differential privacy for all symmetric and log-concave noise densities. Our results allow fine-grained tailoring of the noise distribution to the dimensionality of the query result. We demonstrate that this can yield significantly lower mean squared errors than those incurred by the currently used Laplace and Gaussian mechanisms for the same $\epsilon$ and $\delta$.