Gaussian Mechanisms Against Statistical Inference: Synthesis Tools

TL;DR

This paper develops semidefinite programming tools to design Gaussian mechanisms that maximize privacy by minimizing information leakage while maintaining data utility through controlled distortion.

Contribution

It introduces a novel synthesis framework for Gaussian privacy mechanisms using semidefinite programs to optimize privacy-utility trade-offs.

Findings

Effective Gaussian mechanisms synthesized for privacy preservation.

Framework minimizes mutual information between private data and disclosures.

Tools applicable to various privacy-preserving data release scenarios.

Abstract

In this manuscript, we provide a set of tools (in terms of semidefinite programs) to synthesize Gaussian mechanisms to maximize privacy of databases. Information about the database is disclosed through queries requested by (potentially) adversarial users. We aim to keep part of the database private (private sensitive information); however, disclosed data could be used to estimate private information. To avoid an accurate estimation by the adversaries, we pass the requested data through distorting (privacy-preserving) mechanisms before transmission and send the distorted data to the user. These mechanisms consist of a coordinate transformation and an additive dependent Gaussian vector. We formulate the synthesis of distorting mechanisms in terms of semidefinite programs in which we seek to minimize the mutual information (our privacy metric) between private data and the disclosed distorted data given a desired distortion level -- how different actual and distorted data are allowed to be.