Gaussian Data Privacy Under Linear Function Recoverability

TL;DR

This paper analyzes how to maximize user data privacy when responding to linear function queries on Gaussian data, ensuring recoverability with prescribed accuracy, and provides an optimal scheme matching theoretical bounds.

Contribution

It offers an exact characterization of maximum privacy under recoverability constraints and presents an explicit optimal scheme that achieves this bound.

Findings

Maximum privacy characterized exactly under linear recoverability.

An explicit optimal scheme matches the theoretical upper bound.

Provides a practical method for privacy-preserving data responses.

Abstract

A user's data is represented by a Gaussian random variable. Given a linear function of the data, a querier is required to recover, with at least a prescribed accuracy level, the function value based on a query response provided by the user. The user devises the query response, subject to the recoverability requirement, so as to maximize privacy of the data from the querier. Recoverability and privacy are both measured by $\ell_2$-distance criteria. An exact characterization is provided of maximum user data privacy under the recoverability condition. An explicit optimal achievability scheme for the user is given whose privacy is shown to match a converse upper bound.