List Privacy Under Function Recoverability

TL;DR

This paper investigates how to maximize privacy when releasing function-based query responses, providing bounds and schemes that balance data utility with privacy guarantees.

Contribution

It introduces a general upper bound on list privacy and demonstrates its tightness for binary functions using an add-noise scheme.

Findings

Established a tight upper bound for list privacy.

Designed an explicit add-noise scheme achieving optimal privacy.

Provided theoretical insights into privacy-utility trade-offs.

Abstract

For a given function of user data, a querier must recover with at least a prescribed probability, the value of the function based on a user-provided query response. Subject to this requirement, the user forms the query response so as to minimize the likelihood of the querier guessing a list of prescribed size to which the data value belongs based on the query response. We obtain a general converse upper bound for maximum list privacy. This bound is shown to be tight for the case of a binary-valued function through an explicit achievability scheme that involves an add-noise query response.