Data Privacy for a $\rho$-Recoverable Function

TL;DR

This paper investigates how to design query responses that allow a querier to recover a function of user data with high probability while maximizing the user's privacy, using explicit randomization mechanisms.

Contribution

It introduces a framework for optimizing privacy in $ ho$-recoverable functions through explicit schemes and analyzes single and multiple query scenarios.

Findings

Explicit randomization mechanisms achieve near-optimal privacy.

Multiple queries can enhance privacy under the $ ho$-recoverability constraint.

The framework applies to predicate privacy of user data.

Abstract

A user's data is represented by a finite-valued random variable. Given a function of the data, a querier is required to recover, with at least a prescribed probability, the value of the function 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. Privacy is measured by the probability of error incurred by the querier in estimating the data from the query response. We analyze single and multiple independent query responses, with each response satisfying the recoverability requirement, that provide maximum privacy to the user. In the former setting, we also consider privacy for a predicate of the user's data. Achievability schemes with explicit randomization mechanisms for query responses are given and their privacy compared with converse upper bounds.