Non-Stochastic Private Function Evaluation

TL;DR

This paper introduces a novel framework for private function evaluation that balances privacy and utility through perfect and almost perfect privacy concepts, extending to multi-party scenarios and leveraging quantization techniques.

Contribution

It defines perfect and almost perfect privacy for private function evaluation, generalizes to multi-party settings, and proposes quantization-based privacy guarantees.

Findings

Perfect privacy achieved for functions of common uncertain variables.

Almost perfect privacy uses conditional disassociation for better utility.

Quantization of responses ensures privacy proportional to privacy budget.

Abstract

We consider private function evaluation to provide query responses based on private data of multiple untrusted entities in such a way that each cannot learn something substantially new about the data of others. First, we introduce perfect non-stochastic privacy in a two-party scenario. Perfect privacy amounts to conditional unrelatedness of the query response and the private uncertain variable of other individuals conditioned on the uncertain variable of a given entity. We show that perfect privacy can be achieved for queries that are functions of the common uncertain variable, a generalization of the common random variable. We compute the closest approximation of the queries that do not take this form. To provide a trade-off between privacy and utility, we relax the notion of perfect privacy. We define almost perfect privacy and show that this new definition equates to using conditional disassociation instead of conditional unrelatedness in the definition of perfect privacy. Then, we generalize the definitions to multi-party function evaluation (more than two data entities). We prove that uniform quantization of query responses, where the quantization resolution is a function of privacy budget and sensitivity of the query (cf., differential privacy), achieves function evaluation privacy.