Locality Sensitive Hashing with Extended Differential Privacy

TL;DR

This paper introduces mechanisms using locality sensitive hashing to achieve extended differential privacy with angular distance, enabling privacy-preserving friend matching in high-dimensional data.

Contribution

It extends differential privacy to angular distance metrics using LSH, broadening applications beyond Euclidean space with theoretical analysis and practical evaluation.

Findings

Mechanisms provide extended DP with angular distance.

Effective friend matching with high utility under extended DP.

LDP requires large privacy budgets; RAPPOR unsuitable for this task.

Abstract

Extended differential privacy, a generalization of standard differential privacy (DP) using a general metric, has been widely studied to provide rigorous privacy guarantees while keeping high utility. However, existing works on extended DP are limited to few metrics, such as the Euclidean metric. Consequently, they have only a small number of applications, such as location-based services and document processing. In this paper, we propose a couple of mechanisms providing extended DP with a different metric: angular distance (or cosine distance). Our mechanisms are based on locality sensitive hashing (LSH), which can be applied to the angular distance and work well for personal data in a high-dimensional space. We theoretically analyze the privacy properties of our mechanisms, and prove extended DP for input data by taking into account that LSH preserves the original metric only approximately. We apply our mechanisms to friend matching based on high-dimensional personal data with angular distance in the local model, and evaluate our mechanisms using two real datasets. We show that LDP requires a very large privacy budget and that RAPPOR does not work in this application. Then we show that our mechanisms enable friend matching with high utility and rigorous privacy guarantees based on extended DP.