Locality Sensitive Hashing with Extended Differential Privacy
Natasha Fernandes, Yusuke Kawamoto, Takao Murakami

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…
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