Locality Sensitive Hashing with Extended Differential Privacy

Extended differential privacy, which is a generalization of standard differential privacy (DP) using a general metric rather than the Hamming metric, has been widely studied to provide rigorous privacy guarantees while keeping high utility. However, existing works on extended DP focus on a specific metric such as the Euclidean metric and the Earth Mover's metric, and cannot be applied to other metrics. Consequently, existing extended DP mechanisms are limited to a small number of applications such as location-based services and document processing. In this paper, we propose a new mechanism providing extended DP with a wide range of metrics. Our mechanism is based on locality sensitive hashing (LSH) and the randomized response, and can be applied to metrics including the angular distance (or cosine) metric, Jaccard metric, Earth Mover's metric, and $l_p$ metric. Moreover, our mechanism works well for personal data in a high-dimensional space. We theoretically analyze the privacy property of our mechanism, and prove that it provides concentrated and probabilistic versions of extended DP. Then we apply our mechanism to friend matching based on personal data in a high-dimensional space with an angular distance metric. We show through experiments that our mechanism provides much higher utility than the multivariate Laplace mechanism, and makes possible friend matching with rigorous privacy guarantees and high utility.