Linear and Range Counting under Metricbased Local Differential Privacy
Abstract
Local differential privacy (LDP) enables private data sharing and analytics without the need for a trusted data collector. Erroroptimal primitives (for, e.g., estimating means and item frequencies) under LDP have been well studied. For analytical tasks such as range queries, however, the best known error bound is dependent on the domain size of private data, which is potentially prohibitive. This deficiency is inherent as LDP protects the same level of indistinguishability between any pair of private data values for each data downer. In this paper, we utilize an extension of $\epsilon$LDP called MetricLDP or $E$LDP, where a metric $E$ defines heterogeneous privacy guarantees for different pairs of private data values and thus provides a more flexible knob than $\epsilon$ does to relax LDP and tune utilityprivacy tradeoffs. We show that, under such privacy relaxations, for analytical workloads such as linear counting, multidimensional range counting queries, and quantile queries, we can achieve significant gains in utility. In particular, for range queries under $E$LDP where the metric $E$ is the $L^1$distance function scaled by $\epsilon$, we design mechanisms with errors independent on the domain sizes; instead, their errors depend on the metric $E$, which specifies in what granularity the private data is protected. We believe that the primitives we design for $E$LDP will be useful in developing mechanisms for other analytical tasks, and encourage the adoption of LDP in practice.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.11778
 Bibcode:
 2019arXiv190911778X
 Keywords:

 Computer Science  Cryptography and Security;
 Computer Science  Data Structures and Algorithms