The power of synergy in differential privacy: Combining a small curator with local randomizers

TL;DR

This paper explores a hybrid differential privacy model combining local randomizers with a small trusted curator, demonstrating enhanced capabilities for complex tasks and the necessity of interaction, thus advancing practical privacy-preserving data analysis.

Contribution

It introduces and analyzes the (m,n)-hybrid model, showing its advantages over pure local or curator models and highlighting tasks requiring interaction for differential privacy.

Findings

Hybrid model can solve tasks impossible for local or curator models alone.

Interaction between curator and local users is necessary for certain tasks.

Hybrid approach offers a promising toolkit for differential privacy applications.

Abstract

Motivated by the desire to bridge the utility gap between local and trusted curator models of differential privacy for practical applications, we initiate the theoretical study of a hybrid model introduced by "Blender" [Avent et al.,\ USENIX Security '17], in which differentially private protocols of n agents that work in the local-model are assisted by a differentially private curator that has access to the data of m additional users. We focus on the regime where m << n and study the new capabilities of this (m,n)-hybrid model. We show that, despite the fact that the hybrid model adds no significant new capabilities for the basic task of simple hypothesis-testing, there are many other tasks (under a wide range of parameters) that can be solved in the hybrid model yet cannot be solved either by the curator or by the local-users separately. Moreover, we exhibit additional tasks where at least one round of interaction between the curator and the local-users is necessary -- namely, no hybrid model protocol without such interaction can solve these tasks. Taken together, our results show that the combination of the local model with a small curator can become part of a promising toolkit for designing and implementing differential privacy.