Differentially Private Aggregation via Imperfect Shuffling

TL;DR

This paper introduces the imperfect shuffle differential privacy model, demonstrating that existing protocols can be adapted to this setting without additional error, thus enabling private aggregation with near-optimal utility.

Contribution

It extends the shuffle differential privacy model to imperfect shuffles and adapts existing protocols to achieve optimal utility without extra error overhead.

Findings

Standard split-and-mix protocol achieves near-optimal utility in imperfect shuffle model

No additional error overhead is necessary in the imperfect shuffle setting

The model allows for effective private summation with minimal utility loss

Abstract

In this paper, we introduce the imperfect shuffle differential privacy model, where messages sent from users are shuffled in an almost uniform manner before being observed by a curator for private aggregation. We then consider the private summation problem. We show that the standard split-and-mix protocol by Ishai et. al. [FOCS 2006] can be adapted to achieve near-optimal utility bounds in the imperfect shuffle model. Specifically, we show that surprisingly, there is no additional error overhead necessary in the imperfect shuffle model.