On the Renyi Differential Privacy of the Shuffle Model

TL;DR

This paper establishes the first non-trivial Renyi Differential Privacy guarantees for general discrete mechanisms in the shuffle model, improving privacy bounds significantly through composition and subsampling techniques.

Contribution

It introduces novel RDP analysis for discrete local mechanisms in the shuffle model, enabling better privacy guarantees compared to existing approximate DP methods.

Findings

RDP guarantees improve privacy bounds by up to 8x with composition.

Combining RDP with Poisson subsampling yields at least 10x better privacy guarantees.

New analysis techniques for RDP in the shuffle model may be useful for future research.

Abstract

The central question studied in this paper is Renyi Differential Privacy (RDP) guarantees for general discrete local mechanisms in the shuffle privacy model. In the shuffle model, each of the $n$ clients randomizes its response using a local differentially private (LDP) mechanism and the untrusted server only receives a random permutation (shuffle) of the client responses without association to each client. The principal result in this paper is the first non-trivial RDP guarantee for general discrete local randomization mechanisms in the shuffled privacy model, and we develop new analysis techniques for deriving our results which could be of independent interest. In applications, such an RDP guarantee is most useful when we use it for composing several private interactions. We numerically demonstrate that, for important regimes, with composition our bound yields an improvement in privacy guarantee by a factor of $8\times$ over the state-of-the-art approximate Differential Privacy (DP) guarantee (with standard composition) for shuffled models. Moreover, combining with Poisson subsampling, our result leads to at least $10\times$ improvement over subsampled approximate DP with standard composition.