Privacy Amplification via Shuffling: Unified, Simplified, and Tightened

TL;DR

This paper introduces a unified framework called variation-ratio reduction for tighter privacy amplification analysis in shuffle models of differential privacy, improving privacy bounds and efficiency for various data analysis protocols.

Contribution

It proposes a comprehensive, tight, and general framework for privacy amplification in shuffle models, enhancing privacy bounds and computational efficiency.

Findings

Tighter privacy amplification bounds, especially for extremal local randomizers.

Significant privacy budget savings: up to 30% for single-message, 75% for multi-message, and 75-95% for parallel composition.

An efficient algorithm that amplifies privacy for 10^8 users in under 10 seconds.

Abstract

The shuffle model of differential privacy provides promising privacy-utility balances in decentralized, privacy-preserving data analysis. However, the current analyses of privacy amplification via shuffling lack both tightness and generality. To address this issue, we propose the \emph{variation-ratio reduction} as a comprehensive framework for privacy amplification in both single-message and multi-message shuffle protocols. It leverages two new parameterizations: the total variation bounds of local messages and the probability ratio bounds of blanket messages, to determine indistinguishability levels. Our theoretical results demonstrate that our framework provides tighter bounds, especially for local randomizers with extremal probability design, where our bounds are exactly tight. Additionally, variation-ratio reduction complements parallel composition in the shuffle model, yielding enhanced privacy accounting for popular sampling-based randomizers employed in statistical queries (e.g., range queries, marginal queries, and frequent itemset mining). Empirical findings demonstrate that our numerical amplification bounds surpass existing ones, conserving up to $30\%$ of the budget for single-message protocols, $75\%$ for multi-message ones, and a striking $75\%$-$95\%$ for parallel composition. Our bounds also result in a remarkably efficient $\tilde{O}(n)$ algorithm that numerically amplifies privacy in less than $10$ seconds for $n=10^8$ users.