Asymptotic Framework Sharpens Shuffle Differential Privacy Guarantees

Global: Asymptotic Framework Sharpens Shuffle Differential Privacy Guarantees

A team of computer scientists has introduced an asymptotic framework that more precisely quantifies the privacy amplification achieved by shuffling in distributed data analysis. The work, posted on arXiv in January 2026, focuses on the shuffled mechanism’s (ε_n,δ_n)-differential privacy guarantee and identifies a scalar parameter χ, termed the shuffle index, that captures the influence of the underlying local randomizer.

Background on Shuffle Differential Privacy

Shuffling, which randomly permutes messages from locally differentially private users before aggregation, is known to improve overall privacy. Existing analyses typically treat the local DP parameter ε_0 as the only adjustable knob and provide generic upper bounds that can be loose, especially for mechanisms such as the Gaussian mechanism.

Asymptotic Blanket Divergence Analysis

By revisiting the blanket divergence bound introduced by Balle et al., the authors develop an asymptotic analysis that applies to a broad class of local randomizers under mild regularity assumptions, without requiring pure local DP. The resulting expressions yield both upper and lower bounds that converge, forming a tight band for δ_n in the shuffled mechanism’s (ε_n,δ_n)-DP guarantee.

Shuffle Index and Its Role

The leading term of the blanket divergence depends on the local mechanism solely through the scalar χ, which the authors label the shuffle index. This reduction simplifies the characterization of privacy amplification, allowing practitioners to assess the impact of a given local randomizer by evaluating a single parameter.

Conditions for Tight Bounds

The paper derives a necessary and sufficient structural condition under which the asymptotic upper and lower bounds coincide. Families of k‑ary randomized response (k‑RR) with k≥3 satisfy this condition, while generalized Gaussian mechanisms may not, though the resulting band remains tight in practice.

Practical Computation via FFT

To complement the theory, the authors present an FFT‑based algorithm that computes the blanket divergence for finite sample sizes n with rigorously controlled relative error and near‑linear runtime in n. This tool enables concrete numerical analysis of shuffle DP for realistic dataset sizes.

Implications for Future Research

The tightened characterization of shuffle DP is expected to inform the design of more efficient privacy‑preserving protocols and to guide the selection of local randomizers in large‑scale analytics. Moreover, the FFT implementation provides a practical benchmark for validating future theoretical advances.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.