What question did this study set out to answer?

The research aims to establish a rigorous privacy framework for amplification by shuffling within the Gaussian regime.

March 3, 2026Open Access

Universal Shuffle Asymptotics: Sharp Privacy Analysis in the Gaussian Regime

Key Points

The research aims to establish a rigorous privacy framework for amplification by shuffling within the Gaussian regime.
Developed exact likelihood-ratio identities for privacy analysis.
Performed conditional-expectation linearization with quantitative remainders.
Established Gaussian Differential Privacy equivalence using Berry-Esseen rates.
Conducted Local Asymptotic Normality analysis with quantitative Le Cam distance.
Proved sharp Jensen-Shannon expansions with a leading constant and a uniform remainder.
Established exact finite-n privacy curves, showing precise privacy levels for small sample sizes.
Demonstrated the comparison between bundled and unbundled multi-message privacy analysis.

Abstract

Sharp experiment-level privacy theory for amplification by shuffling with fixed finite-output local randomizers. We prove exact likelihood-ratio identities, conditional-expectation linearization with quantitative remainders, and sharp Jensen–Shannon expansions with universal leading constant Iπ/(8n) and uniform O(n⁻²) remainder. We establish Gaussian Differential Privacy equivalence with Berry–Esseen rates, Local Asymptotic Normality with quantitative Le Cam distance, exact finite-n privacy curves, and unbundled multi-message analysis with a strict bundled-vs-unbundled comparison. All proportional-composition constants use the correct fixed-composition covariance Σπ = (1−π)Σ₀ + πΣ₁.

Universal Shuffle Asymptotics: Sharp Privacy Analysis in the Gaussian Regime

Key Points

Abstract

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