Universal Shuffle Asymptotics: Sharp Privacy Analysis in the Gaussian Regime
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915880024145920 |
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| author | Shvets, Alex |
| author_facet | Shvets, Alex |
| contents | We develop a sharp, experiment-level privacy theory for amplification by shuffling in the Gaussian regime: a fixed finite-output local randomizer with full support and neighboring binary datasets differing in one user. We first prove exact likelihood-ratio identities for shuffled histograms and a complete conditional-expectation linearization theorem with explicit typical-set remainders. We then derive sharp Jensen-Shannon divergence expansions, identifying the universal leading constant I_pi/(8n) for proportional compositions and emphasizing the correct fixed-composition covariance Sigma_pi=(1-pi)Sigma_0+pi*Sigma_1. Next we establish equivalence to Gaussian Differential Privacy with Berry-Esseen bounds and obtain the full limiting (epsilon,delta) privacy curve. Finally, for unbundled multi-message shuffling we give an exact degree-m likelihood ratio, asymptotic GDP formulas, and a strict bundled-versus-unbundled comparison. Further results include Local Asymptotic Normality with quantitative Le Cam equivalence, exact finite-n privacy curves, a boundary Berry-Esseen theorem for randomized response, and a frequency-estimation application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Shuffle Asymptotics: Sharp Privacy Analysis in the Gaussian Regime Shvets, Alex Information Theory 62G10, 94A17, 68P27 F.2.2; K.4.1 We develop a sharp, experiment-level privacy theory for amplification by shuffling in the Gaussian regime: a fixed finite-output local randomizer with full support and neighboring binary datasets differing in one user. We first prove exact likelihood-ratio identities for shuffled histograms and a complete conditional-expectation linearization theorem with explicit typical-set remainders. We then derive sharp Jensen-Shannon divergence expansions, identifying the universal leading constant I_pi/(8n) for proportional compositions and emphasizing the correct fixed-composition covariance Sigma_pi=(1-pi)Sigma_0+pi*Sigma_1. Next we establish equivalence to Gaussian Differential Privacy with Berry-Esseen bounds and obtain the full limiting (epsilon,delta) privacy curve. Finally, for unbundled multi-message shuffling we give an exact degree-m likelihood ratio, asymptotic GDP formulas, and a strict bundled-versus-unbundled comparison. Further results include Local Asymptotic Normality with quantitative Le Cam equivalence, exact finite-n privacy curves, a boundary Berry-Esseen theorem for randomized response, and a frequency-estimation application. |
| title | Universal Shuffle Asymptotics: Sharp Privacy Analysis in the Gaussian Regime |
| topic | Information Theory 62G10, 94A17, 68P27 F.2.2; K.4.1 |
| url | https://arxiv.org/abs/2602.09029 |