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March 19, 20260 citationsOpen Access

Growing Alphabets Do Not Automatically Amplify Shuffle Privacy: A Sharp Geometric Dichotomy

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ASAlex Shvets

Key Points

  • The study aims to explore how growing output alphabets affect shuffle-model differential privacy and its geometric properties.
  • Analyzed privacy mechanisms using exact compression techniques
  • Investigated the universal χ² bound
  • Developed an explicit obstruction family
  • Evaluated the sharp diluting/persistent dichotomy
  • Identified that growing alphabets do not enhance shuffle privacy as expected
  • Demonstrated a clear geometric dichotomy in privacy outcomes
  • Provided insights independent of existing literature on universal shuffle asymptotics

Abstract

Exact compression, universal χ² bound, explicit obstruction family, and sharp diluting/persistent dichotomy for shuffle-model differential privacy on growing output alphabets. Independent of but informed by the trilogy "Universal Shuffle Asymptotics" (arXiv:2602.09029, arXiv:2603.10073, arXiv:2603.13407).

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Cite This Study

Alex Shvets (2026) studied this question.

synapsesocial.com/papers/69bb938e496e729e629817bbhttps://doi.org/10.5281/zenodo.19058575
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