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

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