Universal Shuffle Asymptotics: Sharp Privacy Analysis via Limit Experiments (Parts I–III)

Key Points

• The aim is to develop a complete asymptotic theory for privacy amplification through shuffling techniques.
• Developed sharp Gaussian equivalence and privacy curves for fixed local randomizers.
• Identified non-Gaussian limit experiments at the critical scaling boundary.
• Provided proofs for linearization and GDP asymptotics in multi-message scenarios.
• Established exact finite-n privacy curves for local randomizers.
• Introduced new non-Gaussian limit experiments related to privacy amplification.
• Completed proofs leading to a Berry–Esseen theorem connecting Gaussian and Poisson regimes.