Exact Second-Order Jensen–Shannon Asymptotics in the Unbundled Shuffle Model

Key Points

• To derive a second-order asymptotic expansion for Jensen–Shannon divergence in the unbundled shuffle model.
• Analytical proof techniques were used to develop the expansion.
• The model focuses on unbundled multi-message shuffling.
• Complete control over the remainder term was achieved.
• The analysis reveals an exponential separation between bundled and unbundled shuffling.
• Bundling amplifies divergence exponentially with the number of messages per user.
• In contrast, unbundled shuffling maintains linear scaling.