Shuffle Model Privacy for Federated Learning: Asymptotic GDP Analysis and Bundled/Unbundled Separation

Exact asymptotic GDP parameters for shuffle model federated learning via chi-squared divergence. Proves exponential separation between bundled and unbundled shuffling designs in feasible SGD iterations. - After publication, the following related works were identified that share conceptual connections with this paper: 1. Su, Cheng, Wang (arXiv:2504.07414, 2025) analyze "joint composition" in shuffle model where user outputs are shuffled as a tuple — conceptually similar to our "bundled" regime. Their focus is on (ε,δ)-DP bounds via FFT, not µ-GDP with χ²-parameterization. 2. Su, Cheng, Wang (arXiv:2511.15051, 2025) show χ²(P‖Q) appears in mutual information asymptotics for shuffle model. Our contribution uses χ² for µ-GDP (differential privacy), not information-theoretic leakage. 3. Chen, Cao, Ge (AAAI 2024, arXiv:2312.14388) provide f-DP analysis for personalized LDP shuffle settings. They do not derive closed-form µ² expressions parameterized solely by χ²(W₁‖W₀). The core contributions of this paper remain novel: • Exact closed-form µ²n,un = mχ²/n and µ²n,bd = ((1+χ²)^m - 1)/n • Explicit exponential separation ratio Θ((1+χ²)^m/m) • SGD iteration bounds under µ-GDP budget A revised version with expanded Related Work is planned for journal submission.