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 µ²₍, ₔ₍ = mχ²/n and µ²₍, ₁₃ = ( (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.