Exact Jensen–Shannon Divergence in Gaussian Secure Aggregation
Abstract
Exact asymptotic expansion of Jensen–Shannon divergence for Gaussian secure aggregation: **JSD = SNR/(8n) − SNR²/(64n²) + O(n⁻³)** The second-order coefficient −1/64 exhibits sign reversal compared to +3/64 for discrete randomized response. Both cases satisfy the universal relation JSD = χ²_agg/8 + O((χ²_agg)²). **Prior art:** Leading-order asymptotics follow from low-SNR mutual information expansions [Guo–Shamai–Verdú, IEEE TIT 2005]. Novel contributions: (1) secure aggregation/DP context with neighboring-dataset semantics, (2) sign reversal identification, (3) unified χ² framework.
Fields of Study & Subjects
Random Matrices and Applications
Statistical Mechanics and Entropy
Bayesian Methods and Mixture Models
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 11 January 2026
- Language
- EN
- Document type
- Preprint