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This research aims to provide a complete analysis of the Jensen–Shannon divergence in the context of Gaussian secure aggregation.

January 14, 2026Open Access

Exact Jensen–Shannon Divergence in Gaussian Secure Aggregation

Key Points

This research aims to provide a complete analysis of the Jensen–Shannon divergence in the context of Gaussian secure aggregation.
Derived the exact asymptotic expansion of Jensen–Shannon divergence
Utilized the Gaussian secure aggregation model
Conducted a mathematical audit and independent numerical verification.
Established the formula JSD = SNR/(8n) − SNR²/(64n²) + O(n⁻³)
Identified a negative second-order coefficient in the expansion
Highlighted a qualitative contrast with discrete randomized response.

Abstract

This release provides the exact asymptotic expansion of the Jensen–Shannon divergence between neighboring datasets in the Gaussian secure aggregation model. We proveJSD = SNR/ (8n) − SNR²/ (64n²) + O (n⁻³), with a negative second-order coefficient, highlighting a qualitative contrast with discrete randomized response. The result establishes the universal leading-order relation JSD = χ²ₐgg/8 + O ( (χ²ₐgg) ²). This version updates and supersedes the previous Zenodo record, incorporating a complete mathematical audit and independent numerical verification.

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