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January 14, 20260 citationsOpen Access

Exact Jensen–Shannon Divergence for the Gaussian Secure Aggregation Model

ASAlex B. ShvetsUniversity of Illinois Urbana-Champaign

Key Points

This research aims to derive an asymptotic expansion for the Jensen–Shannon divergence in the Gaussian secure aggregation model.
Developed mathematical formulas to express Jensen–Shannon divergence between datasets.
Investigated Gaussian local randomization focusing on variance and user shift.
Analyzed the behavior of divergence coefficients under bounded signal-to-noise ratios.
Established a significant negative second-order coefficient for Jensen–Shannon divergence.
Showed differences in behavior compared to discrete randomized-response scenarios.

Abstract

We derive a rigorous asymptotic expansion for the Jensen–Shannon divergence (JSD) between neighboring datasets in the Gaussian secure aggregation model, where the analyst observes only the noisy aggregate sum of n user reports. For Gaussian local randomization with variance σ² and a single-user shift µ, letting SNR = µ²/σ², we prove JSD(P0,P1) = SNR/(8n) − SNR²/(64 n²) + O(SNR³/n³),uniformly for bounded SNR and n large enough. The second-order coefficient is negative (−1/64), contrasting with the positive coefficient in the discrete randomized-response case, reflecting the log-normal (exponential) likelihood-ratio structure.

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