Second-Order Expansion of Privacy Amplification Under f-Divergence Criteria

2026-09-10

AI Summary

该研究通过使用f-散度标准下的二阶渐近分析方法，解决了从无记忆源中提取随机性时的隐私放大问题。

Abstract

We derive the second-order asymptotics of randomness extraction from memoryless sources with side information under security criteria based on a broad class of Csiszàr f-divergences, treating both a fixed reference side-information marginal and optimization over that marginal. The conditional varentropy decomposes into fluctuations of the conditional entropy across different values of the side information and the average variance of the conditional surprisal for each value. Without marginal optimization, these contributions yield a Gaussian-mixture second-order profile. With marginal optimization, they combine into the total conditional varentropy, yielding a single Gaussian profile. As corollaries, we obtain second-order expansions for Rényi-entropy criteria of all orders $α\in (0,1)$ and recover the known expansion for total variation distance.

Problem

• f-Divergence
• Privacy Amplification
• Randomness Extraction
• Second-Order Asymptotics
• Conditional Varentropy

Innovation

• second-order asymptotics
• f-divergences
• conditional varentropy
• Gaussian-mixture profile
• marginal optimization