Second-Order Expansion of Privacy Amplification Under f-Divergence Criteria
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∈ (0,1) and recover the known expansion for total variation distance.
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BibTeX
@misc{berta2026secondorder,
title = {{Second-Order Expansion of Privacy Amplification Under f-Divergence Criteria}},
author = {Mario Berta and Hao-Chung Cheng and Marco Tomamichel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11794},
eprint = {2609.11794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11794},
}
RIS
TY - UNPB
TI - Second-Order Expansion of Privacy Amplification Under f-Divergence Criteria
AU - Mario Berta
AU - Hao-Chung Cheng
AU - Marco Tomamichel
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11794
UR - https://arxiv.org/abs/2609.11794
AB - 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∈ (0,1) and recover the known expansion for total variation distance.
ER -