Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy

Shun Watanabe; Masahito Hayashi

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arXiv · 1211.5252

Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy

Shun Watanabe·Masahito Hayashi

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Abstract

This paper investigates the privacy amplification problem, and compares the existing two bounds: the exponential bound derived by one of the authors and the min-entropy bound derived by Renner. It turns out that the exponential bound is better than the min-entropy bound when a security parameter is rather small for a block length, and that the min-entropy bound is better than the exponential bound when a security parameter is rather large for a block length. Furthermore, we present another bound that interpolates the exponential bound and the min-entropy bound by a hybrid use of the Renyi entropy and the inf-spectral entropy.

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Shun Watanabe, Masahito Hayashi. 2012-11-22. Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy. https://arxiv.org/abs/1211.5252

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