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How to Smooth Entropy?

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SOFSEM 2016: Theory and Practice of Computer Science (SOFSEM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9587))

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Abstract

Smooth entropy of X is defined as possibly biggest entropy of a distribution Y close to X. It has found many applications including privacy amplification, information reconciliation, quantum information theory and even constructing random number generators. However the basic question about the optimal shape for the distribution Y has not been answered yet. In this paper we solve this problem for Renyi entropies in non-quantum settings, giving a formal treatment to an approach suggested at TCC’05 and ASIACRYPT’05. The main difference is that we use a threshold cut instead of a quantile cut to rearrange probability masses of X. As an example of application, we derive tight lower bounds on the number of bits extractable from Shannon memoryless sources.

M. Skorski—This work was partly supported by the WELCOME/2010-4/2 grant founded within the framework of the EU Innovative Economy Operational Programme.

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Authors and Affiliations

  1. Cryptology and Data Security Group, University of Warsaw, Warsaw, Poland

    Maciej Skorski

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  1. Maciej Skorski
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Correspondence to Maciej Skorski .

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Editors and Affiliations

  1. University of Latvia, Riga, Latvia

    Rūsiņš Mārtiņš Freivalds

  2. University of Paderborn, Paderborn, Germany

    Gregor Engels

  3. University of Genoa, Genoa, Italy

    Barbara Catania

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Skorski, M. (2016). How to Smooth Entropy?. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_32

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  • DOI: https://doi.org/10.1007/978-3-662-49192-8_32

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  • Print ISBN: 978-3-662-49191-1

  • Online ISBN: 978-3-662-49192-8

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