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Generalized Strong Extractors and Deterministic Privacy Amplification

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Book cover Cryptography and Coding (Cryptography and Coding 2005)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3796))

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Abstract

Extracting essentially uniform randomness from a somewhat random source X is a crucial operation in various applications, in particular in cryptography where an adversary usually possesses some partial information about X. In this paper we formalize and study the most general form of extracting randomness in such a cryptographic setting. Our notion of strong extractors captures in particular the case where the catalyst randomness is neither uniform nor independent of the actual extractor input. This is for example important for privacy amplification, where a uniform cryptographic key is generated by Alice and Bob sharing some partially secret information X by exchanging a catalyst R over an insecure channel accessible to an adversary Eve. Here the authentication information for R creates, from Eve’s viewpoint, a dependence between X and R. We provide explicit constructions for this setting based on strong blenders. In addition, we give strong deterministic randomness extractors for lists of random variables, where only an unknown subset of the variables is required to have some amount of min-entropy.

This work was partially supported by the Swiss National Science Foundation, project No. 200020-103847/1.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Swiss Federal Institute of Technology (ETH), Zurich, CH-8092, Zurich, Switzerland

    Robert König & Ueli Maurer

Authors
  1. Robert König
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  2. Ueli Maurer
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Editor information

Editors and Affiliations

  1. Dept. Computer Science, University of Bristol, Woodland Road, BS8 1UB, Bristol, United Kingdom

    Nigel P. Smart

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König, R., Maurer, U. (2005). Generalized Strong Extractors and Deterministic Privacy Amplification. In: Smart, N.P. (eds) Cryptography and Coding. Cryptography and Coding 2005. Lecture Notes in Computer Science, vol 3796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11586821_22

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  • DOI: https://doi.org/10.1007/11586821_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30276-6

  • Online ISBN: 978-3-540-32418-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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