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Security Ranking Among Assumptions Within the Uber Assumption Framework

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7807))

Abstract

In order to analyze a variety of cryptosystems, Boneh, Boyen and Goh introduced a general framework, the Uber assumption. In this article, we explore some particular instances of this Uber assumption; namely the n-\(\mathsf {CDH}\)-assumption, the \(n^{th}\)-\(\mathsf {CDH}\)-assumption and the \(Q\)-\(\mathsf {CDH}\)-assumption. We analyse their relationships from a security point of view. Our analysis does not rely on any other property of the considered group and, in particular, does not use the generic group model.

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Notes

  1. 1.

    Remember that the oracle is stateless and thus not allowed to misbehave by counting the questions and giving an answer that depends on the position of the question. It would be easy to adapt to this case, but we have not considered it.

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Author information

Authors and Affiliations

  1. CryptoExperts, Paris, France

    Antoine Joux

  2. Chaire de Cryptologie de la Fondation de l’UPMC, Paris, France

    Antoine Joux

  3. Laboratoire d’Informatique de Paris 6, UPMC Sorbonnes Universités, Paris, France

    Antoine Joux

  4. Laboratoire PRISM - Université de Versailles Saint-Quentin-en-Yvelines, Versailles, France

    Antoine Rojat

Authors
  1. Antoine Joux
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  2. Antoine Rojat
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Correspondence to Antoine Joux .

Editor information

Editors and Affiliations

  1. University of Texas at Dallas, Richardson, Texas, USA

    Yvo Desmedt

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Joux, A., Rojat, A. (2015). Security Ranking Among Assumptions Within the Uber Assumption Framework. In: Desmedt, Y. (eds) Information Security. Lecture Notes in Computer Science(), vol 7807. Springer, Cham. https://doi.org/10.1007/978-3-319-27659-5_28

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  • DOI: https://doi.org/10.1007/978-3-319-27659-5_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27658-8

  • Online ISBN: 978-3-319-27659-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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