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International Conference on Principles of Security and Trust

POST 2012: Principles of Security and Trust pp 209–228Cite as

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Verified Indifferentiable Hashing into Elliptic Curves

Verified Indifferentiable Hashing into Elliptic Curves

  • Gilles Barthe18,
  • Benjamin Grégoire19,
  • Sylvain Heraud19,
  • Federico Olmedo18 &
  • …
  • Santiago Zanella Béguelin18 
  • Conference paper
  • 1296 Accesses

  • 9 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7215)

Abstract

Many cryptographic systems based on elliptic curves are proven secure in the Random Oracle Model, assuming there exist probabilistic functions that map elements in some domain (e.g. bitstrings) onto uniformly and independently distributed points in a curve. When implementing such systems, and in order for the proof to carry over to the implementation, those mappings must be instantiated with concrete constructions whose behavior does not deviate significantly from random oracles. In contrast to other approaches to public-key cryptography, where candidates to instantiate random oracles have been known for some time, the first generic construction for hashing into ordinary elliptic curves indifferentiable from a random oracle was put forward only recently by Brier et al. We present a machine-checked proof of this construction. The proof is based on an extension of the CertiCrypt framework with logics and mechanized tools for reasoning about approximate forms of observational equivalence, and integrates mathematical libraries of group theory and elliptic curves.

Keywords

  • Hash Function
  • Elliptic Curve
  • Elliptic Curf
  • Random Oracle
  • Statistical Distance

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Gilles Barthe, Federico Olmedo & Santiago Zanella Béguelin

  2. INRIA Sophia Antipolis-Méditerranée, France

    Benjamin Grégoire & Sylvain Heraud

Authors
  1. Gilles Barthe
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  2. Benjamin Grégoire
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  3. Sylvain Heraud
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  4. Federico Olmedo
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  5. Santiago Zanella Béguelin
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy

    Pierpaolo Degano

  2. Computer Science, Worcester Polytechnic Institute, 100 Institute Road, 01609, Worcester, MA, USA

    Joshua D. Guttman

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© 2012 Springer-Verlag Berlin Heidelberg

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Barthe, G., Grégoire, B., Heraud, S., Olmedo, F., Zanella Béguelin, S. (2012). Verified Indifferentiable Hashing into Elliptic Curves. In: Degano, P., Guttman, J.D. (eds) Principles of Security and Trust. POST 2012. Lecture Notes in Computer Science, vol 7215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28641-4_12

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