Efficient Indifferentiable Hashing into Ordinary Elliptic Curves

  • Eric Brier
  • Jean-Sébastien Coron
  • Thomas Icart
  • David Madore
  • Hugues Randriam
  • Mehdi Tibouchi
Conference paper

DOI: 10.1007/978-3-642-14623-7_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6223)
Cite this paper as:
Brier E., Coron JS., Icart T., Madore D., Randriam H., Tibouchi M. (2010) Efficient Indifferentiable Hashing into Ordinary Elliptic Curves. In: Rabin T. (eds) Advances in Cryptology – CRYPTO 2010. CRYPTO 2010. Lecture Notes in Computer Science, vol 6223. Springer, Berlin, Heidelberg

Abstract

We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart’s deterministic encoding from Crypto 2009. While almost as efficient as Icart’s encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model.

We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.

Download to read the full conference paper text

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Eric Brier
    • 1
  • Jean-Sébastien Coron
    • 2
  • Thomas Icart
    • 2
  • David Madore
    • 3
  • Hugues Randriam
    • 3
  • Mehdi Tibouchi
    • 2
    • 4
  1. 1.Ingenico 
  2. 2.Université du Luxembourg 
  3. 3.TELECOM-ParisTech 
  4. 4.École normale supérieure 

Personalised recommendations