Encyclopedia of Cryptography and Security

2011 Edition
| Editors: Henk C. A. van Tilborg, Sushil Jajodia

Cayley Hash Functions

  • Christophe Petit
  • Jean-Jacques Quisquater
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-5906-5_126

Related Concepts


Cayley hash functions are collision-resistant hash functions constructed from Cayley graphs of non-Abelian groups.


The idea of using Cayley graphs for building hash functions was introduced by Zémor in a first proposal back in 1991 [8]. After cryptanalysis of the first scheme, a second scheme following the same lines was proposed by Tillich and Zémor [5]. The design was rediscovered more than 15 years later by Charles et al. [1]. Many of the initial concrete proposals have been broken today, but the existing attacks either do not generalize or can be thwarted easily. The very interesting properties of the generic design suggest to look for other, more secure instances.


Let G be a non-Abelian group and let \(S =\{ {s}_{0},...,{s}_{k-1}\}\)
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Recommended Reading

  1. 1.
    Charles D, Goren E, Lauter K (2009) Cryptographic hash functions from expander graphs. J Cryptol 22(1):93–113MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Grassl M, Ilic I, Magliveras S, Steinwandt R (2009) Cryptanalysis of the Tillich-Zémor hash function. Cryptology ePrint Archive, Report 2009/376, 2009. http://eprint.iacr.org/. J Cryptol (to appear)
  3. 3.
    Petit C, Lauter K, Quisquater J-J (2008) Full cryptanalysis of LPS and Morgenstern hash functions. In: Ostrovsky R, Prisco RD, Visconti I (eds) SCN, Lecture notes in computer science, vol 5229. Springer, Heidelberg, pp 263–277Google Scholar
  4. 4.
    Petit C, Quisquater J-J (2009) Preimages for the Tillich-zémor hash function. In: Alex Biryukov, Guang Gong, Douglos Stinson (eds), SAC 2010 (to appear in LNCS revie)Google Scholar
  5. 5.
    Tillich J-P, Zémor G (1994) Hashing with SL2. In: Desmedt Y (ed) CRYPTO, Lecture notes in computer science, vol 839. Springer, Heidelberg, pp 40–49Google Scholar
  6. 6.
    Tillich J-P, Zémor G (2008) Collisions for the LPS expander graph hash function. In: Smart NP (ed) EUROCRYPT, Lecture Notes in computer Science, vol 4965. Springer, pp 254–269Google Scholar
  7. 7.
    Tillich J-P, Zémor G (1993) Group-theoretic hash functions. In: Proceedings of the First French-Israeli Workshop on Algebraic Coding, London, UK, Springer-Verlag, pp 90–110Google Scholar
  8. 8.
    Zémor G (1991) Hash functions and graphs with large girhts. In: EUROCRYPT, pp 508–511Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Christophe Petit
    • 1
  • Jean-Jacques Quisquater
    • 1
  1. 1.Microelectronics LaboratoryUniversité catholique de LouvainLouvain-la-NeuveBelgium