Reference Work Entry

Encyclopedia of Cryptography and Security

pp 183-184

Cayley Hash Functions

  • Christophe PetitAffiliated withMicroelectronics Laboratory, Université catholique de Louvain
  • , Jean-Jacques QuisquaterAffiliated withMicroelectronics Laboratory, Université catholique de Louvain

Related Concepts

Collision Resistance; Hash Functions; One-Way Functions

Definition

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

Background

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.

Theory

Let G be a non-Abelian group and let \(S =\{ {s}_{0},...,{s}_{k-1}\}\) be a subset thereof such that \({s}_{i}\neq {s}_{j},{s}_{j}^{-1}\) for any ...

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