Recent Developments in Cayley Hash Functions

Abstract

In 1994, Tillich and Zémor proposed a scheme for a family of hash functions. In the scheme, they used products of 2 × 2 matrices in special linear group over a field. Since then, other hash functions based on the Tillich and Zémor’s design have been proposed. These cryptographic hash functions are called Cayley hash functions because of the correspondence between their constructions and Cayley graphs of (semi)groups. Most instances of Cayley hash functions have been proved insecure, but the algorithms used to break Cayley hash functions target specific vulnerabilities of each underlying (semi)group used. However, these algorithms don’t seem to invalidate the generic scheme. An overview is presented of some of the latest proposals for Cayley hash functions and related open problems.