Girth of the Cayley graph and Cayley hash functions

TL;DR

This paper surveys Cayley hash functions, highlighting a simple, secure variant that allows efficient updates by multiplication, offering advantages over traditional hash functions like SHA.

Contribution

It identifies and analyzes a simple Cayley hash function with unbroken security, emphasizing its efficiency in document updates.

Findings

Cayley hash functions enable efficient document amendments.

A specific simple Cayley hash function remains secure.

Survey of existing Cayley hash functions and their properties.

Abstract

Cayley hash functions are based on a simple idea of using a pair of semigroup elements, A and B, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the semigroup. The main advantage of Cayley hash functions compared to, say, hash functions in the SHA family is that when an already hashed document is amended, one does not have to hash the whole amended document all over again, but rather hash just the amended part and then multiply the result by the hash of the original document. In this article, we survey some of the previously proposed Cayley hash functions and single out a very simple hash function whose security has not been compromised up to date.