Cryptographic hash functions and expander graphs: The end of the story?

Abstract

Cayley hash functions are a family of cryptographic hash functions constructed from the Cayley graphs of non-Abelian finite groups. Their security relies on the hardness of mathematical problems related to long-standing conjectures in graph and group theory. We recall the Cayley hash design and known results on the underlying problems. We then describe related open problems, including the cryptanalysis of relevant parameters as well as new applications to cryptography and outside, assuming either that the problem is “hard” or easy.