Notes on a preimage-resistant hash function

Abstract

Bérczes, Folláth and Pethö constructed a preimage-resistant hash
function. In this paper to investigate the avalanche criterion of this function, we
will generalize the results of Coulter and Mathews regarding planar polynomials.
At the same time a necessary and sufficient condition for being planar is
given for Dembowski-Ostrom monomials. In the even characteristic case both a
weaker asymptotic statement and practical test results are presented regarding
the avalanche criterion.