A new multi-linear universal hash family

Abstract

A new universal hash family is described which generalises a previously known multi-linear hash family. Messages are sequences over a finite field $${\mathbb{F}_q}$$ while keys are sequences over an extension field $${\mathbb{F}_{q^n}}$$ . A linear map $${\psi}$$ from $${\mathbb{F}_{q^n}}$$ to itself is used to compute the output digest. Of special interest is the case q = 2. For this case, we show that there is an efficient way to implement $${\psi}$$ using a tower field representation of $${\mathbb{F}_{q^n}}$$ . From a practical point of view, the focus of our constructions is small hardware and other resource constrained applications. For such platforms, our constructions compare favourably to previous work.