Paper 2008/216

A New Multi-Linear Universal Hash Family

Palash Sarkar

Abstract

A new universal hash family is described. Messages are sequences over a finite field ${\text{rF}}_q$ while keys are sequences over an extension field ${\text{rF}}_{q^n}$. A linear map $\psi$ from ${\text{rF}}_{q^n}$ 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 ${\text{rF}}_{q^n}$. 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.

Note: Handling variable length messages has been simplified and a standard encoding technique works.