A new multi-linear universal hash family

A new universal hash family is described. Messages are sequences over a finite field IFq while keys are sequences over an extension field IFqn . A linear map ψ from IFqn 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 ψ using a tower field representation of IFqn . 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.