Fast Modular Reduction over Euclidean Rings and Its Application to Universal Hash Functions

In this letter, we propose a fast modular reduction method over Euclidean rings, which is a generalization of Barrett’s reduction algorithm over the ring of integers. As an application, we construct new universal hash function families whose operations are modular arithmetic over a Euclidean ring, which can be any of three rings, the ring of integers, the ring of Gauss integers and the ring of Eisenstein integers. The implementation of these families is efficient by using our method. key words: modular reduction, Euclidean ring, lattice, universal hash function family, message authentication code