Modular reduction in GF(2 n ) without pre-computational phase

Abstract

In this study we show how modular multiplication with Barrett and Montgomery reductions over certain finite fields of characteristic 2 can be implemented efficiently without using a pre-computational phase. We extend the set of moduli that is recommended by Standards for Efficient Cryptography (SEC) by defining two distinct sets for which either Barrett or Montgomery reduction is applicable. As the proposed algorithm is very suitable for a fast modular multiplication, we propose an architecture for the fast modular multiplier that can efficiently be used without pre-computing the inverse of the modulus. © 2008 Springer-Verlag Berlin Heidelberg.