In this paper, we give faster versions of Montgomery modular multiplication algorithm without pre-computational phase for GF(p) and GF(2m ) which can be considered as a generalization of ,  and . We propose sets of moduli different than ,  and  which can be used in PKC applications. We show that one can obtain efficient Montgomery modular multiplication architecture in view of the number of AND gates and XOR gates by choosing proposed sets of moduli. We eliminate precomputational phase with proposed sets of moduli. These methods are easy to implement for hardware. © 2011 Springer Science+Business Media B.V.