An Efficient Implementation of the Montgomery Algorithm Using the Akushsky Core Function

Abstract

This paper examines the practical implementation of the Montgomery algorithm in asymmetric cryptosystems using the Residue Number System. Residue Number System enables concurrent computations of additions and multiplications across multiple channels, eliminating the need for bit carrying between them. Base extension is an essential aspect of RNS implementation for asymmetric cryptosystems. In this research, we introduce a novel method for conducting base expansion using the Akushsky Core Function. Our findings show that this innovative technique significantly reduces computational expenses compared to existing methods. The proposed approach enhances the efficiency of the Montgomery algorithm and advances the field of asymmetric cryptography by introducing a streamlined process for base expansion in the context of Residue Number Systems.