Analyzing and comparing Montgomery multiplication algorithms

Abstract

Montgomery multiplication methods constitute the core of modular exponentiation, the most popular operation for encrypting and signing digital data in public-key cryptography. In this article, we study the operations involved in computing the Montgomery product, describe several high-speed, space-efficient algorithms for computing MonPro(a, b), and analyze their time and space requirements. Our focus is to collect several alternatives for Montgomery multiplication, three of which are new. However, we do not compare the Montgomery techniques to other modular multiplication approaches.