Modular multiplication using the core function in the residue number system

Abstract

Modular multiplication can be performed in the residue number system (RNS) using a type of Montgomery reduction. This paper presents an alternative in which RNS modular multiplication are performed by using the core function. All of the intermediate calculations use short wordlength operations within the RNS. This work contributes to the long wordlength modular multiplication operation $$Z = A \times B \mod M$$Z=A×BmodM, the basis of many DSPs and public-key cryptosystems.