Fast Base Extension using Single Redundant Modulus in a Residue Number System

Abstract

The Residue Number Systems (RNS) has been around for a long time. Even though RNS proposes carry free addition and multiplication, there has been hesitancy in utilizing RNS to build efficient hardware. This is in small part due to the inability of RNS to perform division and scaling natively. In this paper we propose a new method which would allow us to scale any number in an RNS with respect to another modulus. This paper proposes a new technique for the calculation of base extension in Residue Number System using a single redundant modulus. The method is based upon the usage of the well-known Chinese Remainder Theorem for base extension. The base extension is achieved in modest time as the operands at all levels are kept as reminders of smaller numbers, therefore, allowing us to attain superior hardware implementation over the naive method.