Fast base extension using a redundant modulus in RNS

Abstract

A technique to extend the base of a residue number system (RNS) based on the Chinese remainder theorem (CRT) and the use of a redundant modulus, is proposed. The technique obtains the residue(s) of a given number in the extended moduli without resorting to the traditional mixed-radix conversion (MRC) algorithm. The base extension can be achieved in log/sub 2/n table lookup cycles, where n is the number of moduli in the RNS. The superiority of the technique, compared in terms of latency and hardware requirements to the traditional Szabo-Tanaka method is demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>