A Simplified Modulo (2ⁿ-1) Squaring Scheme for Residue Number System

摘要

Residue Number System (RNS) is a valuable tool for fast and parallel arithmetic and has a variety of applications in digital signal processing, fault tolerant systems, etc. One of the most fundamental moduli in Residue Number System is modulo (2ⁿ-1). Based on the properties of this modulo, the arithmetic operations of addition, subtraction, multiplication and squaring are easily carried out. In this paper, we target the squaring scheme in modulo (2ⁿ-1) and propose a method to simplify the modular squaring in this modulo that results in smaller operand size and consequently less partial products.