Study of Different Arithmetic Operations Number System Polynomial: Efficient Implementation of Polynomial Modular Number System Arithmetic

Abstract

We propose a new number representation and arithmetic for the elementsof the ring of integers modulo p. The so- called Polynomial Modular NumberSystem (PMNS) allows for fast polynomial arithmetic and easy parallelization.The most important contribution of this paper is the fundamen­tal theorem of aModular Number System, which provides a bound for the coefficients of the polynomialsused to rep­resent the set  However, we alsopropose a complete set of algorithms to perform the arithmetic operations overa PMNS, which make this system of practical interest for people concerned aboutefficient implementation of modu­lar arithmetic.