Study of Different Arithmatic Operations Number System Polynomial

A New Approach to Efficient Modular Arithmetic

Abstract

Wepropose a new number representation and arithmetic for the elements of the ringof integers modulo p. The so- called Polynomial Modular Number System (PMNS)allows for fast polynomial arithmetic and easy parallelization. The mostimportant contribution of this paper is the fundamen­tal theorem of a ModularNumber System, which provides a bound for the coefficients of the polynomialsused to rep­resent the set  However,we also propose a complete set of algorithms to perform the arithmeticoperations over a PMNS, which make this system of practical interest for peopleconcerned about efficient implementation of modu­lar arithmetic.