Arithmetic operations in the polynomial modular number system

We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The so-called polynomial modular number system (PMNS) allows for fast polynomial arithmetic and easy parallelization. The most important contribution of this paper is the fundamental theorem of a modular number system, which provides a bound for the coefficients of the polynomials used to represent the set Z_p. However, we also propose a complete set of algorithms to perform the arithmetic operations over a PMNS, which make this system of practical interest for people concerned about efficient implementation of modular arithmetic.