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 socalled 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 Zp. 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.

• Type: Conference
• Year: 2005
• Where: ARITH
• Authors: Jean-Claude Bajard, Laurent Imbert, Thomas Plantard
• Keywords: Applied Computing, ARITH 2005, Integers Modulo P, Modular Number System, Polynomial Modular Number