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Arithmetic Operations in the Polynomial Modular Number System

Jean-Claude Bajard 1 Laurent Imbert 1 Thomas Plantard 2 
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : 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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00387051
Contributor : Jean Claude Bajard Connect in order to contact the contributor
Submitted on : Friday, May 22, 2009 - 5:25:15 PM
Last modification on : Friday, March 18, 2022 - 3:41:24 AM

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  • HAL Id : lirmm-00387051, version 1

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Jean-Claude Bajard, Laurent Imbert, Thomas Plantard. Arithmetic Operations in the Polynomial Modular Number System. ARITH'05: 17th IEEE Symposium on Computer Arithmetic, 2005, USA, pp.206-213. ⟨lirmm-00387051⟩

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