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Arithmetic Operations in the Polynomial Modular Number System

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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Contributor : Jean Claude Bajard <>
Submitted on : Friday, May 22, 2009 - 5:25:15 PM
Last modification on : Friday, January 10, 2020 - 3:36:04 PM


  • HAL Id : lirmm-00387051, version 1



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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