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Randomization of Arithmetic Over Polynomial Modular Number System

Autor: Jérémy Marrez, Laurent-Stéphane Didier, Pascal Véron, Nadia El Mrabet, Fangan-Yssouf Dosso

Publikováno v: ARITH
26th IEEE International Symposium on Computer Arithmetic
26th IEEE International Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.199-206, ⟨10.1109/ARITH.2019.00048⟩

International audience; The Polynomial Modular Number System (PMNS) is an integer number system designed to speed up arithmetic operations modulo a prime p. Such a system is defined by a tuple B = (p, n,\gamma ,\rho, E) where E \in Z[X] and E(\gamma)

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::badbb1e5f864e9180ee70f89e988c35e
https://doi.org/10.1109/arith.2019.00048

Arithmetic Operations in the Polynomial Modular Number System

Autor: Laurent Imbert, J. C. Bajard, Thomas Plantard

Publikováno v: ARITH'05: 17th IEEE Symposium on Computer Arithmetic
ARITH'05: 17th IEEE Symposium on Computer Arithmetic, 2005, USA, pp.206-213
Scopus-Elsevier
IEEE Symposium on Computer Arithmetic

PDF : voir RR 04030 (00109201); International audience; 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 arithmeti

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd2dea403b567a00a00c6aac808ae48f
https://hal-lirmm.ccsd.cnrs.fr/lirmm-00387051

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On Polynomial Modular Number Systems over $ \mathbb{Z}/{p}\mathbb{Z} $

Autor: Bajard, Jean Claude, Marrez, Jérémy, Plantard, Thomas, Véron, Pascal

Publikováno v: Advances in Mathematics of Communications
Advances in Mathematics of Communications, In press, ⟨10.3934/amc.2022018⟩

Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation is simple,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b0df51cfe2ecd5c5edd5a586c671d210
https://doi.org/10.3934/amc.2022018