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Journal Articles Advances in Mathematics of Communications Year : 2023

PMNS for Cryptography : A Guided Tour

Abstract

The Polynomial Modular Number System (PMNS) offers an alternative to the conventional binary multi-precision representation system for large integers. Its effectiveness has been demonstrated for various cryptosystems using prime field arithmetic [2, 4, 6], with prime sizes ranging from 256 to 736 bits. However, as the size of p increases, the relative performance of PMNS compared to standard arithmetic diminishes. Furthermore, the generation process of a PMNS has a worst-case complexity of O(2 n), where n denotes the number of symbols used to represent an integer modulo p in this representation system. In this paper, we present several alternatives and improvements to the construction and implementation processes of PMNS, which are tailored to the size of p.
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hal-04195613 , version 1 (04-09-2023)

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Public Domain

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Nicolas Méloni, François Palma, Pascal Véron. PMNS for Cryptography : A Guided Tour. Advances in Mathematics of Communications, In press, ⟨10.3934/amc.2023033⟩. ⟨hal-04195613⟩

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