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- Title
PMNS for cryptography: A guided tour.
- Authors
Méloni, Nicolas; Palma, François; Véron, Pascal
- 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 $ {\mathcal 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 $.
- Subjects
NUMBER systems; ARITHMETIC; MODULAR arithmetic; CRYPTOSYSTEMS; TRAVELING salesman problem; FINITE fields; CRYPTOGRAPHY
- Publication
Advances in Mathematics of Communications, 2024, Vol 18, Issue 2, p1
- ISSN
1930-5346
- Publication type
Article
- DOI
10.3934/amc.2023033