Paper 2023/1231
PMNS revisited for consistent redundancy and equality test
Abstract
The Polynomial Modular Number System (PMNS) is a non-positional number system for modular arithmetic. A PMNS is defined by a tuple $(p, n, \gamma, \rho, E)$, where $p$, $n$, $\gamma$ and $\rho$ are positive non-zero integers and $E\in\mathbb{Z}_{n}[X]$ is a monic polynomial such that $E(\gamma) \equiv 0 \pmod p$. The PMNS is a redundant number system. This redundancy property has already been used to randomise the data during the Elliptic Curve Scalar Multiplication (ECSM). In this paper, we refine the results on redundancy and propose several new results on PMNS. More precisely, we study a generalisation of the Montgomery-like internal reduction method proposed by Negre and Plantard, along with some improvements on parameter bounds for smaller memory cost to represent elements in this system. We also show how to perform equality test in the PMNS.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Modular arithmeticPolynomial modular number systemInternal reductionEuclidean latticesRedundancyEquality test
- Contact author(s)
-
fanganyssouf dosso @ emse fr
alexandre berzati @ thalesgroup com
nadia el-mrabet @ emse fr
julien proy @ thalesgroup com - History
- 2023-09-01: revised
- 2023-08-14: received
- See all versions
- Short URL
- https://ia.cr/2023/1231
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/1231,
author = {Fangan Yssouf Dosso and Alexandre Berzati and Nadia El Mrabet and Julien Proy},
title = {{PMNS} revisited for consistent redundancy and equality test},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1231},
year = {2023},
url = {https://eprint.iacr.org/2023/1231}
}
