Welcome to the resource topic for 2023/1231
Title:
PMNS revisited for consistent redundancy and equality test
Authors: Fangan Yssouf Dosso, Alexandre Berzati, Nadia El Mrabet, Julien Proy
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. In~\cite{rando-pmns-arith26}, Didier et al. used this redundancy property 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.
ePrint: https://eprint.iacr.org/2023/1231
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