Hyperelliptic curves of genus three over finite fields of even characteristic
type: Item
instance of: scholarly article
title: Hyperelliptic curves of genus three over finite fields of even characteristic
zbMATH Open document ID: 1049.11063
author: Daniel Sadornil
author: Enric Nart
published in: Finite Fields and their Applications
publication date: 2004-08-06T00:00:00Z
review text: The interest on hyperelliptic curves over a finite field of characteristic 2 of genus 2 or 3 was renewed after \textit{N. Koblitz}'s paper [J. Cryptology 1, 139--150 (1989; Zbl 0674.94010)] and \textit{L. M. Adleman}, \textit{J. DeMarrais} and \textit{M. Huang}'s paper [Algorithmic number theory, ANTS-I, 1994, Lect. Notes Comput. Sci. 877, 28--40 (1994; Zbl 0829.11068)], where connections with cryptography matters were established. Such curves of genus 2 were classified by \textit{G. Cardona}, \textit{E. Nart} and \textit{J. Pujolàs} [http:\slash\slash www.arxiv.org/math.NT/0210105]. In this paper, the genus 3 case is studied. By using a similar method as in the aforementioned paper, the authors succeed in classifying the curves in this case via rational models with a given structure of its ramification divisor.
reviewed by: Fernando Torres
Mathematics Subject Classification ID: 11G20
zbMATH DE Number: 2083585
zbMATH Keywords: hyperelliptic curves
zbMATH Keywords: automorphism group
zbMATH Keywords: moduli spaces
MaRDI profile type: Publication
full work available at URL: j.ffa.2003.08.002
OpenAlex ID: W2077261278
cites work: Q4847910
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cites work: Q3374896
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DOI: 10.1016/J.FFA.2003.08.002
description: scientific article; zbMATH DE number 2083585