A Review on the Isomorphism Classes of Hyperelliptic Curves of Genus 2 over Finite Fields Admitting a Weierstrass Point

The reduced equations for the isomorphism classes of hyperelliptic curves of genus 2 admitting a Weierstrass point over a finite field of arbitrary characteristic, are shown and the number of such classes is included. This work picks up in a unified way a series of previous results published by seve...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2006-09, Vol.93 (1-3), p.299-318
Main Authors: Espinosa Garcia, J, Hernandez Encinas, L, Munoz Masque, J
Format: Article
Language:English
Subjects:
Algorithms
Classifications
Computer systems
Cryptography
Digital signatures
Digital transmission
Isomorphism
Mathematical analysis
Mathematical problems
National security
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Summary:The reduced equations for the isomorphism classes of hyperelliptic curves of genus 2 admitting a Weierstrass point over a finite field of arbitrary characteristic, are shown and the number of such classes is included. This work picks up in a unified way a series of previous results published by several authors by using different methodologies. These classifications are of interest in designing and implementing of hyperelliptic curve cryptosystems.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-006-9045-2