The Isomorphism Classes of Hyperelliptic Curves over Finite Fields with Characteristic 2
Date Issued
2005
Date
2005
Author(s)
Yang, Tse-Chung
DOI
en-US
Abstract
In this thesis we will find the number of isomorphism classes of hyperelliptic curves of genus 4 over a finite field F_q with characteristic 2. We prove the formula of the number N of isomorphism classes as the following:
N=2q^7+q^4-q^3 if 2 divides m
N=2q^7+q^4-q^3+4q^2-4q+4 if 6 divides m
N=2q^7+q^4-q^3+4q^2-4q+16 if 2 divides m,but 6 does not divide m.
These results can be used in the classification problems and the hyperelliptic curve cryptosystems.
Subjects
超橢圓曲線
超橢圓曲線密碼系統
同構類
hyperelliptic curves
hyperelliptic curve cryptosystem
isomorphism classes
Type
thesis
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