Isomorphism classes of elliptic and hyperelliptic curves over finite fields F_((2g+1)~n)

Youngju Choie; Eunkyung Jeong

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Isomorphism classes of elliptic and hyperelliptic curves over finite fields F_((2g+1)~n)

机译：有限域F _（（2g + 1）〜n）上的椭圆曲线和超椭圆曲线的同构类

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摘要

We give the number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields F_((2g+1)~n), g = 1,2,3. These results have applications to hyperelliptic curve cryptography.

机译：我们给出了在有限域F _（（2g + 1）〜n），g = 1,2,3上定义的g类超椭圆曲线的同构类的数量和代表。这些结果已应用于超椭圆曲线密码学。

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来源
《Finite fields and their applications》 |2004年第4期|p.583-614|共32页
作者
Youngju Choie; Eunkyung Jeong;
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作者单位

Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea;

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原文格式 PDF
正文语种 eng
中图分类数理科学和化学;
关键词
cryptography; elliptic curves; hyperelliptic curves; finite fields; isomorphism classes; representatives;

机译：密码学;椭圆曲线;超椭圆曲线;有限域;同构类;代表;

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1. Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with odd characteristic [J] . Yingpu Deng, Mulan Liu European journal of combinatorics . 2008,第6期

机译：奇数有限域上属4的尖超椭圆曲线的同构类计数
2. A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point [J] . Garcia JE, Encinas LH, Masque JM Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications . 2006,第1a3期

机译：容许Weierstrass点的有限域上2类超椭圆曲线的同构类的综述
3. Isomorphism classes of hyperelliptic curves of genus 3 over finite fields [J] . Yingpu Deng Finite fields and their applications . 2006,第2期

机译：有限域上属3的超椭圆曲线的同构类
4. The number of the isomorphism classes of hyperelliptic curves of genus four over finite fields [C] . Lin You, Fugeng Zeng 2010 Sixth International Conference on Information Assurance and Security . 2010

机译：有限域上四类超椭圆曲线的同构类数
5. Character Sums and Hyperelliptic Curves Associated with Subsets of Finite Fields with Square Order. [D] . Simon, Lois Susan. 2011

机译：与平方阶有限域子集相关的字符和和超椭圆曲线。
6. Moments of zeta functions associated to hyperelliptic curves over finite fields [O] . Michael O. Rubinstein, Kaiyu Wu -1

机译：与有限域上的超椭圆曲线相关的zeta函数的矩
7. Isomorphism classes of elliptic and hyperelliptic curves over finite fields F(2g+1)n [O] . Choie Youngju, Jeong Eunkyung 2004

机译：有限域F（2g + 1）n上的椭圆曲线和超椭圆曲线的同构类

Isomorphism classes of elliptic and hyperelliptic curves over finite fields F_((2g+1)~n)

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