Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic

doi:10.1007/s10114-010-7186-8

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	Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic
	Chu, Huah 3; Deng, Ying Pu1,2 ; Yang, Tse-Chung 3
	2010-06-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	26 期号:6 页码:1019-1054
摘要	This paper is devoted to counting the number of isomorphism classes of pointed hyperelliptic curves over finite fields. We deal with the genus 4 case and the finite fields are of even characteristics. The number of isomorphism classes is computed and the explicit formulae are given. This number can be represented as a polynomial in q of degree 7, where q is the order of the finite field. The result can be used in the classification problems and it is useful for further studies of hyperelliptic curve cryptosystems, e.g. it is of interest for research on implementing the arithmetics of curves of low genus for cryptographic purposes. It could also be of interest for point counting problems; both on moduli spaces of curves, and on finding the maximal number of points that a pointed hyperelliptic curve over a given finite field may have.
关键词	hyperelliptic curves hyperelliptic curve cryptosystems Jacobians isomorphism classes stabilizer
DOI	10.1007/s10114-010-7186-8
语种	英语
资助项目	National Natural Science Foundation of China[10501049] ; National Natural Science Foundation of China[60821002] ; 973 Project[2004CB318000]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000277409800003
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10128
专题	系统科学研究所
通讯作者	Deng, Ying Pu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Grad Univ, State Key Lab Informat Secur, Beijing 100049, Peoples R China 3.Natl Taiwan Univ, Dept Math, Taipei 10764, Taiwan
推荐引用方式 GB/T 7714	Chu, Huah,Deng, Ying Pu,Yang, Tse-Chung. Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2010,26(6):1019-1054.
APA	Chu, Huah,Deng, Ying Pu,&Yang, Tse-Chung.(2010).Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic.ACTA MATHEMATICA SINICA-ENGLISH SERIES,26(6),1019-1054.
MLA	Chu, Huah,et al."Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic".ACTA MATHEMATICA SINICA-ENGLISH SERIES 26.6(2010):1019-1054.