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

文献类型：期刊论文

作者Chu, Huah3; Deng, Ying Pu1,2; Yang, Tse-Chung3
刊名ACTA MATHEMATICA SINICA-ENGLISH SERIES
出版日期2010-06-01
卷号26期号:6页码:1019-1054
关键词hyperelliptic curves hyperelliptic curve cryptosystems Jacobians isomorphism classes stabilizer
ISSN号1439-8516
DOI10.1007/s10114-010-7186-8
英文摘要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.
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
语种英语
WOS记录号WOS:000277409800003
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/10127]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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