Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2  

作　　者：DENG Yingpu LIU Mulan 

机构地区：[1]Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100080, China Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100080, China

出　　处：《Science China Mathematics》2006年第2期173-184,共12页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.10501049&90304012);973 Project(Grant No.2004CB318000).

摘　　要：In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields Fq with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 (|) m, then the formula is 2q3 + q2 - q;if 4 | m, then the formula is 2q3 + q2 - q + 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields Fq with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 + m, then the formula is 2q3 + q2 - q; if 4 | m, then the formula is 2q3 + q2 - q + 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.

关 键 词：hyperelliptic CURVES hyperelliptic curve CRYPTOSYSTEMS JACOBIAN GROUPS ISOMORPHISM classes. 

分 类 号：N[自然科学总论]