| Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2 |
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| 作者姓名： | DENG Yingpu & LIU Mulan Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China |
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| 作者单位： | DENG Yingpu & LIU Mulan Institute of Systems Science，Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | 中国科学院资助项目;科技部科研项目 |
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| 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.
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| 收稿时间： | 19 September 2004 |
| 修稿时间： | 19 September 2005 |
Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2 |
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| DENG Yingpu & LIU Mulan Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing ,China.Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2[J].Science in China(Mathematics),2006,49(2):173-184. |
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| Authors: | DENG Yingpu LIU Mulan |
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| Institution: | Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100080, China |
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| Abstract: | 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. |
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| Keywords: | hyperelliptic curves hyperelliptic curve cryptosystems Jacobian groups isomorphism classes |
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