亏格为3的超椭圆曲线除子类群的计算公式

亏格为3的超椭圆曲线除子类群的计算公式

付治国, 术洪亮, 张树功

吉林大学数学学院, 长春 130012

收稿日期:2008-06-02 修回日期:1900-01-01 出版日期:2009-03-26 发布日期:2009-03-26
通讯作者: 张树功

Formulae for Arithmetic on Genus 3 Hyperelliptic Curves

FU Zhiguo, SHU Hongliang, ZHANG Shugong

College of Mathematics, Jilin University, Changchun 130012, China

Received:2008-06-02 Revised:1900-01-01 Online:2009-03-26 Published:2009-03-26
Contact: ZHANG Shugong

摘要/Abstract

摘要： 根据传统的Cantor算法, 结合亏格为3的超椭圆曲线除子的特点, 给出了其约化除子加法和翻倍运算的计算公式. 实验结果表明, 用公式导出的直接算法明显优于Cantor算法.

关键词: 超椭圆曲线, 公钥密码系统, Cantor算法, 除子计算公式

Abstract: The explicit formula is presented for computing the reduced sum of two divisors of genus 3 hyperelliptic curves in term of Cantor’ algorithm. The experimental results indicate that our algorithm is superior to Cantor’s algorithm.

Key words: hyperelliptic curves, public key cryptosystem, Cantor’s algorithm, explicit formulae

中图分类号:

O156.2

付治国, 术洪亮, 张树功. 亏格为3的超椭圆曲线除子类群的计算公式[J]. J4, 2009, 47(02): 201-206.

FU Zhiguo, SHU Hongliang, ZHANG Shugong. Formulae for Arithmetic on Genus 3 Hyperelliptic Curves[J]. J4, 2009, 47(02): 201-206.