亏格2超椭圆曲线除子类群的直接算法

J4 ›› 2010, Vol. 48 ›› Issue (05): 774-776.

亏格2超椭圆曲线除子类群的直接算法

付治国¹, 丁秀欢², 张树功¹

1. 吉林大学数学学院, 长春 130012|2. 浙江海洋学院数学与信息学院, 浙江舟山 316000

收稿日期:2010-01-22 出版日期:2010-09-26 发布日期:2010-09-21
通讯作者: 付治国 E-mail:fuzg@jlu.edu.cn

Formulae Derived by NUCOMP Algorithm forArithmetic on Genus 2

FU Zhiguo¹, DING Xiuhuan², ZHANG Shugong¹

1. College of Mathematics, Jilin University, Changchun 130012, |China;2. College of Mathematics and Information, Zhejiang Ocean University, Zhoushan 316000, Zhejiang Province, China

Received:2010-01-22 Online:2010-09-26 Published:2010-09-21
Contact: FU Zhiguo E-mail:fuzg@jlu.edu.cn

摘要/Abstract

摘要：

针对亏格2超椭圆曲线的情形, 从以下三方面改进了NUCOMP算法: (1) 用有限域F_q中元素的求逆运算代替NUCOMP算法中的多项式求逆运算; (2) 利用Montgomery的求逆技巧将多个元素求逆用一个元素求逆实现; (3) 在NUCOMP算法计算中省去了部分多项式的系数计算. 实验结果表明, 改进后的算法比NUCOMP算法效率显著提高.

关键词: 超椭圆曲线公钥密码系统, Cantor算法, NUCOMP算法

Abstract:

We used the following technique to improve the NUCOMP algorithm for the hyperelliptic curves of genus 2:
(1) avoiding the computation of the polynomial’s inverse by resultant;
(2) Montgomery’s trick of simultaneous inversions;
(3) Reordering of normalization steps to save some field operations.
The experimental results show that our algorithm is more efficient than the NUCOMP algorithm.

Key words: hyperelliptic curves cryptosystem, Cantor algorithm,
NUCOMP algorithm

中图分类号:

付治国, 丁秀欢, 张树功. 亏格2超椭圆曲线除子类群的直接算法[J]. J4, 2010, 48(05): 774-776.

FU Chi-Guo, DING Xiu-Huan, ZHANG Shu-Gong. Formulae Derived by NUCOMP Algorithm forArithmetic on Genus 2[J]. J4, 2010, 48(05): 774-776.