超椭圆曲线上斜-Frobenius映射及有效标量乘算法研究  

Research on Skew-Frobenius Mapping and Effective Scalar Multiplication Algorithm on Hyperlliptic Curves

作　　者：卢宇[1] 汪学明[1] 

机构地区：[1]贵州大学计算机科学与技术学院,贵阳550025

出　　处：《计算机工程》2017年第6期78-83,91,共7页Computer Engineering

基　　金：国家自然科学基金(61163049);贵州省自然科学基金(黔科合J字[2011]2197号)

摘　　要：为提高超椭圆曲线上标量乘计算效率,将椭圆曲线上的斜-Frobenius映射推广到超椭圆曲线上,在亏格为4的超椭圆曲线上构造斜-Frobenius映射,通过对亏格为2,3,4的超椭圆曲线上的斜-Frobenius映射,提出超椭圆曲线上斜-Frobenius映射的一般形式。基于超椭圆曲线上的斜-Frobenius映射的一般形式构造新的标量乘算法,提高计算超椭圆曲线上标量乘的效率。实验结果表明,提出的基于超椭圆曲线上的斜-Frobenius映射标量乘效率比基于二进制标量乘算法提高了39%。In order to improve the computing efficiency of scalar multiplication on hyperelliptic curves, the skew- Frobenius mapping on the elliptic curve is extended to hyperelliptic curves,and a skew-Frobenius mapping is constructed on the hyperelliptic curve with a genus of 4, through the skew-Frobenius mapping on the hyperelliptic curve which is defined on genus 2,3 and 4. The general form of skew-Frobenius mapping on the hyperelliptic curve is proposed. A new scalar multiplication algorithm is constructed based on the genetal form of skew-Frobenius mapping on hyperelliptic curves, which improve the efficiency of scalar multiplication on hyperelliptic curves. Experimental results show the scalar multiplication of the skew-Frobenius mapping on the hyperelliptic curve is about 39% faster than that of the binary scalar multiplication algorithm.

关 键 词：超椭圆曲线 椭圆曲线 斜-Frobenius映射 标量乘算法 效率分析 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]