计算机工程

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超椭圆曲线上斜-Frobenius映射及有效标量乘算法研究

卢宇,汪学明   

  1. (贵州大学 计算机科学与技术学院,贵阳 550025)
  • 收稿日期:2016-06-21 出版日期:2017-06-15 发布日期:2017-06-15
  • 作者简介:卢宇(1992—),男,硕士研究生,主研方向为密码学、信息安全;汪学明(通信作者),教授、博士。
  • 基金项目:
    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)。

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

LU Yu,WANG Xueming   

  1. (College of Computer Science and Technology,Guizhou University,Guiyang 550025,China)
  • Received:2016-06-21 Online:2017-06-15 Published:2017-06-15

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%。

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

Abstract: 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.

Key words: hyperelliptic curve, elliptic curve, skew-Frobenius mapping, scalar multiplication algorithm, efficiency analysis

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