Koblitz椭圆曲线标量乘法的二次研究

计算机工程与应用 ›› 2008, Vol. 44 ›› Issue (4): 141-144.

Koblitz椭圆曲线标量乘法的二次研究

刘连浩¹,申勇^1,2

1.中南大学信息科学与工程学院，长沙 410083
2.中国人民解放军75230部队，广东韶关 512100

收稿日期:2007-05-30 修回日期:2007-09-10 出版日期:2008-02-01 发布日期:2008-02-01
通讯作者: 刘连浩

Re-research on scalar multiplication of Koblitz elliptic curves

LIU Lian-hao¹,SHEN Yong^1,2

1.The School of Information Science and Engineering，Central South University，Changsha 410083，China
2.75230 PLA Troops，Shaoguan，Guangdong 512100，China

Received:2007-05-30 Revised:2007-09-10 Online:2008-02-01 Published:2008-02-01
Contact: LIU Lian-hao

摘要/Abstract

摘要： Koblitz椭圆曲线通过Frobenius 映射实现了不需要倍点运算的标量乘法，很大程度上提高了标量乘法的效率。特征2和特征3的这类Koblitz曲线是以一次欧式环的素元来分解k，对此设想是否可以二次欧式环的素元为基底来二次分解k从而进一步提高效率。基于这一设想，通过数学分析诠释了上述设想的可行性，并给出了相应算法，效率明显提高。

关键词: Koblitz椭圆曲线, 标量乘法, 二次欧式环, Frobenius映射

Abstract: Koblitz elliptic curves implement scalar multiplication without point-doubling operation by Frobenius map，this method improves the efficiency of scalar multiplication greatly.Koblitz curves over a finite field of characteristic 2 and characteristic 3 disassembles k using prime element of simple Euclidean domain.To further improve the efficiency，presents an assumption of disassembling k based on prime element of quadratic Euclidean domain.To prove this assumption，this paper interprets the feasibility by math analysis，gives out corresponding algorithms，and finally proves that the method can improve the efficiency evidently.

Key words: Koblitz elliptic curves, scalar multiplication, quadratic Euclidean domain, Frobenius map

刘连浩¹,申勇^1,2. Koblitz椭圆曲线标量乘法的二次研究[J]. 计算机工程与应用, 2008, 44(4): 141-144.

LIU Lian-hao¹,SHEN Yong^1,2. Re-research on scalar multiplication of Koblitz elliptic curves[J]. Computer Engineering and Applications, 2008, 44(4): 141-144.

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