改进的Koblitz曲线上数字签名算法  

IMPROVEMENT OF DIGITAL SIGNATURE ALGORITHM ON KOBLITZ CURVE

作　　者：尹灿[1] 武海鹰[1] 卢忱[1] 

机构地区：[1]武警工程学院通信工程系,陕西西安710086

出　　处：《计算机应用与软件》2011年第4期298-301,共4页Computer Applications and Software

摘　　要：标量乘法的效率决定着椭圆曲线密码体制的性能,而JSF算法是当前最流行的计算椭圆曲线双标量乘的算法;Koblitz曲线上的快速标量乘算法是标量乘法研究的重要课题。Lee[12]算法采用Frobenius映射扩展正整数k并将其扩展后的系数改写成二进制形式有效地提高标量乘算法效率。将JSF应用到扩展后的系数中,以较小存储空间为代价来提高算法效率,并将算法运用到改进的ECDSA算法中,减少乘法运算次数,加速签名及验证过程,节约数字签名时间。The performance of ECC depends on the efficiency of scalar multiplication.JSF is the most popular method for calculating the elliptic curve by double-scalar algorithm.Furthermore,the fast scalar multiplication algorithm on Koblitz curve is the top demanding task in the research of scalar multiplication.In Lee algorithm,Frobenius map is utilised to expand integer k and each coefficient of the expansion is represented as a binary string,therefore the efficiency of scalar multiplication has been improved effectively.In this paper,we applied the Joint Sparse Form to the expanded coefficients to improve the efficiency of the algorithm at the cost of a lower storage requirement.The algorithm was applied to the improved ECDSA algorithm to reduce the times of multiplication,and to accelerate the processes of signature and authentication,and to decrease the time of digital signature.

关 键 词：KOBLITZ曲线 联合稀疏形 Frobenius映射 标量乘 椭圆曲线数字签名 

分 类 号：TP393.08[自动化与计算机技术—计算机应用技术]