Hessian椭圆曲线上基于Co-Z运算的标量乘算法  

Scalar Multiplication on Hessian Curves Based on Co-z Operations

作　　者：赖忠喜[1] 张占军[1] 

机构地区：[1]台州职业技术学院机电研究所,浙江台州318000

出　　处：《科技通报》2016年第2期28-33,共6页Bulletin of Science and Technology

基　　金：台州职业技术学院重点课题(2014ZD03);浙江省教育厅科研项目资助(Y201533946)

摘　　要：为了提高Hessian椭圆曲线标量乘算法的效率和安全性,在Co-Z点加算法的基础上提出了Hessian椭圆曲线上只有(X,Y)坐标的Co-Z点加,共轭点加及倍点-点加算法,将这些运算应用到传统的Montgomery阶梯算法和无零有符号二进制标量乘算法中,提出了两种改进的的标量乘算法。理论分析表明:新改进的两种标量乘算法比原来传统的标量乘算法效率大约提高了14%,而且其抵抗侧信道攻击和故障攻击的性能得到明显增强。To raise the efficiency and security of scalar multiplication on hessian elliptic curves, Based on the Co-Z addition operation, (X,Y)-only Co-Z addition, conjugate addition and double–addition operations on hessian elliptic curves were proposed. Applied these operations to traditional Montgomery ladder and zero- less signed- digit scalar multiplication algorithm, two kinds of improved scalar multiplication algorithm were put forward. The theoretical analysis results show that the efficiency of the two modified algorithms were increased by about 14% compared with the original traditional ones, and their performance of resisting against side-channel attack and fault attack were improved significantly.

关 键 词：椭圆曲线密码体制 Hessian椭圆曲线 标量乘法 Co-Z运算 投影坐标 

分 类 号：O23[理学—运筹学与控制论]