3特征域椭圆曲线群点的快速计算算法  

Fast arithmetic operations of elliptic curve over GF（3~m）

作　　者：端木庆峰[1] 张雄伟[1] 王衍波[1] 张凯泽[1] 雷凤宇[2] 

机构地区：[1]解放军理工大学通信工程学院,江苏南京210007 [2]华中科技大学计算机学院,湖北武汉430074

出　　处：《解放军理工大学学报（自然科学版）》2011年第1期1-6,共6页Journal of PLA University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60703048)

摘　　要：GF(3m)作为小素数扩域GF(pm)更加特殊的一种类型,定义于其上的椭圆曲线密码算法更加优越。基于有限域GF(3m)特殊性质,详细研究了GF(3m)上椭圆曲线群基本点算术运算,给出并证明了GF(3m)上超奇异和非超奇异椭圆曲线在仿射、射影、雅可比、Chudnovsky雅可比和López Dahab坐标系下普通点加、混合点加、倍点和3倍点计算公式,并分析比较其计算性能。结果表明,GF(3m)-ECC各基本点算术运算在仿射坐标系下的效率明显优于其他坐标系统。The algorithms of elliptic curve cryptography over GF（3m）,a special type of small prime extension fields GF（pm）,have superior advantages.Based on the features of GF（3m）,the arithmetic operations on supersingular and non-supersingular elliptic curve over GF（3m） were researched.The computational formulas of point addition,mixed point addition,2P and 3P in affine,Projective,Jacobian,Chudnovsky and López Dahab coordinate systems were proposed and confirmed,and their computational costs analyzed and compared.The analysis results show that the efficiency of GF（3m）-ECC arithmetic operations in affine coordinate system was better than those in any other coordinate systems.

关 键 词：三元域 椭圆曲线 标量乘法 射影坐标系 

分 类 号：TP918.1[自动化与计算机技术]