GF(3^m)椭圆曲线群快速算术运算研究  

Research on Fast Arithmetic of Elliptic Curve over GF（3^m）

作　　者：端木庆峰[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,南京210007 [2]华中科技大学计算机学院信息安全系,武汉430074

出　　处：《计算机科学》2009年第5期96-98,114,共4页Computer Science

基　　金：国家自然科学基金课题(60703048)资助

摘　　要：详细研究了GF(3m)上椭圆曲线基本算术运算,给出并证明GF(3m)上超奇异和非超奇异椭圆曲线仿射坐标系下点加、倍点、3倍点和3k倍点计算公式,提出高效3k倍点递归算法,在逆乘率较高时,其效率要优于逐次3倍点算法。在此基础上,提出一种新的变长滑动窗口wrNAF标量乘算法,其在保证较少点加法运算优点的同时可有效降低3倍点的计算量。The arithmetic on supersingular and non-supersingular elliptic curve over GF（3^m ） were researched, and computational formulas of point addition, 2P,3P and 3^kp in affine coordinate were given and confirmed. Based on these,a new 3^kP recursive algorithm was proposed which was prior to multiple tripling point algorithms when the speed ratio of field inversion to field multiplication was high.Furthermore,we proposed a new variable length sliding window base-3 wrNAF scalar multiplication algorithm which can reduce the cost of tripling points needed in kP computatior.

关 键 词：椭圆曲线 标量乘法 小素数扩域 三元域 

分 类 号：TN918.1[电子电信—通信与信息系统]