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）

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.