GF（2^m）域上椭圆曲线点乘算法的改进

Improvement of scalar multiplication algorithm on elliptic curve over GF(2m)

介绍了在GF(2 m)域上实现非超异椭圆曲线的点乘的算法 ,它是Montgomery算法的改进。该算法无需乘法预处理 ,运算速度快于IEEEP1363草案标准上“加 -减”算法 ,而且占用的内存资源少 ,易于软、硬件方式的实现。因此 ,该算法更利于在那些资源有限的环境中实现椭圆曲线加密体制。

This paper describes an algorithm for computing scalar multiplications on non-supersingular elliptic curve defined over GF(2m). This algorithm is an optimized version of Montgomery's method. It requires no precomputed multiples of a point and is faster than the addition-subtraction method described in draft standard IEEE P1363. In addition, it is easy to implement in both hardware and software, requires less memory than projective schemes. Therefore, it is much convenient to implement ECC in restricted environments.