椭圆曲线中一种计算7P和7^kP的改进算法

Improved algorithms for computing 7P and 7^kP on elliptic curves

为了提高椭圆曲线底层域运算的效率,基于将乘法运算转换为平方运算的思想,提出在素数域GF_P上用仿射坐标直接计算7P和7-k P的改进算法,其运算量分别为I＋18M＋12S和I＋（17k＋2）M＋（14k＋1）S,与已有的最好算法相比,效率分别提升了8.3%和10.3%。另外,基于相同的思想给出了素数域GF_P上用仿射坐标系直接计算5-k P的改进算法,其运算量为I＋（9k＋2）M＋（14k＋1）S,与徐凯平和Mishra等人所提的算法相比,效率分别提升了17.2%和35.7%。

To raise the efficiency of field operations on elliptic curve,based on the idea of trading multiplications for squares,two improved algorithms are proposed to compute 7P and 7^kP directly over GFp in terms of affine coordinates,their computational complexity is I＋18M＋12S and I＋（17k ＋ 2）M＋（14k ＋1）S respectively,and the new algorithm＇s efficiency is improved by 8.3% and 13.5% respectively compared with the best algorithms at present.In addition,based on the same idea,a modified method is given to compute 5kP directly over GFp in terms of affine coordinates,its computational complexity is I＋（9k ＋ 2）M＋（14k＋ 1）S,and the efficiency of the new method is improved by 17.2% and 35.7%respectively compared with Xu Kaiping＇ s and MISHRA＇ s method.