Study on fast method of field operation in elliptic curves
Lai Zhongx · Computer Engineering and Applications Journal · 2014
To raise the efficiency of field operation on elliptic curve, based on the idea of trading inversions for multiplications, two efficient algorithms are proposed to compute 4P and 5P directly over prime field F P in terms of affine coordinates. Their computational complexity are I+7M+8S and I+12M+10S respectively, which are improved to 4.6% and 2.6% respectively than those of Duc-Phong's and Xu Kaiping's method. Moreover, a fast method is given to compute 5kP directly in terms of affine coordinates. Its computational complexity is I +(15k + 1)M +(10k- 1)S and the efficiency of the new method is improved to 5.7% and 26.8% respectively than those of Xu Kaiping's and Mishra's method.