Optimizing fast scalar multiplication in elliptic curves
Haibo Zhou · Jisuanji yingyong yanjiu · 2012
Trading field multiplications for field squaring is an algebraic method to improve the performance of scalar multiplication in ECC.This paper gave the algorithms of 3P and 3~kP over F_p in terms of Jacobian coordinates.And their computational complexity were 6[M]+10[S] and(6k)[M]+(10k)[S] respectively,which was improved to 11.8% and 10.5% respectively than the best algorithms at present.In addition,this paper improved the algorithms of 2~kP and 3~kP over F_p in terms of affine coordinates on the basis of literature .And their computational complexity was improved to 6.3% and 3.3% respectively than literature .