Study on fast method of scalar multiplication in elliptic curve cryptography
GU Jingjing · Computer Engineering and Applications Journal · 2011
In the elliptic curve cryptosystem,scalar multiplication is the most expensive operation,and the number of inversion determines the performance of scalar multiplication.Trading inversions for multiplications can decrease the number of inversion.Based on it,an efficient algorithm is proposed to computer 5P directly over Fp in terms of affine coordinates,saving two field inversions compared to the traditional method.Moreover,a method is given to compute 5kP directly,which is more efficient than k repeated 5P.Finally,the two algorithms are applied to scalar multiplication combined with multibase chains.The experimental results show that the proposed method requires about 6.5~14 less running time than traditional methods,and the ration I/M of break-even point can be reduced to 1.1.