环Z_n上圆锥曲线加法的改进

Improved Addition of Conic Curve over the Ring Z_n

环Zn圆锥曲线上的加法都要以(x,y)的形式表示出来作为判定条件,分别考虑运算结果属于C1,C2,C3,O的情况,因此计算比较繁琐.根据环Zn上的加法的定义对环上加法进行改进.运算过程中,圆锥曲线上的点都以参数t表示,不用每一步都计算出(x,y),利用中国剩余定理对点P坐标进行分解,然后将(tmp,tnq)合并,计算nP的坐标,运算时只需要对参数t进行操作,简化了环Zn上圆锥曲线的加法运算,明显减低计算的时间复杂度,算法优于改进前的加法运算.

In conic curve cryptology,all the values of points in the operation of addition on conic curve over the ring Zn should be expressed in the （x,y） form as the criteria then what condition（C1,C2,C3 or O ）the result of operation belongs to should be taken into consideration one by one,of which the computation is so tiresome. The operation of addition on conic curve of the ring is therefore to be improved in accordance to the definition of the addition on the ring Zn. It is proposed that the values of all points （x,y） on conic curve shall be expressed with the parameter t,and the （x,y） of all points are not required to work out in each and every step but the coordinates of the point P are to be decomposed according to the Chinese remainder theorem,i.e.,incorporating the terms （tmp,tnq）to work out the coordinates of nP. Thus,during the operation of addition only the parameter t is needed so as to simplify such an operation of addition on conic curve over the ring Zn. As a result,the time required and computational complexity are both reduced obviously,which implies that the algorithm proposed is better than the operation of addition before the improvement.