关键词: 圆锥曲线, 加法, 中国剩余定理, 公钥密码

Abstract: 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.