Augmented Addition Operation of Conic Curves over Ring Zn

In the recent research of conic curve cryptology, all rational points over Ring Zn could be expressed as C_n(a, b) = C₁ cup C₂ cup C₃ cup O. By for now, in the addition of conic curves over Z_n, all points on the curves are expressed by the form of (x, y) as the determinant condition. Then, the points belonging to C₁, C₂, C₃, O are computed and the results are discussed respectively. As a consequence too much cost is spent during the calculation. In mobile environment, more attention is paid to cut down the signature execution cost. How to make the signature more efficient is thus more important. The paper reconsiders the addition operation on conic curves over ring Zn as to reduce the amount of calculation. In the progress of the proposed addition operation, the value of (x, y) doesnpsilat need to be computed and all points could be expressed by parameter t. As a result, the computational cost is reduced.