An Addition Algorithm in Jacobian of C3,4 Curve

Abstract. This paper gives an efficient algorithm to compute addition in Jacobian of C34 curves. The paper modifies the addition algorithm of [1], by classifying the forms of Groebner bases of all ideals involved in the addition in Jacobian, and by computing Groebner bases of ideals without using Buchberger algorithm. The algorithm computes the addition in Jacobian of C34 curves in about 3 times amount of computation of the one in elliptic curves, when the sizes of groups are set to be the same.