An Addition Algorithm in Jacobian of C34 Curve
Seigo Arita · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2005
This paper gives an efficient algorithm to compute addition in Jacobian of C 34 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 C 34 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.2 C 34 Curve and Its Jacobian Group C 34 curve, which is a special case of C ab curve found by Miura [11,9], is a nonsingular plan curve defined by the following form of polynomial F (X, Y ):