C_ab CURVES: A QUICK SHORT-CUT

The objective of this paper is to state and prove some useful theorems for realizing the group law in the Jacobians of Cab curves, which provide an efficient and easy-to-implement algorithm for computations within the group. The idea is a generalization of a method previously presented in 2005, which gave an algorithm to realizing the group law on the superelliptic curves of genus 3 or 4. As an example of our approach, we will show how this method can be used to formulate a reasonably fast arithmetic in the Jacobian of C_35 curve.