Abstract

Abstract. The objective of this paper is to state and prove some useful theorems for realizing the group law in the Jacobians of C ab 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 C35 curve.