Improving group law algorithms for jacobians of hyperelliptic curves

Abstract

In this paper, we propose three ideas to speed up the computation of the group operation in the Jacobian of a hyperelliptic curve: 1. Division of polynomials without inversions in the base field, and an extended gcd algorithm which uses only one inversion in the base field. 2. The omission of superfluous calculations in the reduction part. 3. Expressing points on the Jacobian in a slightly different form.