Fast arithmetic on hyperelliptic curves via continued fraction expansions

@inproceedings{Jacobson2007FastAO,
title={Fast arithmetic on hyperelliptic curves via continued fraction expansions},
author={Michael J. Jacobson},
year={2007}
}

In this paper, we present a new algorithm for computing the reduced sum of two divisors of an arbitrary hyperelliptic curve. Our formulas and algorithms are generalizations of Shanks’s NUCOMP algorithm, which was suggested earlier for composing and reducing positive definite binary quadratic forms. Our formulation of NUCOMP is derived by approximating the irrational continued fraction expansion used to reduce a divisor by a rational continued fraction expansion, resulting in a relatively simple… CONTINUE READING