Point counting in families of hyperelliptic curves in characteristic 2
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
Let E_G be a family of hyperelliptic curves over F2^(alg cl) with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute the zeta function of E_g for g in a degree n extension field of F, which has as time complexity O(n^3) and memory requirements O(n^2). With a slightly different algorithm we can get time O(n^2,667) and memory O(n^2,5), and the computation of O(n) curves of the family can be done in time and space O(n^3). All these algorithms are polynomial in the genus.
Keywords
Cite
@article{arxiv.math/0607346,
title = {Point counting in families of hyperelliptic curves in characteristic 2},
author = {Hendrik Hubrechts},
journal= {arXiv preprint arXiv:math/0607346},
year = {2007}
}
Comments
23 pages