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Point counting in families of hyperelliptic curves in characteristic 2

Hendrik Hubrechts
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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.

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BibTeXRIS

Hendrik Hubrechts. 2006-07-14. Point counting in families of hyperelliptic curves in characteristic 2. https://arxiv.org/abs/math/0607346

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