4 citations · 4 across the 3 of their papers we have counts for
4 papers
On the complexity of computing integral bases of function fields
Simon Abelard
Let be a plane curve given by an equation with a monic squarefree polynomial. We study the problem of computing an integral basis of the alg…
Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus
Simon Abelard
We present a probabilistic Las Vegas algorithm for computing the local zeta function of a genus- hyperelliptic curve defined over with explicit real multiplication…
Counting points on genus-3 hyperelliptic curves with explicit real multiplication
Simon Abelard, Pierrick Gaudry, Pierre-Jean Spaenlehauer
We propose a Las Vegas probabilistic algorithm to compute the zeta function of a genus-3 hyperelliptic curve defined over a finite field , with explicit real multiplic…
Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
Simon Abelard, Pierrick Gaudry, Pierre-Jean Spaenlehauer
We present a probabilistic Las Vegas algorithm for computing the local zeta function of a hyperelliptic curve of genus defined over . It is based on the approache…