The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2
Journal of Cryptology
Point Counting in Families of Hyperelliptic Curves
Foundations of Computational Mathematics
Counting points on Cab curves using Monsky--Washnitzer cohomology
Finite Fields and Their Applications
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In this paper we describe a generalisation and adaptation of Kedlaya's algorithm for computing the zeta-function of a hyperelliptic curve over a finite field of odd characteristic that the author used for the implementation of the algorithm in the Magma library. We generalise the algorithm to the case of an even degree model. We also analyse the adaptation of working with the x^idx/y^3 rather than the x^idx/y differential basis. This basis has the computational advantage of always leading to an integral transformation matrix whereas the latter fails to in small genus cases. There are some theoretical subtleties that arise in the even degree case where the two differential bases actually lead to different redundant eigenvalues that must be discarded.