Papers › Enumerating hyperelliptic curves over finite fields in quasilinear time
Enumerating hyperelliptic curves over finite fields in quasilinear time
Everett W. Howe
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We present an algorithm that, for every fixed genus g, will enumerate all hyperelliptic curves of genus g over a finite field k of odd characteristic in quasilinear time; that is, the time required for the algorithm is O(q²ᵍ⁻¹), where q=#k. Such an algorithm already exists in the case g=2, thanks to work of Mestre and Cardona and Quer, and in the case g=3, thanks to work of Lercier and Ritzenthaler. Experimentally, it appears that our new algorithm is about two orders of magnitude faster in practice than ones based on their work.
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