Improved Complexity Bounds for Counting Points on Hyperelliptic Curves
نویسندگان
چکیده
We present a probabilistic Las Vegas algorithm for computing the local zeta function of a hyperelliptic curve of genus g defined over Fq. It is based on the approaches by Schoof and Pila combined with a modelling of the l-torsion by structured polynomial systems. Our main result improves on previously known complexity bounds by showing that there exists a constant c > 0 such that, for any fixed g, this algorithm has expected time and space complexity O((log q)) as q grows and the characteristic is large enough.
منابع مشابه
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عنوان ژورنال:
- CoRR
دوره abs/1710.03448 شماره
صفحات -
تاریخ انتشار 2017