Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: New Results

Improved Complexity Bounds for Counting Points on Hyperelliptic Curves

Participants : Simon Abelard, Pierrick Gaudry, Pierre-Jean Spaenlehauer.

In [16], 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 modeling of the -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((logq)cg) as q grows and the characteristic is large enough.