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Symbolic trisection polynomials for genus 2 curves in odd characteristic. (English) Zbl 1440.11107

Summary: We provide a symbolic trisection polynomial for Jacobians of genus 2 curves over finite field \(\mathbb{F}_q\) of odd characteristic. These polynomials can be used to improve the efficiency of trisection algorithms, which may then be used to obtain faster point counting algorithms.

MSC:

11G20 Curves over finite and local fields
14H40 Jacobians, Prym varieties
14H45 Special algebraic curves and curves of low genus
13P15 Solving polynomial systems; resultants

Software:

Magma; NTL
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References:

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