Abstract
We show how to invert the multiplication-by-2 map in Jacobians of genus 2 curves $\mathrm{C}$ over finite fields $\mathbf{F}_{q}$ of odd characteristic. For any divisor $D\in \mathrm{Jac}(\mathrm{C})(\mathbf{F}_{q})$ we provide a method to construct the coordinates of all divisors $D'\in \mathrm{Jac}(\mathrm{C})(\mathbf{F}_{q})$ such that $2D'=D$.
Citation
Josep M. Miret. Jordi Pujolàs. Anna Rio. "Bisection for genus 2 curves in odd characteristic." Proc. Japan Acad. Ser. A Math. Sci. 85 (4) 55 - 61, April 2009. https://doi.org/10.3792/pjaa.85.55
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