Open Access
April 2009 Bisection for genus 2 curves in odd characteristic
Josep M. Miret, Jordi Pujolàs, Anna Rio
Proc. Japan Acad. Ser. A Math. Sci. 85(4): 55-61 (April 2009). DOI: 10.3792/pjaa.85.55


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 $2D'=D$.


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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.


Published: April 2009
First available in Project Euclid: 2 April 2009

zbMATH: 1213.11130
MathSciNet: MR2517297
Digital Object Identifier: 10.3792/pjaa.85.55

Primary: 11G20 , 14H40 , 14H45

Keywords: finite field , genus 2 curves , Jacobian

Rights: Copyright © 2009 The Japan Academy

Vol.85 • No. 4 • April 2009
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