Explicit 2-power torsion of genus 2 curves over finite fields (Q540360)

The authors reverse Cantor's doubling algorithms to construct an algorithm for determining the structure of the 2-Sylow subgroup of the Jacobian of a curve of genus two over a finite field of odd characteristic. This algorithm, which uses the 2-torsion points as seeds for successive halvings, is based upon that of [\textit{I. Kitamura, M. Katagi} and \textit{T. Takagi}, A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two. Lect. Notes Comput. Sci. 3574, 146--157 (2005; Zbl 1127.94347)] for the case of even characteristic.