Trisection for supersingular genur 2 curves in characteristic 2

Abstract

By reversing reduction in divisor class arithmetic we provide efficient trisection algorithms for Jacobians of supersingular genus 2 curves over finite fields of characteristic 2. With our technique we obtain new results for these Jacobians: we show how to find their 3-torsion subgroup, we prove there is none with 3-torsion subgroup of rank 3 and we prove their the maximal 3-power order subgroup is isomorphic to either Z/3^vZ or (Z/3^{v/2}Z)^2 or (Z/3^{v/4}Z)^4, where v is the 3-adic valuation v3(#Jac(C)(F2^m}). Ours are the first trisection formulae available in literature.