Abstract

By reversing reduction in divisor class arithmetic we provide efficient trisection algorithms for supersingular Jacobians of 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 that the maximal 3-power order subgroup is isomorphic to either Z/3(nu)Z or (Z/3(nu/2)Z)(2) or (Z/3(nu/4)Z)(4), where nu is the 3-adic valuation nu(3)(#Jac(C)(F(2)m)). Ours are the first trisection formulae available in literature.