2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154914We prove that in most cases relevant to cryptography, the Frobenius endomorphism on the Jacobian of a genus two curve is represented by a diagonal matrix with respect to an appropriate basis of the subgroup of l-torsion points. From this fact we get an explicit description of the Weil-pairing on the subgroup of l-torsion points. Finally, the explicit description of the Weil-pairing provides us with an efficient, probabilistic algorithm to find generators of the subgroup of l-torsion points on the Jacobian of a genus two curve.Algebraic Geometry11G20 (Primary); 11T71, 14G50, 14H45 (Secondary)text