We give an explicit description of the matrix representation of the Frobenius endomorphism on the Jacobian of a genus two curve on the subgroup of l-torsion points. By using this description, we can describe the matrix representation of the Weil-pairing on the subgroup of e-torsion points explicitly. 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.
机构:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford,OX2 6GG, United KingdomMathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford,OX2 6GG, United Kingdom
Flynn, E. Victor
Khuri-Makdisi, Kamal
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Mathematics Department, American University of Beirut, Bliss Street, Beirut, LebanonMathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford,OX2 6GG, United Kingdom