Abstract
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 ℓ-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.
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Ravnshøj, C.R. (2008). Generators for the ℓ-Torsion Subgroup of Jacobians of Genus Two Curves. In: Galbraith, S.D., Paterson, K.G. (eds) Pairing-Based Cryptography – Pairing 2008. Pairing 2008. Lecture Notes in Computer Science, vol 5209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85538-5_16
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DOI: https://doi.org/10.1007/978-3-540-85538-5_16
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