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Published in:
2008 | OriginalPaper | Chapter
Generators for the ℓ-Torsion Subgroup of Jacobians of Genus Two Curves
Author : Christian Robenhagen Ravnshøj
Published in: Pairing-Based Cryptography – Pairing 2008
Publisher: Springer Berlin Heidelberg
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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.