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arXiv · 0802.1450

Generators of Jacobians of Genus Two Curves

Christian Robenhagen Ravnshoj
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Abstract

We 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.

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Christian Robenhagen Ravnshoj. 2008-02-18. Generators of Jacobians of Genus Two Curves. https://arxiv.org/abs/0802.1450

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