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Generators of Jacobians of Genus Two Curves
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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. |
BibTeX
@misc{eprint-2008-17747, title={Generators of Jacobians of Genus Two Curves}, booktitle={IACR Eprint archive}, keywords={Jacobians, hyperelliptic genus two curves, pairings, embedding degree}, url={http://eprint.iacr.org/2008/070}, note={ cr@imf.au.dk 13927 received 11 Feb 2008, last revised 18 Feb 2008}, author={Christian Robenhagen Ravnshoj}, year=2008 }