### Generators of Jacobians of Genus Two Curves

Christian Robenhagen Ravnshoj

##### 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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
Jacobianshyperelliptic genus two curvespairingsembedding degree
Contact author(s)
cr @ imf au dk
History
2008-02-18: revised
See all versions
Short URL
https://ia.cr/2008/070

CC BY

BibTeX

@misc{cryptoeprint:2008/070,
author = {Christian Robenhagen Ravnshoj},
title = {Generators of Jacobians of Genus Two Curves},
howpublished = {Cryptology ePrint Archive, Paper 2008/070},
year = {2008},
note = {\url{https://eprint.iacr.org/2008/070}},
url = {https://eprint.iacr.org/2008/070}
}

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