Paper 2008/070
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.
Metadata
- Available format(s)
-
PDF
PS
- 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
- 2008-02-18: received
- See all versions
- Short URL
- https://ia.cr/2008/070
- License
-
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},
url = {https://eprint.iacr.org/2008/070}
}
