Paper 2008/029
Non-Cyclic Subgroups of Jacobians of Genus Two Curves
Christian Robenhagen Ravnshoj
Abstract
Let E be an elliptic curve defined over a finite field. Balasubramanian and Koblitz have proved that if the l-th roots of unity m_l is not contained in the ground field, then a field extension of the ground field contains m_l if and only if the l-torsion points of E are rational over the same field extension. We generalize this result to Jacobians of genus two curves. In particular, we show that the Weil- and the Tate-pairing are non-degenerate over the same field extension of the ground field. From this generalization we get a complete description of the l-torsion subgroups of Jacobians of supersingular genus two curves. In particular, we show that for l>3, the l-torsion points are rational over a field extension of degree at most 24.
Metadata
- Available format(s)
-
PDF PS
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Jacobianshyperelliptic genus two curvespairingsembedding degreesupersingular curves
- Contact author(s)
- cr @ imf au dk
- History
- 2008-01-28: received
- Short URL
- https://ia.cr/2008/029
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/029,
author = {Christian Robenhagen Ravnshoj},
title = {Non-Cyclic Subgroups of Jacobians of Genus Two Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/029},
year = {2008},
url = {https://eprint.iacr.org/2008/029}
}