### 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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
Jacobianshyperelliptic genus two curvespairingsembedding degreesupersingular curves
Contact author(s)
cr @ imf au dk
History
Short URL
https://ia.cr/2008/029

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},
note = {\url{https://eprint.iacr.org/2008/029}},
url = {https://eprint.iacr.org/2008/029}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.