### Non-Cyclic Subgroups of Jacobians of Genus Two Curves with Complex Multiplication

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 with complex multiplication. In particular, we show that the Weil- and the Tate-pairing on such a Jacobian are non-degenerate over the same field extension of the ground field.

Note: The preprint was presented at AGCT 11, november 2007.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
Keywords
Jacobianshyperelliptic curvesembedding degreecomplex multiplicationcryptography
Contact author(s)
cr @ imf au dk
History
Short URL
https://ia.cr/2008/025

CC BY

BibTeX

@misc{cryptoeprint:2008/025,
author = {Christian Robenhagen Ravnshoj},
title = {Non-Cyclic Subgroups of Jacobians of Genus Two Curves with Complex Multiplication},
howpublished = {Cryptology ePrint Archive, Paper 2008/025},
year = {2008},
note = {\url{https://eprint.iacr.org/2008/025}},
url = {https://eprint.iacr.org/2008/025}
}

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