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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
Creative Commons Attribution
CC BY
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