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

Authors:
Christian Robenhagen Ravnshoj
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URL: http://eprint.iacr.org/2008/025
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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.
BibTeX
@misc{eprint-2008-17702,
  title={Non-Cyclic Subgroups of Jacobians of Genus Two Curves with Complex Multiplication},
  booktitle={IACR Eprint archive},
  keywords={Jacobians, hyperelliptic curves, embedding degree, complex multiplication, cryptography},
  url={http://eprint.iacr.org/2008/025},
  note={ cr@imf.au.dk 13896 received 18 Jan 2008, last revised 18 Jan 2008},
  author={Christian Robenhagen Ravnshoj},
  year=2008
}