Cryptology ePrint Archive: Report 2008/025

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.

Category / Keywords: Jacobians, hyperelliptic curves, embedding degree, complex multiplication, cryptography

Date: received 18 Jan 2008, last revised 18 Jan 2008

Contact author: cr at imf au dk

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

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

Version: 20080122:132306 (All versions of this report)

Short URL: ia.cr/2008/025

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