Welcome to the resource topic for 2008/025
Title:
Non-Cyclic Subgroups of Jacobians of Genus Two Curves with Complex Multiplication
Authors: 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.
ePrint: https://eprint.iacr.org/2008/025
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