On prime-order elliptic curves with embedding degrees k = 3, 4, and 6

Authors:
Koray Karabina;Edlyn Teske
Affiliations:
Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada;Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

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Abstract

We further analyze the solutions to the Diophantine equationsfrom which prime-order elliptic curves of embedding degrees k =3, 4 or 6 (MNT curves) may be obtained.We give an explicit algorithm togenerate such curves. We derive a heuristic lower bound for the numberE(z) of MNT curves with k = 6 and discriminant D ≤ z, and comparethis lower bound with experimental data.