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On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6

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Algorithmic Number Theory (ANTS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5011))

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Abstract

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

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Authors and Affiliations

  1. Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, 0N2L 3G1

    Koray Karabina & Edlyn Teske

Authors
  1. Koray Karabina
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  2. Edlyn Teske
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Alfred J. van der Poorten Andreas Stein

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© 2008 Springer-Verlag Berlin Heidelberg

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Karabina, K., Teske, E. (2008). On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_6

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  • DOI: https://doi.org/10.1007/978-3-540-79456-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79455-4

  • Online ISBN: 978-3-540-79456-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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