Cryptology ePrint Archive: Report 2007/425

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

Koray Karabina and Edlyn Teske

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 $D\le z$, and compare this lower bound with experimental data.

Category / Keywords: public-key cryptography / Elliptic curves, pairing-based cryptosystems, embedding degree, MNT curves.

Date: received 12 Nov 2007, last revised 13 Nov 2007

Contact author: eteske at uwaterloo ca

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Version: 20071118:222142 (All versions of this report)

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