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

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.

• Type: Conference
• Year: 2008
• Where: ANTS
• Authors: Koray Karabina, Edlyn Teske
• Keywords: Algorithms, ANTS 2008, Lower Bound, MNT Curves, Prime-order Elliptic Curves