Generating More MNT Elliptic Curves
نویسندگان
چکیده
In their seminal paper, Miyaji, Nakabayashi and Takano [12] describe a simple method for the creation of elliptic curves of prime order with embedding degree 3, 4, or 6. Such curves are important for the realisation of pairing-based cryptosystems on ordinary (non-supersingular) elliptic curves. We provide an alternative derivation of their results, and extend them to allow for the generation of many more suitable curves.
منابع مشابه
On prime-order elliptic curves with embedding
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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عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004