Cryptology ePrint Archive: Report 2004/058

Generating more MNT elliptic curves

Michael Scott and Paulo S.L.M Barreto

Abstract: In their seminal paper, Miyaji, Nakabayashi and Takano~\cite{miyaji-nakabayashi-takano} 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.

Category / Keywords: public-key cryptography / Elliptic curves, pairing-based cryptosystems

Date: received 23 Feb 2004, last revised 9 Mar 2004

Contact author: mike at computing dcu ie

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Note: Minor revisions/corrections

Version: 20040309:121411 (All versions of this report)

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