## Cryptology ePrint Archive: Report 2009/404

Pairing-Friendly Elliptic Curves With Various Discriminants

Woo Sug Kang and Ki Taek Kim

Abstract: In this paper, we extend the Brezing-Weng method by parameterizing the discriminant $D$ by a polynomial $D(x)$ and give a construction of families of pairing-friendly elliptic curves with various discriminants. For $k =$ 5, 8, 9, 15, 16, 20, 24 and 28, our method gives smaller $\rho$ value than the ones in previous results.

Category / Keywords: implementation / pairing, pairing-friendly elliptic curves, embedding degree, elliptic curve, Brezing-Weng method

Date: received 19 Aug 2009, last revised 20 Aug 2009, withdrawn 25 Aug 2009

Contact author: wsgkang at korea ac kr

Available format(s): (-- withdrawn --)

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