Cryptology ePrint Archive: Report 2004/365

Ordinary abelian varieties having small embedding degree

Steven D. Galbraith, and J. McKee and P. Valenca

Abstract: Miyaji, Nakabayashi and Takano (MNT) gave families of group orders of ordinary elliptic curves with embedding degree suitable for pairing applications. In this paper we generalise their results by giving families corresponding to non-prime group orders. We also consider the case of ordinary abelian varieties of dimension 2. We give families of group orders with embedding degrees 5, 10 and 12.

Category / Keywords: public-key cryptography / elliptic curves, hyperelliptic curves, pairings

Date: received 16 Dec 2004

Contact author: Steven Galbraith at rhul ac uk

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Version: 20041220:211517 (All versions of this report)

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