Ordinary abelian varieties having small embedding degree

Authors:
S. D. Galbraith;J. F. Mckee;P. C. ValençA
Affiliations:
Mathematics Department, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK;Mathematics Department, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK;Mathematics Department, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK
Venue:
Finite Fields and Their Applications
Year:
2007

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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.