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Paper 2005/363

Elliptic Curves with Low Embedding Degree

Florian Luca and Igor E. Shparlinski

Abstract

Motivated by the needs of the {\it pairing based cryptography\/}, Miyaji, Nakabayashi and Takano have suggested a construction of so-called MNT elliptic curves with low embedding degree. We give some heuristic arguments which suggest that there are only about $z^{1/2+o(1)}$ of MNT curves with complex multiplication discriminant up to $z$. We also show that there are very few finite fields over which elliptic curves with small embedding degree and small complex multiplication discriminant may exist (regardless of the way they are constructed).

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curvesembedding degreepairing
Contact author(s)
igor @ ics mq edu au
History
2005-10-09: received
Short URL
https://ia.cr/2005/363
License
Creative Commons Attribution
CC BY
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