Elliptic curves with low embedding degree | Macquarie University ResearchOnline

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Title: Elliptic curves with low embedding degree
Related: Journal of cryptology, Vol. 19, Issue 4, p.553-562
DOI: 10.1007/s00145-006-0544-0
Publisher: Springer
Date: 2006
Author/Creator: Luca, Florian
Author/Creator: Shparlinski, Igor E
Description: Miyaji, Nakabayashi and Takano have recently suggested a construction of the so-called MNT elliptic curves with low embedding degree, which are also of importance for pairing-based cryptography. 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).
Description: 10 page(s)
Subject Keyword: elliptic curves
Subject Keyword: pairing
Subject Keyword: embedding degree
Subject Keyword: MNT curves
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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