Elliptic curves with low embedding degree

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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 z1/2+ 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).

Original languageEnglish
Pages (from-to)553-562
Number of pages10
JournalJournal of Cryptology
Issue number4
Publication statusPublished - Oct 2006


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