International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Florian Luca

Publications

Year
Venue
Title
2006
JOFC
2005
EPRINT
Elliptic Curves with Low Embedding Degree
Florian Luca Igor E. Shparlinski
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).

Coauthors

Igor E. Shparlinski (2)