[Resource Topic] 2005/363: Elliptic Curves with Low Embedding Degree

Welcome to the resource topic for 2005/363

Title:
Elliptic Curves with Low Embedding Degree

Authors: Florian Luca, 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).

ePrint: https://eprint.iacr.org/2005/363

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .