Elliptic Curves with Low Embedding Degree

被引：0

作者：

Florian Luca

Igor E. Shparlinski

机构：

[1] Instituto de Matematicas,

[2] Universidad Nacional Autonoma de Mexico,undefined

[3] C.P. 58089,undefined

[4] Morelia,undefined

[5] Department of Computing,undefined

[6] Macquarie University,undefined

来源：

Journal of Cryptology | 2006年 / 19卷

关键词：

Elliptic Curve; Elliptic Curf; Prime Divisor; Heuristic Argument; Weil Pairing;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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).

引用

页码：553 / 562

页数：9