Isolated elliptic curves and the MOV attack

Journal of mathematical cryptology

article

Travis Scholl¹ 

[1] Department of Mathematics, University of Washington

关键词: Elliptic curves;    isogenies;    isolated curves;    embedding degree;    cryptography;    distribution of primes;   

DOI  :  10.1515/jmc-2016-0053

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We present a variation on the CM method that produces elliptic curves over prime fields with nearly prime order that do not admit many efficiently computable isogenies. Assuming the Bateman–Horn conjecture, we prove that elliptic curves produced this way almost always have a large embedding degree, and thus are resistant to the MOV attack on the ECDLP.

【 授权许可】

CC BY|CC BY-NC-ND