On the ρ-values of complete families of pairing-friendly elliptic curves

Journal of mathematical cryptology

article

Keiji Okano¹ 

[1] Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science

关键词: Elliptic curves;    pairing-based cryptography;    embedding degree;   

DOI  :  10.1515/jmc-2012-0011

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Abstract. The parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1. Especially, the situation is ideal. We study whether a complete family of pairing-friendly elliptic curves has a ρ-value 1 or not. In this paper, we consider the original idea of Brezing and Weng that we put a parameter for constructing families of elliptic curves as cyclotomic polynomials. We show that the ρ-values cannot be 1 in many cases.

【 授权许可】

CC BY|CC BY-NC-ND