A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves

Journal of mathematical cryptology

article

Kisoon Yoon¹ 

[1] NSHC Inc. 55

关键词: Elliptic curves;    finite fields;    pairing-based cryptography;    complete families;   

DOI  :  10.1515/jmc-2013-0017

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper we present a new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves with small rho-values, and we improve on previously known best rho-values of families [J. Cryptology 23 (2010), 224–280], [Lecture Notes in Comput. Sci. 5209, Springer (2008), 126–135] for the embedding degrees k=16$k=16$, 22, 28, 40 and 46. We consider elements of the form (a+b-D)ζk$(a+b\sqrt{-D})\zeta _k$ for rational numbers a , b and a square-free positive integer D , where ζk$\zeta _k$ is a primitive k -th root of unity. We also investigate the conditions for an element of the proposed form to be suitable for our construction. Our construction uses fixed discriminants.

【 授权许可】

CC BY|CC BY-NC-ND