Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2012; 49(1): 75-88

Printed January 1, 2012

https://doi.org/10.4134/BKMS.2012.49.1.75

Copyright © The Korean Mathematical Society.

Constructing pairing-friendly curves with variable CM discriminant

Hyang-Sook Lee and Cheol-Min Park

Ewha Womans University, National Institute for Mathematical Sciences

Abstract

A new algorithm is proposed for the construction of Brezing-Weng-like elliptic curves such that polynomials defining the CM discriminant are linear. Using this construction, new families of curves with variable discriminants and embedding degrees of $k \in \{8,16,20,24\}$, which were not covered by Freeman, Scott, and Teske [9], are presented. Our result is useful for constructing elliptic curves with larger and more flexible discriminants.

Keywords: elliptic curves, pairing-friendly curves, CM discriminant

MSC numbers: Primary 11T71, 94A60