Constructing pairing-friendly curves with variable CM discriminant
Bull. Korean Math. Soc. 2012 Vol. 49, No. 1, 75-88
Published online January 1, 2012
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
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