CONSTRUCTING PAIRING-FRIENDLY CURVES WITH VARIABLE CM DISCRIMINANT
Hyang-Sook Lee, Cheol‐Min Park · Bulletin of the Korean Mathematical Society · 2012
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.