Generating Pairing-Friendly Curves with the CM Equation of Degree 1 [chapter]

Hyang-Sook Lee, Cheol-Min Park
2009 Lecture Notes in Computer Science  
Refinements of the Brezing-Weng method have provided families of pairing-friendly curves with improved ρ-values by using noncyclotomic polynomials that define cyclotomic fields. We revisit these methods via a change-of-basis matrix and completely classify a basis for a cyclotomic field to produce a family of pairing-friendly curves with a CM equation of degree 1. Using this classification, we propose a new algorithm to construct Brezing-Weng-like elliptic curves having the CM equation of degree
more » ... 1, and we present new families of curves with larger discriminants.
doi:10.1007/978-3-642-03298-1_5 fatcat:xc7djfd5rrecnorhn24agvaebi