Constructing elliptic curves over finite fields using complex multiplication
Øystein Øvreås Thuen · NORA - Norwegian Open Research Archives · 2006
We study and improve the CM-method for the creation of elliptic curves with specified group order over finite fields. We include a thorough review of the mathematical theory needed to understand this method. The ability to construct elliptic curves with very special group order is important in pairing-based cryptography.