| Elliptic Curve Cryptography is a form of public key cryptography that offers good security and smaller key sizes then competing methods. The foundation of a secure elliptic curve cryptography system is a well-chosen curve. There are many considerations when generating a curve, the main one being its order. This is often the most costly part of an implementation of an elliptic curve cryptography system and because of this much research has been completed in this area.;This thesis has two main goals. First, to offer a solid background in the mathematics of finite fields and elliptic curves so that the reader will understand the advanced topics. Second, to explain and demonstrate the requirements for choosing a secure elliptic curve, with an emphasis on finding the order of the curve and avoiding known attacks. |
