ECE 842 Report Implementation of Elliptic Curve Cryptography

The aim of this report is to illustrate the issues in implementing a practical elliptic curve cryptographic system. Before doing the implementation, I will review group operation defined on elliptic curve over finite field. From that perspective, the efficiency of elliptic curve cryptographic system can be improved in two steps. The first step is to find a good representation of field element such that arithmetic over finite field can be done with less efforts. The other one is to find a good representation of point on elliptic curve such that time consuming field operation could be avoided. These two steps will be discussed in detail. Finally, we will implement a simple public key elliptic curve cryptographic system and show how computation time can be saved by applying these techniques.