Elliptic curve cryptosystem and its applications

Abstract

Elliptical curve cryptography (ECC) is a public key encryption technique based on elliptic curve theory that can be used to create faster, smaller and more efficient cryptographic keys. It establishes equivalent security with lower computing power and battery resource usage; it is becoming widely used for mobile applications. With this understanding of the advantage of ECC, the project goal is to develop an efficient encryption scheme based on ECC. This report introduces the fundamentals of elliptic curve cryptography theory as well as various elliptic curve cryptosystem algorithms such as Elliptic curve Elgamal and Elliptic curve Menezes Vanstone and summarizes what have been done in this project including the design and implementation of elliptic curve cryptosystem in Java. This report also cover the analysis of the algorithm performance which is the efficiency in encrypt, decrypt the message.