Elliptic curve cryptography

In this thesis, the mathematical foundations of elliptic curves arestudied and the simulation of an elliptic curve crypto system is realized.Also, the cryptanalysis of elliptic curve crypto systems are covered.The algorithm of the elliptic curve cryptography is compared with thealgorithms of other public key crypto systems such as RSA and DSA. Inpublic key cryptography, the mathematical methods behind thealgorithms are found to be more important than the length of thealgorithm. For the simulation of the elliptic curve crypto system aprogram is written in C++.Key Words : Elliptic curves, Cryptography, RSA, Hash function