Research On The Elliptic Curve Cryptography And Its Application

Since the idea of Public-key cryptography was put forward by Diffle -Hellman in 1976, many types of Public-key cryptography have been raised from then on. Among them, the elliptic curve cryptography is being taken in more and more account and will be more widely used in the future due to its high security in theory and its advantages in good performance in storage and little needs in communication.In this thesis, our main work is as follows:(1) Discuss the method in converting data to the points on the elliptic curve and select a proper scheme. Analyse and discuss the optimization of point multiplication and its addition which has greatest influence to the performance during encryption and signature with elliptic curves.(2) Bring the idea of forward security to elliptic curve signature, and raise forward secure schemes for elliptic curve signature based on the square remain theory.(3) After analyzing the characteristics of many types of Email protoco, we put forward a secure protocol SMAIL for Email system based on the elliptic curve digital signature and encryption and the AES encrypt algorithm. In addition to implementing the secure trasition for Email and the irrepudiation for both the sender and receiver, the protocol can resist many kinds of attack to Email system. In the end, the protocol have been fully implemented on the 224 bits primitive field with Visual C++6. 0.