Elliptic Curve Cryptosystem And Algorithm Improvements

Elliptic curve cryptography is a research hotspot in public key cryptography. With the emphasis of the algorithms for the fast implementation of the elliptic curve, the correlative content of elliptic curve cryptosystems theory is introduced. In this dissertation, the basic concept of elliptic curve cryptography is sketched. Then we discuss the discrete logarithm problem of elliptic curves and the actual attack, and analyze the methods of choosing secure elliptic curve. By investigating the elliptic curve cryptosystems, the problems are reduced the fast computations of scalar multiplication of the elliptic curve. Especially, a new method is proposed, after several of the algorithms for the fast implementation are studied. In comparison with other algorithms, ours is performed easily, has fast computational speed. At the end part of the dissertation, we contrast the ECC with RS A and point out the excellence ofECC.