The Optimization And Design Of The Elliptic Curve Cryptography

The security of the Elliptic Curve Cryptography is built upon the difficulty of solving the Elliptic Curve Discrete Problem. Compared with other public key cryptography, ECC has advantages of fast execution speech, short key size and high security. More and more people are attracted by this task ,and it has become the hotspot of public cryptography.The major work of this paper is the research of ECC over GF ( 2~m). Firstly, the point multiplication and the core operation kP + lQof application layer are optimized. Then we do some research about the basic protocols, the elliptic curve diffie-hellman protocol is improved as it can't make identity authentity and can't resist third party's attacks; at the same time, the signature equation of elliptic curve digital signature algorithm is reconstructed, and the improved kP + lQalgorithm is applied into verification stage, the whole speech of the protocol is improved greatly. Upon the above research, this paper designs cryptography schemes according to practical requirements. Base on the improved elliptic curve digital signature algorithm, we designs a new multi-signature scheme with high security and great operation quality; then, by combining the signature and encryption operation, the signcryption scheme which provides third party's verification and forward security is given. At last, according to the above optimizations and improvements, an Elliptic Curve Cryptosystem is implemented and is applied into Virtual Private Net design.Experiment shows, as the optimization of this paper, the speech and security of the elliptic curve cryptosystem is improved in a certain extent, this makes it can adapt to resource limited enviorment such as VPN,wireless net and smat cards more.