The Research On The Elliptic Curves Cryptosystem And Its Application In The 3G Mobile Communication

On account of the limited computational resources as well as the advantages of the single-key cryptography in computed velocity and the complexity in completion in 2G and 3G mobile system, the single-key cryptographic algorithm is applied to design authentication schemes. However, only the public-key cryptographic algorithm has going to be applied, the problems of the management of the authentication keys, which is complicated and troublesome and caused by the single-key algorithms in the mobile system, and the payment dissension between the mobile subscribers and the vendors could be thoroughly settled.As compared with other kind of public-key encryption schemes, the elliptic curves cryptosystem has its own advantages which are vital to the smart cards. That is, as the so limited recourses of the hardware of the smart cards, the memory capacity and the computational ability has been restricted in the accomplishment of the security system. The merits of the ECC, which has short encryption keys, have make up the localization of the hardware of the smart cards, as well as to cut down the producing cost of the smart cards and make it more practicable.In this paper, the development process and the characteristics of ECC have been firstly analyzed, and the feasibility as well as the significance of the ECC in mobile system have also been discussed. And then a though analyzing has been made to the foundation of cryptography, elliptic curves and ECC, as well as introduce some accomplish schemes and attack means. Next a research has been made to the security architecture and the security performance of the 3G system, as well as the authentication and the key distribution schemes in 3GPP networks, and the hidden trouble in security has also been pointed out.In the last of this paper, ECC has been applied in the mobile networks, and a new authentication and key distribution scheme applied in mobile networks base on ECC has been proposed, the correctness and the security of the scheme has also been analyzed. The results of the analyzing shows that this protocol not only implemented the function of authentication and key distribution, but also combined the characteristics of the ECC, which is suitable of the mobile system.