Application Of The Elliptical Curve Cryptosystem On The 3～(rd) Generation Mobil Communication

ECC(Elliptical Curve Crypto system) is suit for the mobile communication equipment for its advantage of short key and low cost. This paper mainly discuss the application of the ECC on the 3rd generation mobile communication system. First, it presents the basic concept and theory of the elliptic curve, discussing the choice of the coordinate system and fast realization of several point multiplication algorithm, studying all kinds of operation of the field element. Then , it introduce several Cryptographic protocol based on elliptical curve, including Diffie-Hellman key switching, ElGamal Encryption and decryption, ElGamal digital signature, ECDSA, etc. Based on these, the author analyze kinds of security threat faced to 3G system and discuss the security rule and security objectives. Third, this paper introduce the security structure, security system and algorithm of the 3G system ,discussing the security measure of 3G system in the aspect of wireless interface in detail, which including user identity confidentiality, authentication integrality data , etc. Finally, the author stress analyzing the 3G authentication, key agreement protocol and its security, finding the security hole and putting forward new authentication and key agreement protocol based on ECC.