Study Of Mutual Authentication And Key Exchange Protocols Based On ECC

The security of elliptic curve cryptography(ECC) is based on the difficulty of elliptic curve discrete logrithom problem(ECDLP), and the elliptic curve cryptosystems described in this paper are dependent on the presumed difficulty of ECDLP. Comparing with other asymmetric cryptography, ECC has stronger security, shorter key length, quicker speed, lower requirement for system parameters, which make elliptic curve cryptography the most suitable to be implemented in environments with several constraints related to processor speed, bandwidth, security and memory.In a wireless communication system, user and network servers need authenticate one another and agree on a session key to be used for encryption purposes in their conversation. Mutual authentication and key agreement protocol (MAKEP) for wireless communication can meet these requirement perfectly. Furthermore, it is essential for any secure MAKEP to achieve some essential security requirement including forward secrecy, man-in-middle attack and unknown key-share, since an adversary can reasonably be assumed to have these capabilities in wireless network.The math foundation of elliptic curve and its good cryptology properties are firstly introduced, and the principle of how to select a security elliptic curve and the base point on it is concluded by our research of the cryptanalysis of ECDLP. Then, several cryptographic protocols based on elliptic curve are introduced, which includes the elliptic curve Diffie-Hellman key switching, elliptic curve encryption and decryption and elliptic curve data signature etc. Finally, by cryptanalysis of two kinds of typical MAKEP based on elliptic curve cryptography, two of new improved protocols are presented respectively which be proved that they can meet the desirable attributes of a security MAKEP for wireless communication.