Elliptic Curve Cryptosystems And Its Application In Broadband IP Wireless Network

In this paper, software implementations of elliptic curve cryptosystems (ECC) and its application in broadband IP wireless network are investigated. It consists of four chapters. In chapter one, some introductive materials are presented, including public-key cryptography and the motivations and the developments of the elliptic curve cryptosystems. In chapter two, some necessary and basic materials of the elliptic curve theory are introduced. The discrete logarithm problem of elliptic curves and the available attack are discussed in this chapter. In chapter three, we present an extensive study of the software implementation on PCs of the elliptic curves over prime fields. We present the results of our implementation in C and assembler on a Pentium III 1 GHz PC. In chapter four, we put forward a kind of scheme based on ECC and digital certificate to provide strong security of Wireless LAN.