Study On Elliptic Curve For Wireless Security

The highest safety strength of private key per bit in the Public-Key Cryptography is the Elliptic Curve Cryptography recently. Under similar secure conditions, the ECC has the advantages such as: less computation amounts, shorter length of private key, smaller storing and bandwidth. Moreover, it has been declared as standard documents adopted by many international standard institutions and regarded as the most universally used public key system, especially suitable in the wireless environment .At present, all of electronic commerce activities on the Internet employ the certificate-based public key cryptosystem to solve their related security issues. However, many security systems in lineate environment are not suitable for wireless environment, due to the noticeable difference between wireless environment and conventional lineate environment, for instance, the relatively narrow network bandwidth, the greater transmission delay time, the unstable network, the lower memory capacity and electronic power, etc.In this paper, we focus on the identity authentication system suitable for wireless environment.Firstly we introduce elliptic curve cryptosystem closely related to the thesis, then make a detailed analysis concerning algorithms and protocols about identity authentication and application in wireless environment, finally develop a self-certified identity authentication system based on elliptic curve over ( )GF 2 m,combining ellipticcurve cryptosystem and self-certified public key cryptosystem. The project includes the mian works as follows:①Owing to be based on elliptic curve over ( )GF 2 m, the project has the following advantages: the shorter key length and the higher efficiency, which are very suitable for wireless environment;②Discuss some major fast scalar algorithms. Make further study and improvement on two of them in to quicken the computational speed ;③Adopt self-certified public key cryptosystems, verify the validity of public key without certification and reduce the operation of validating certification and the amount of computation;④Owing to no need of certificates, the Certification Authority needs not to spend more time on managing the catalog of certificates, therefore reduce the operation of CA;⑤Both verification of the validity of public key and identity authentication can be achieved simultaneously.Based on the analysis of security and complexity of system, we believe that the project can effectively reduce the length of key, complexity of computation and the cost of transmission, which is very suitable for mobile equipments and wireless environments.