Elliptic Curve Cryptography In Wireless Authentication Environment

The highest safety strength of private key per bit in the Public-Key Cryptographyis the Elliptic Curve Cryptography recently. Under similar secure conditions, the ECChas the advantages such as: less computation amounts, shorter length of private key,smaller storing and bandwidth. Moreover, it has been declared as standard documentsadopted by many international standard institutions and regarded as the most universallyused public key system, especially suitable in the wireless environment .Firstly we introduce elliptic curve cryptosystem closely related to the thesis, thenmake a detailed analysis concerning algorithms and protocols about identityauthentication and application in wireless environment, finally develop a self-certifiedidentity authentication system based on elliptic curve over GF(2m ),combining ellipticcurve cryptosystem and self-certified public key cryptosystem. The project includes themian works as follows:①Owing to be based on elliptic curve over GF(2m ), the project has the followingadvantages: the shorter key length and the higher efficiency, which are very suitable forwireless environment;②Then wedo some research about the basic protocols, the elliptic curvediffie-hellman protocol isimproved as it can't make identity authentity and can't resistthird party's attacks;at thesame time,the signature equation of elliptic curve digitalsignature algorithm isreconstructed,and the improved kP+lQalgorithm is applied intoverification stage,thewhole speech of the protocol is improved greatly.Upon the aboveresearch,this paperdesigns cryptography schemes according to practical requirements.③Base on the improvedelliptic curve digital signature algorithm, we designs a newmulti-signature scheme withhigh security and great operation quality;then,by combiningthe signature and encryptionoperation,the signcryption scheme which provides thirdparty's verification and forwardsecurity is given;④At last,according to the above optimizations and improvements, anElliptic Curve Cryptosystem is implemented and is applied into Virtual Private Net design;Experiment shows, as the optimization of this paper,the speech and security of theelliptic curve cryptosystem is improved in a certain extent, this makes it can adapt toresource limited enviorment such as VPN,wireless net more.