Research On Elliptic Curve Cryptosystem Over OEF And Its Application

Elliptic Curve Cryptosystem (ECC) is an important subject in the field of modern public key cryptography. ECC is based on the elliptic curve discrete logarithm. It enjoys advantages of higher security, less computation, shorter key size, faster process speed, less memory space and lower bandwidth,etc. Therefore it has wide application in information security field.The selection of secure elliptic curve and the high efficiency in implementation are two main research for ECC. Considering finite field, this thesis selects OEF which is best suitable for PCs, and studies the ECC on the basis of OEF. Firstly, the field operations on OEF are analyzed, focusing on how to analyze and improve the multiplication which is most time-consuming in scalar multiplication. Then, the safety of elliptic curve based on OEF is discussed, and the selection criterions and the selection algorithm of secure elliptic curve are given. Several key problems in the implementation of ECC based on OEF are analyzed, which includes validating the parameters, selecting base point and the algorithms for scalar multiplication. According to the results, the implementation speed of ECC based on OEF is faster in comparison to ECC in large prime fields.Finally, a Signcryption Scheme based on Bilinear Pairings is designed according to the Bilinear Pairings of elliptic curve, and put into use in security Email system. Ompared with the traditional security Email technology, it has faster speed on Encryption and Decryption, and it does not need Certificate Management.