Research On And Implementation Of Secure Elliptic Curve Cryptosystem

With the fast development of Internet, the problem of information security looks increasingly important.Then on the basis of safe and high efficient encryption algorithm,some related network protocols are produced.Compared with some other public key cryptosystems, elliptic curve cryptosystem(ECC) has many merits,so the special attention is paid to it by the network safety specialist in the world.ECC is widely argued because of no standard source code.In this article,the research is on the ECC theory and the implementation of it is also done.In this thesis,the basic problem of network security, some correlative protocols and cryptology are discussed at first,math theory in point is also studied.Especially, a sort of new matrix method of solving quadratic equation over GF(2m) is given,which is the key of selecting random point over elliptic curves.No better solution has been found in related literature in the world.Compared with IEEE P1363's method,it is easy to implement the software and obtain high efficiency,etc.Then the basic operation of elliptic curve is debated and the steps of finding secure curve and basis point over GF(2m) are presented.Moreover,the encryption and decryption schemes of the ECC are designed and the security problem of ECC is also considered.In the end, ECC by Koblitz curves are implemented.