Research On And Implementation Of Key Algorithms On Elliptic Curve Cryptosystem Over GF(2～m)

With the fast development of Internet, the problem of information security looks increasingly important.But now,Computer has higher compute ability,so it must have safer and higher efficient encryption algorithm. Compared with some other public key cryptosystem, elliptic curve cryptosystem(ECC) has many merits,for example,shorter secret key,higher security and so on, so the infinite attention is paid to it by the network safety specialist in the world. In this article,the research on the theory about elliptic curve cryptosystem over GF(2~m) and the implementation of it are done.At first, the basic problem of network security,some network secure technology, cryptology and some famous public key algorithms are discussed in the thesis.Refer to IEEE P1363 Draft , math theory and basic algorithm in point is also full studied,they are:the basic operation over GF(2~m), finding secure elliptic curve and basis point over GF(2~m) .Especially, After studying some published fast algorithms for the point multiplication on elliptic curves, the paper presents a new concept of effective NAF.In order to improve the rate of point multiplication algorithm,base point and random point must adopt different methods,then two new methods based on effective NAF are presented. Theory analysis and the experiment prove that: these new point multiplication algorithms have higher efficiency. Moreover,a new encryption and decryption schemes of the ECC are designed,its merit is no plaintext-insert. In the end, ECC by Koblitz curves over GF(2233) are implemented, the new scheme has better time performance through experments.