The Research And Application Of Elliptic Curve Cryptosystems

Because of the coming of information times,the safe transfer of information becomes more important. So the research and application of cryptosystems have become very important in computer science.There are two kinds of cyptosystems at prensent:symmetric cryptosystems and public key cryptosystems. But there are many disadvantages in current public cyptosystems:the too long keys and the slow computation speed.Except, there are some enviroments of those fields are special such as intelligence card or mobile environment,in which the bindwidth,computation ablity and store ablity are limited,so the traditional public key cryptosystems are not fit for those new fields.To solve those above problems,this paper illustrates a new public key crypto-system,which is based on elliptic curve,and whose security is based on the elliptic curve discreet logarithm problem(ECDLP).In contrast with those wellknown public key cryptosystems,the Elliptic Curve Cryptosystems(ECC) maintain reliable security with key lengths that are shorter(therefore more practical).So in the enviroment whose computation ablity, bindwidth and store ablity are limited,the advantage of ECC is more important.And the security scheme based on ECC have less energy cost.Those advantages of the ECC lead itselt to wider application in more fields such as mobile commerce,cell phone systems,e-cash,notebook PC and intelligent card.The following are the points of this paper:(l)The illustration of the basic theories and algoithms of ECC,including those mathematic theory,compuation in infinite field and some basic algorithms such as key exchange algorithms,encyption algorithms and digital signature algorithms.(2)The illustration about how to construct a new elliptic curve cryptosystem including obtaining an elliptic curve random and judging it safe or not by computing its order.(3)Using the five elliptic curve which NIST recommend to construct an Elliptic Curve Cryptosystem on binary field, implementing the Elliptic Curve Diffie-Hellman key exchange algorithm,the Elliptic Eurve ElGamal algorithm and the Elliptic Curve Sigital Signature Algorithm,and trying to apply elliptic curve Diffie-Hellman to CDMA...