Study On Elliptic Curve Cryptosystem

The security of Elliptic Curve Cryptogrphy(ECC)is based on the difficulty of elliptic curve discrete logarithm. So far,the Elliptic Curve Cryptosystem(ECC) provides the highest strength-per-bit of any cryptosystem known.In addition to its high security,ECC also has many other merits, such as less computation overheads shorter key size,considerable bandwidth savings,and so on.All of these merits have made it become the best public-key cryptosystem that is suitable for use in the future.This article firstly presents some introductive materials,including public-key cryptography and the motivations and the developments of the elliptic curve cryptosystems.Then, this paper introduces the math foundation required by ECC,including the addition rule for elliptic curve point defined over finite field.Thirdly, we present an extensive study of the software implementation on PCs of the elliptic curves over prime fields.Fourthly, an elliptic curve cryptographic protocol,the dynamic secret sharing scheme based on elliptic curve cryptosystem,is designed.We also show that our proposed scheme is more secure and efficient than some other schemes. Finally,the evolutive trend and research direction are discussed.