Research And Implementation Of Elliptic Curve Cryptography

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 conception of finite group and finite field that is the foundation of ECC. Thirdly, finite field arithmetic is vividly described. Fourthly, the conception of ECC is mainly provided and some point multiplication algorithms of ECC are discussed and researched.Fithly we present implement scheme elliptic curve cryptography and related algorithms.Then, we provide the simple implementation of ECC.Finally,the evolutive trend and research direction are discussed.