The Design And Implementation Of The Elliptic Curve Cryptography

The security of Elliptic Curve Cryptogrphy(ECC) is based on the difficulty of elliptic curve discrete logarithm.Compared with other asymmetric cryptography,ECC provides higher strength per bit, makes faster computation and requires shorter key length.Therefore ,the application based on elliptic curve encryption algorithm deserves study.This article deals with the design and implementation of a cryptosystem based on elliptic curve .This article first introduces the math foundation required by ECC,including the addition rule for elliptic curve point defined over finite field.Then , the principle of ECC is discussed and its security and efficiency of ECC are analyzed.Third, a cryptosystem is designed through analyzing the security requiration, choosing the elliptic curve domain parameters,denoting field element,elliptic curve and elliptic curve point,choosing associate primitves and schemes andpartitioning functional module.Forth, how to develop a crytosystem based on elliptic curve encryption algorithm is investigated.Fifth, a cryptosystem we have developed by us and the testing result is described.Finally,the evolution trend and research direction are discussed.