The Realization Of The Elliptic Curve Cryptography And Security Analysis

The elliptic curve cryptosystem is more and more be high notice by its special superiority. The main advantage of elliptic curve cryptosystems over other public-key cryptosystems is the fact that they are based on a different intractable problem, and that their keys have smaller sizes for the same level of security. For information security and cryptography, Cryptography universally think that the elliptic curve cryptosystem is going to stead the current RSA cryptosystem at present and become a new current public key cryptosystem. In recent years, several studies have been conducted on implementation of elliptic curve cryptosystem.The ECC, as an optimal scheme of advanced public key cryptosystem become a research focus. The base that using elliptic curve is public-key cryptosystem is become of the points set of elliptic curve on finite field can construct Abelian group, by this, the discrete logarithm on public curve can be define. The discrete logarithm on elliptic curve is very difficult to be solved.In this paper, The Basic contents of the cryptology on elliptic curves are summarized. A description is given to the basic arithmetic and cryptography property on elliptic curves. The major part of this paper is dedicated to select a suitable finite field, select logarithms of secure elliptic curve and basic point, design and implement a fast arithmetic of ECC based over finite prime field, discuss security of elliptic curve cryptography. The ECC and classical public key cryptogram system are compared. Point out that the secure elliptic curve is the master key of constructing the elliptic curve cryptosystem. The scalar multiplication of elliptic curve is one of important problem in the practice of efficiently implementing an elliptic curve cryptosystems. The speed of the scalar multiplication is the key steps of the implement elliptic curve cryptosystem. We discussed the discrete logarithmproblem of elliptic curve and the available attack in the theory, then analyzed some attack methods and for elliptic curve cryptosystems. The newest achievements in this area are covered and views on the development of the cryptosystems are proposed. It is shown that ECC can provide greater strongest , highest speed and smaller keys than other systems, Thus ECC can relatively high security with less cost and time delay.