Digital Signature Based On Elliptic Curve Cryptosystem

Research on the security of the elliptic curve discrete logarithm problem, present the conditions of keeping the security of the elliptic curve discrete logarithm problem. Expatitate on the ideas and methods of constructing elliptic curve cryptosystem is constructing secure elliptic curve cryptosystem over finited field, therefore firstly it is a must to select an elliptic curve suitable to build cryptosystem. Base on it, we then build the cryptosystem. Although the elliptic curve used to bulid cryptosystem is ideally non-supersingular, it is difficult to judge the elliptic curve is non-supersigngular or not. Thus when selecting the elliptic curve, we use the constructing method. Present the method to construct elliptic curve. The elliptic curve constructed by this method is non-supersingular and has common form and can avoid the common attacks.Implement a digital signature scheme based on elliptic curve cryptosystem.The safety of this scheme is based on the elliptic curve discrete logarithm of non-supersingular elliptic curve over finit field, which has no efficient attack up to now. It is secure in theory and practial, the operation of it is convenient and the implementation is easier as well.