The Digital Signature Based On RSA And Elliptic Curve Encryption Algorithm

Information security is becoming more and more important at present. The encryption technology, one of the most important techniques of security, is playing a vital role in information security. The basic conception of the encryption is discussed, and further more, the most popular mechanisms have been introduced in this paper. Digital signature which utilize encryption and public key infrastructure to protect the authenticity, integrality and acceptability of the data, is widely used in the fields of E-government and e-commerce etc.. The digital signature based on elliptic curve encryption algorithm is realized by using the Abel addition groups composed by the point from elliptic curve to construct the discrete logarithm question. This mechanism has the characteristic such as the same complication as the D-H algorithm, fast operation speed, simple realization and so on. This paper is focused on discussing the mathematics principle, implementation method and security analysis of the RSA signature algorithm and elliptic curve encryption algorithm. The elliptic curve encryption algorithm has been analized and discussed carefully. Fist of all, with the analysis of the principle of the elliptic curve encryption, it is showed that the principle of the encryption algorithm come from the referenced mathmatics question. If the complexity of the mathmatcs question is harder, the possibility of the encryption algorithm cracking is lower. That is, the security of the encryption algorithm is corresponding with the complexity of the mathmatics question. The conceptions of the elliptic curve and discrete logarithm have been introduced in this paper to explain the discrete logarithm question in elliptic curve. The security of the elliptic curve encryption algorithm has been proved by analizing the complexity of the algorithm and the intensity of the algorithm cracking. Further more, the abundance of the elliptic curve in Galois field has been proved by theorty analysis and the corresponding number has been found. A digital signature mechanism based on elliptic curve encryption algorithm has been proposed. It is showed that, compared with RSA and DSA, this mechanism has the advantages in the security level, computing consumption, size of key and communication bandwidth. Finally, the application in public key infrastructure and e-cash mechanism with elliptic curve encryption algorithm has been discussed.