Based On Elliptic Curve Digital Signature And Its Application

This task is to complete the performance of the improved ECDSA and design of the threshold group signature and the directed threshold group signature based on the improved ECDSA.Elliptic curve cryptosystem has the advantages of height security, small computational complexity, high speed, small space and limited band width, and has been adopted as public key cryptography and digital signature standard by several international standard organization. In our country, the electronic signature law has just published. The research and application of ECDSA are not matured enough and the united standard has not formed. The research of the elliptic curve applied to special signatures is only at start. Therefore, it has important significant in the research in ECDSA and its application to special signatures.This paper firstly analysised the cryptosystems, especially the public key cryptosystem. Then some sorts of digital signatures were introduced, especially the ECDSA and the improved algorithm. The whole process of elliptic curve digital signature and authenticate used Java 2 was described in detail. Using the characteristic that the improved signature algorithm is convenient to share secret, a threshold group signature scheme was proposed, which integrated the improved ECDSA, threshold signature and a verifiable threshold signature scheme. The truth, stability and security of the scheme were proved. Further more, a directed threshold group signature scheme with specific receiver was proposed and the truth, stability and security were proved.This paper validated the truth of the improved ECDSA by implementing the algorithm. Using the characteristic that the algorithm can avoid inversion in prime fields, secret was shared and a new threshold group signature scheme and a directed threshold group signature scheme based on elliptic curve was proposed.