Several Kinds Of Threshold Signature Scheme Based On Identity

From1974to1975, Whitfield Diffie of the Stanford University and Martin Hellman and Ralph Merkle of the University of California have discovered that public key cryptography theory (asymmetric cryptography theory). This theory which had a profound impact on technical developed rapidly. Digital signatures is the one important application of this theory.The digital signature is a new approach to sign the electronic documents. American National Standards Institute of Technology (NIST) defined Digital Signature Standard as follow:a method of cryptography which can distinguish the identity of the sender in the process of electronic communication and can distinguish the integrity of data in the same communication. Digital signatures must satisfy the following three properties:①the reality of the sources of message and the content of data can be verified in the same time;②the final signatures can be verified with a third person(the verifier);③the reality of the message and the true identity of the signer can be determined.In the digital signature, when the user’s identity information is used to export its public key, which forms the identity-based digital signature, this identity-based digital signature has some advantages:compared with the CA system, greatly reducing the user’s dependences on certificates, not exist the problems of storage and spending in the process of awarding certificates.The main results of this thesis are as follows:1. Based on C-Z-J scheme[Cai Yong-quan, Zhang Xue-di. Jiang Nan. A novel identity-based threshold signature. Acta electronica sinica,2009,37(4A):102-105.], with the knowledge of bilinear pairings on elliptic curve mapping and the knowledge of identity-based cryptography, this paper will propose a new identity-based threshold proxy signature scheme. The new scheme will require a trusted private key generation center to generate and manage private keys in the same time. This paper will make correctness analysis on the new scheme and safety analysis on it in the same time, such as the verifiability, the distinction, strong recognizability, strong unforgeability, strong non-repudiation and so on. The results show that the new scheme is secure and practical.2. Design of threshold signature schemes which are efficient and provably secure in the standard model(without random oracle) is suitable for applications. Based on Z-H-L scheme[Li Ji-guo, Jiang Ping-jin. An efficient and provably secure identity-based signature scheme in the standard model. Chinese Journal of Computers,2009,32(11):2130-2136.], the threshold signature scheme is presented and is proved secure in the standard model. The new scheme can tolerate any t<n/2+1malicious parties, its key generation algorithm does not need a trusted dealer and only run an interactive algorithm among members. The new scheme proves and secure against existential forgery under the adaptive chosen message attack under the computation Diffie-Hellman assumption.