Threshold Group Signature Schemes Based On RSA

In the daily exsistance, we use the signature to denote our identities; accordingly, digital signature is the legal replacer of the manuscript signature in the Internet. It is Diffe and Hellman who bringed forword the concept of the digital signature.They advanced that each user publicizes a public key to verify the signature; accordingly, he should save a private key to generate the signature.Since Desmedt and Frankel proposed the idea of (t , n ) threshold group signature in 1991, lots of scholars devoted themselves to it and proposed many different schemes, these schemes acheved much in the security of resisting conspiracy attack and so on, but lots of them concerned less on the cheat between each participants, especially there existence less schemes which based on the RSA and whithout the Trusted Center, proceeded, lots of them have the fault of security. So, theis paper proposed two new and more mature threshold group signature schemes based on RSA and the exsisted schemes. The first one has the Trusted Center, and the last one doesn't have.The major works as follows:In the first scheme, to detect the cheat between each participant, this paper proposed the concept of verifying-share and successfully overcomed the deficiency that most of the existed schemes have, improved the security of the signature.Then, in the next scheme, based on the distributed RSA key generation protocol, this paper designed a new mechanism to generate and distribute the system parameters, overcomed the shortcome of low-safy and complexity that most of the existed schemes have.Accordingly, this paper designed two different algorithms of signature and verifier for each scheme, and analysed the security and computation of them.