Research On Group Signature Schemes

With the fast development of internet, digital signatures have been playing an important role in many aspects of information security, i.e. identity authentication, data integrity, non-reputation, anonymity and etc. As a special digital signature, group signatures can allow any group members to sign messages on behalf of the group while remaining anonymity of the signer. In case of dispute later on, the group manager can open the signature and reveal the actual identity of signer. Owing to its anonymity, group signature can be applied in electronic voting, electronic bidding and offline electronic cash and etc. In this thesis, we mainly study the security of group signature, the problem of deleting group members, the construction of dynamic group signature, and the identity-based group signature.The main results of this thesis are as follows:1. Analyze the security of several famous group signature schemes. The result shows that the ACJT2000 group signature scheme is vulnerable to Coalition attack and forging attack. A.Miyaji2004 group signature scheme is not unlinkability too. Furthermore, the CKL2005 group signature scheme is also linkability and traceability.2. Study the problem of deleting group members. And the paper proposes a group signature scheme based on zero knowledge proof, which runs in timeslice manner. The security of the proposed scheme is based on the hardness of the discrete logarithm problem, and the security of both the blinded RSA signature scheme and Rabin cryptosystem. And, it allows the group manager to add new member or delete group members at any time. The most important, both the length of a signature and computational overhead for signing and verifying depend on neither the number of members in the group nor the number of deleted members.3. Finally, analyze and discuss the characteristics of identity-based cryptosystem and identity-based group signature scheme. Identity-based cryptosystem can release the problem of public key authenticating, but private key generator must be unconditionally trusted, which restricts the use of identity-based cryptosystem. Xiaofeng Chen's identity-based group signature scheme without fully-trusted requirement in private key generator was analyzed. In this scheme, users can take party in the process of generating the secret key pairings, so that private key generator may not be trusted unconditionally, and the user may provide a proof to judge whether the private key generator has treachery, however, the efficiency is lower. We make a great improvement on the efficiency of signatures to this scheme with the bilinear pairings.