Study And Design On Group Signature Scheme

Group signature which is a sort of important digital signatures, firstly introduced by D. Chaum and E. van Heyst in 1991, allowed individual members of a group to make signatures on behalf of the group while providing the signer's anonymity. Owing to its anonymity, group signature can be applied in the activity of electronic politics and electronic commerce such as electronic voting, electronic bidding and off-line electronic cash and so on. In this thesis,we mianly study the security of group signature , the construction of dynamic group signature and the deleting problem of group members. The main results of this thesis are as follows:1.We propose a forgery attack on the ACJT group signature scheme. By using the forgery attack, an attacker can forge a valid group signature without forging the group membership certificate. By identifying the forgery attack, we show that their scheme is insecure. Besides ,an improved scheme is proposed, in which two knowledge signatures are used to verify group membership certificate and group member's secret key .And it's proved secure against the forgery attack..2. An efficient and secure dynamic group signature scheme based on ElGamal Encryption and knowledge signature is proposed.It allows the group manager to increase or delete group members flexibly.Furthermore,the length of the group signature ,as well as the computational effort of signing,verifying and opening,are very small and independent of the number of the group members and the deleted group members.So this scheme is much more efficient,and its security is based on RSA assumption, the security of ElGamal Encryption and knowledge signature. 3. A dynamic group singnature based on co-prime knowledge signature is proposed. In this scheme the group member can update the group public key by simple multiplication.When compute signature, the valid group member can use co-prime knowledge signature to verify that he is not deleted. It's very efficient and its security is based on RSA assumption and DDH assumption.