Design Of Group Signature In The Multi-challenge Setting

Group signature which is an important research field of public key cryp-tography has been drawing extensive attention from researchers.It is a special type of digital signature,which has properties of not only unforgeability but also anonymity,traceability and non-frameability.A group signature scheme typically contains a manager and a user group,and each user has its own private key which can be used to represent the entire user group to sign a message.Anonymity means that the signature can be verified by the group public key,but no one except the manager knows the identity of the signer.In special cases,the manager can use his private key to open the group signature and restore the identity of the signer,which is the traceability.Tag-based encryption(TBE)is a special kind of public key encryption scheme,which plays an important role in the construction of group signatrue and security proofs.It makes encryption and decryption operation with an additional "label"(Tag)as part of the input,which can be a binary string of suitable length and does not require other specific structure.In a single challenge setting,there exist tag-based encryption which can achieve selected tag weak security.We extend the security of TBE to the multi-challenge setting and discuss the related reduction loss in security proof.We also prove that if a group signature scheme is fully anonymous in a single challenge setting,it is also fully anonymous in a multi-challenge setting.However,the security loss is closely related to the number of challenges.Furthermore,we prove the full anonymity of Groth's group signature scheme in multi-challenge setting using the security of tag-based encryption in multi-challenge setting.In addition,we show a possible method which can reduce the reduction loss of such kind of group signature.