Research On Attribute-based Group Signature Scheme

The group signature allows group members with signature key to generate group signature on behalf of the group without revealing their identity.The verifier can verify the validity of the signature,that is,someone in the group has signed the signature,but can not determine who the specific signer is(anonymity).When necessary,the group administrator can trace the signer,that is,the group signature has both anonymity and traceability.Attribute-based group signature is an extension of traditional group signature,which divides the identity characteristics of group members by giving users different ‘attributes'.Thus,the group members with different attributes sign on behalf of the group under the corresponding sign policy,which further limits the authority of the signer.The signature generated by a group member satisfying the sign policy will be verified as a valid signature,otherwise the signature will be considered invalid.Therefore,attribute-based group signature,as a fine-grained signature technology based on group signature,has been widely concerned.Therefore,how to design a more secure,flexible and efficient solution is one of the focuses of this thesis.The thesis studies the attribute group signature based on LSSS signature structure and the attribute group signature algorithm based on lattice.The main contributions are as follows:First of all,the current access structure based on bilinear pair-based attribute based group signature schemes only support the threshold and access tree structure,and there are problems of insufficient access structure or low computational efficiency.An attribute-based group signature scheme based on LSSS structure is proposed.The LSSS structure supports AND,OR and threshold operations,and the signature strategy is flexible,and the secret can be reconstructed linearly by using the linear secret sharing scheme to reconstruct the secret,and the signature efficiency is high;in addition,the scheme uses the Groth-Sahai non-interactive proof system to realize the signature Anonymity of attributes.Since the length of the signature of the scheme and the calculation cost are fixed values,it has nothing to do with the number of attributes of the signer,reducing the communication and calculation cost.Realize attribute traceability.The solution has identity and attribute tracking functions.When a user abuses the signature authority,not only the identity of the user can be traced,but also the attributes of the user and the attributes of the signature can be traced.Finally,the safety of the scheme was proved,and the theoretical analysis also showed the effectiveness of the scheme;Secondly,for the current in lattice attribute-based group signature scheme that only has threshold structure,an attribute-based group signature scheme on lattice that supports inner product predicates is proposed.The scheme has high security which can resist quantum attacks,a simple algebraic structure and high computational efficiency.The signature strategy of the scheme is flexible and can support the disjunctive paradigm,conjunctive paradigm and other strategies.The scheme adopts the Stern-like statistical zero-knowledge proof protocol to realize the anonymity of the signer's identity and the anonymity of attributes.The scheme also quotes efficient and compact identity coding technology,so that the group public key size is fixed and storage overhead is reduced.The scheme has the function of identity and attribute tracking.When a user abuses the signature authority,the user's identity and attributes can be traced.Finally,the safety of the scheme is proved,and the theoretical analysis also shows the effectiveness of the scheme.