The Research On Attribute Based Signature With Large Universe Algorithm

Attribute-based signature as a new type of asymmetric cryptography,which solves the difficult problem of certificate management in traditional asymmetric cryptosystem,and provides fine-grained access control for users by fine-grained partitioning of attributes.In this system,the attribute authorization center is responsible for generating the corresponding attribute private key for each legitimate user.If and if only the user attribute set satisfies the access structure,the attribute private can be used for signing.The verifier can only know that the signature was signed by a person who satisfies an access structure.Therefore,the signature system not only provides more fine-grained access control for data,but also has the advantage of concealing the identity of the signer,which has become a research focus of more and more scholars.According to the size of the attribute space supported by the attribute-based signature,the signature can be divided into two categories: an attribute-base signature with small universe and an attribute base signature mechanism with large universe.Specifically,in the attribute-based signature with small universe scheme,the system attribute space is static and must be determined in the initialization phase,and the size of the public parameter is linear with the attribute space.And when the system needs to add a new attribute,faced with the problem of reconstruction,it greatly increased the operational complexity of the system.In the attribute-based signature with large universe scheme,the system initialization stage does not need to set the attribute space size,that is,the attribute space is dynamic,and the system public parameter size does not grow with the expansion of the attribute space,so the scalability is good.The problem of system reconstruction in small attribute sets is avoided.Obviously,one of the great advantages of supporting attribute-based signature with large universe is that there is no need to pre-set the upper bound of the system attribute space during system initialization,which provides favorable conditions for the dynamic expansion of the system in practical applications.This paper focuses on the attribute-based signature with large universe.The main contents include:(1)Reviewing the basic knowledge of math theory related to the thesis,first introduce the commonly used mathematical knowledge in the field of cryptography,such as group domain algebra theory,security difficulties problem,and bilinear pair theory.Then,the secret sharing scheme widely used is briefly described,and the general principles and basic algorithms of the linkable ring signature are explained in detail.Finally,the provable security theory is introduced.(2)By analyzing existing attribute-based signature with large universe schemes,it can be found that there are many issues such as inflexible access policy,and cannot be proved secure under the standard model.To make up for the above shortcomings,based on the linear secret sharing scheme mechanism,we propose an attribute-based signature scheme with large universe and more flexible access strategy.Our scheme achieves large universe functionality and provides more flexible access structure through introducing layer technology(two “layers” are employed: the “attribute layer and the “secret sharing” layer)and LSSS secret sharing method.If and only if the user's attribute set satisfies the message access structure,a valid signature can be generated.In addition,under the adaptive selection message attack and standard model,the proposed scheme proves to be unforgeable under the assumption of the computational Diffie-Hellman exponent difficulty problem.Finally,the performance analysis and efficiency comparison between our scheme and the existing schemes show that although the calculation amount of our scheme has increased,it has certain advantages over the existing schemes in terms of security and access strategy flexibility.(3)Combining the attribute-based cryptography technology,and the idea of linkability is introduced into the attribute-based ring signature mechanism.We propose a large universe attribute-based ring signature scheme that supports linkability.By randomly selecting the parameters to generate the link label,that two signatures by the same signer can be linked.What is more,the linkability can be determined by the signer.It can be proved whether the two signatures are issued by the same person without revealing the identity of the real signer.By the attribute authority injecting identity information for each user's private key during the key generation phase,it is guaranteed that users with complementary attributes cannot launch a collusion attack.Under the adaptive selection message attack and random oracle model,the proposed scheme is proved to be unforgeable under the assumption of computational Diffie-Hellman difficult problem.Simultaneously,it is also proved that the proposal is to be linkable under the assumption of discrete logarithm problem.Finally,the performance analysis and efficiency comparison between our scheme and the existing schemes show that the proposed scheme has certain advantages in performance and security compared with the existing schemes while keeping the calculation amount equivalent to the existing schemes.