Design And Application Of Lattice-Based Efficient Group Signature Schemes

The rapid development of communication and network technology has brought the 21st century into a new information age,and the emerging technologies,such as big data,cloud computing,and blockchain,have also brought unprecedented changes to our society.However,while we are enjoying convenience brought by the network and various information systems,ensuring information security has become a challenging issue.As the support and core technology of information security,cryptography is always of importance.Nowadays,the continuous deepening research of quantum computing has threatened cryptographic algorithms based on the assumptions of the difficulty of large integer decomposition and discrete logarithms.However,cryptographic algorithms based on lattice have the advantages of simple algebraic operation,average-case security and many other advantages,which have become one of the widely recognized post-quantum algorithms.In cryptography,digital signatures have the properties of authentication and unforgeability,and become an important tool for constructing various cryptographic protocols.Among them,group signatures with special properties have important applications in the current cloud computing privacy protection,so this article will focus on the lattice-based group signature scheme.At present,the PLS scheme is a lattice-based efficient group signature scheme published by Pino et al.at the International Conference on Computer Communication Security(CCS)in 2018.However,the zero-knowledge proof protocol used in the scheme does not have standard soundness,so it cannot provide standard security in a malicious adversary environment.This paper improves and optimizes the zero-knowledge proof protocol used in the PLS scheme,and then obtains a standard soundness and efficient group signature scheme.At the 2019 US Cryptography Conference,Yang Rupeng et al.proposed a lattice-based efficient zero-knowledge proof system,which can be regarded as a combination of advantages of Stern type protocol and FSwA(Fiat-Shamir With Abort)type protocol.It has both 1/polyO soundness errors and standard soundness.We apply this protocol to the PLS scheme to construct an efficient group signature scheme with standard soundness.First,we reduce and organize the relationship of zero-knowledge proofs used in the PLS scheme(including a linear equation with short solution and a subset sum of of linear equations),using the skills and ideas of Yang Rupeng and others' US secret article,and introducing a commitment scheme to prevent information leakage,and then get a lattice-based zero-knowledge proof protocol with small soundness error and standard soundness.Applying this zero-knowledge proof protocol to the PLS scheme,we obtain a lattice-based group signature scheme with high security.We compared the proposed scheme with the scheme(LNWX scheme)proposed by Ling et al.at the International Conference on Public Key Cryptology(PKC)in 2018.This scheme is currently the most efficient with standard soundness as far as we know.The size of the signature generated by our scheme is reduced about 7 times and it is more practical.