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As a special group signature, ring signature has been widely used in anonymous voting, anonymous deposit and anonymous transaction because it can not only complete the signature without the cooperation of ring members, but also ensure the anonymity of the signer. Firstly, this paper takes time as the main line, divides the development of ring signatures into different stages, and divides ring signatures into threshold ring signatures, linkable ring signatures, ring signatures with revocable anonymity, and repudiable ring signatures according to the attributes in each stage. Through the analysis of the development process of ring signature, it can be seen that the research progress of ring signature in the field of threshold ring signature and linkable ring signature is prominent, and their application fields are also the most extensive. In the post-quantum era, cryptographic schemes based on traditional number theory problems such as large integer factorization and discrete logarithms are no longer secure, and lattice-based public key cryptography has become the best candidate for cryptographic standards in the post-quantum era because of its advantages such as quantum-immune, the reduction of the worst-case to average-case, and so on. Therefore, this paper focuses on the detailed analysis and efficiency comparison of existing lattice-based threshold ring signatures and lattice-based linkable ring signatures. The inherent anonymity of ring signatures makes them have unique advantages in the era of industrial blockchain, so this paper elaborates on several applications of ring signatures in blockchain. For example, the application of ring signature in anonymous voting, medical data sharing, and Internet of vehicles is summarized and analyzed. The application significance of ring signature in the fields of virtual currency, SIP cloud call protocol, and Ad Hoc network is briefly sorted out. Finally, the research of ring signature technology in recent years is analyzed, and the current problems are summarized.

In the forward secure sequential aggregate (FssAgg) signature scheme, the signer combines signatures generated in different intervals under different secret keys incrementally and sequentially in a layered “onion-like” fashion with the first signature innermost in the aggregate. In contrast with general (not forward-secure) aggregate signature schemes which aggregate signatures from multiple signers, a FssAgg signature scheme aggregates signatures of a single signer not the signatures of different signers, so the verifier uses a single public key to verify the entire aggregate. With the advantages of forward secure signature and the aggregate signature at the same time, the FssAgg signature scheme has been widely applied in logging systems and blockchain since it was proposed in 2007. Although there have been several FssAgg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. So looking for the quantum-immune FssAgg signature is much urgent. Based on the small integer solution over lattice, a FssAgg signature in the standard model is proposed. In order to improve the efficiency, this paper uses the fixed-dimensional lattice basis delegation technique to update the keys, and the forward security is achieved. This paper uses the message addition technique and the pre-image sampling technique to embed the message and the small integer solution into the signature process, and the existentially unforgeability of the scheme is also guranteed in the standard model.

The forward secure sequential aggregate (Fss-Agg) signature has the advantages of forward secure signature and the sequential aggregate signature at the same time. Since its proposal in 2007, it has been widely applied in many application scenarios, such as logging systems, e-business, e-government, blockchain, etc. Although there have been several Fss-Agg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era when the general quantum computers become reality. So looking for the quantum-immune Fss-Agg signature is much urgent. In this paper, the definition of Fss-Agg signature scheme is described, and the forward security and the existential unforgeability under the chosen message attack are combined to define the existential unforgeability of Fss-Agg signature aganist chosen message attack. Based on the small integer solution assumption on lattice, using the pre-image sampling and the lattice basis delegation techniques, the quantum-immune Fss-Agg signature is proposed, which is the first lattice-based Fss-Agg signature scheme. It is proven to be correct, forward secure and existentially unforgeable in the random oracle model.