后量子安全的群签名和环签名

Group signatures and ring signatures allow a user to anonymously sign a message on behalf of a group. It supports security services such as identity authentication while protecting users' privacy and plays essential roles in many scenarios, such as trusted computing platforms, vehicle networks, e-voting, and anonymous cryptocurrencies. The rapid development of quantum computers has a systematic impact on classical cryptography systems. A solution to keep security under quantum computing is to build the public key systems with quantum-resistant properties. As group signatures and ring signatures are important cryptographic primitives, their post-quantum constructions have received extensive attention. This paper reviews some important group signature and ring signature schemes that are based on lattices or the symmetric cryptography primitives, summarizes the model and the design principle of group signatures and ring signatures, and classifies existing solutions from a technical point of view. The characteristics and limitations of the existing schemes are described, and some possible problems to be studied and solved in the future are discussed.