A Survey of Quantum Secure Group Signature Schemes: Lattice-Based Approach

Abstract

The group signatures allow any member to sign the message on behalf of the group. While anyone who does not need to be a group member can verify the signature, they do not know who the signer is. The first examples are constructed using classical techniques such as the discrete logarithm and the integer factorization problem. The fact that the cryptosystems using classical techniques will be broken in polynomial time with quantum computing power increases the interest in post-quantum cryptography. Lattice-based cryptography is a good alternative for the post-quantum world due to its simple structures, efficient implementations, and worst-case hardness. Therefore, the lattice-based group signature schemes have been proposed for quantum era. In this paper, our aim is to review group signature schemes over lattices. We classify the schemes into four groups according to the fact that they allow adding and revoking members: static, group signature schemes with revocation mechanism, partially dynamic and fully dynamic. Firstly, we define the algorithms needed to construct the schemes. We give the development process and requirements for constructing group signatures before we review all group signature schemes over lattices. In addition, we compare all proposed lattice-based group signature schemes in view of underlying lattice problems, security requirements, the sizes of group public and secret signing key, signature size and security model. The main contribution of this study is that it is the first study examining lattice-based group signature schemes in detail.