Abstract
The group signature is a promising cryptographic primitive that allows a signer to anonymously sign a message on behalf of a group. In the literature on existing group signature schemes, most of the proposals support static settings where the group membership is fixed at the initial setup, while group signature schemes in the fully dynamic setting offer the flexibility to add or revoke users during the protocol execution. This adaptability makes the fully dynamic group signature schemes suitable for several real-world applications. However, this rich structure of dynamicity brings the complexity of the construction of dynamic group signatures, resulting in a few number of proposals in the literature. In this work, we propose an efficient fully dynamic group signature scheme relying on the lattice-based hard problems, ensuring quantum resistance. Our approach introduces a lattice-based updatable Merkle tree accumulator in the ring setting, which efficiently manages user membership proofs and updates user information, ensuring the scheme’s dynamic functionality. We have analyzed the correctness and security of our proposed ring-based updatable Merkle tree accumulator. Our construction of the fully dynamic signature scheme eliminates the need for trapdoor constructions and incorporates an efficient exact zero-knowledge proof system. A comprehensive security analysis of our fully dynamic signature scheme is provided, based on the hardness of lattice-based Ring Short Integer Solution (RSIS) and Ring Learning With Errors (RLWE) problems. We have presented a comparison table showing that our signature size is comparable to the existing lattice-based fully dynamic group signature schemes, as well as partial dynamic and static group signature schemes. Our proposed fully dynamic group signature scheme achieves a concrete signature size of 2.38 MB at 128-bit security.
