Lattice-based dynamic universal accumulator: Design and application

Dynamic universal accumulator is a crucial cryptography primitive. This type of accumulator can provide a succinct witness for a member (resp. nonmember) in order to make sure whether such member (resp. nonmember) is accumulated in a set, and supports deleting and adding operations from the accumulated set, as well as updating the existing witnesses. In recent years, lattice-based accumulator has given rise to increasing attention with the advent of quantum computing. However, none of existing lattice-based accumulators is both universal and dynamic. Therefore, in this work, we first design a lattice-based dynamic universal accumulator scheme with undeniability and indistinguishability. And we construct a Stern-like zero-knowledge argument protocol about a fresh relation to show that this accumulator supports set membership proofs. Moreover, we use this accumulator and the protocol to construct a full dynamic group signature with stateless updates from lattices, holding traceability and full anonymity. Furthermore, we give an implementation of our accumulator scheme, and the experiment results show that the update algorithms in this scheme have good practicability.