Lattice-Based Accumulator with Efficient Updating

An accumulator is a function that hashes a set of inputs into a short, constant-size string while preserving the ability to efficiently prove the inclusion of a specific input element in the hashed set. A concrete accumulator is constructed by using strong RSA assumption. Thanks to their practical features, accumulators are used in various protocols such as zero-knowledge proofs, group signatures, and blockchain. However, lattice-based accumulators are not as well studied as the strong RSA assumption. In 2019, Ling et al. constructed a lattice-based accumulator that is enable to update the member in the list, called LLNW in this paper. However, the update algorithm of the LLNW scheme is not complete, since it requires recalculation to any member regardless of whether or not the member is updated. In this paper, we propose an efficient update algorithm, called EfficientAccWitUpdate, to LLNW, which enables us to update members more efficiently than that in LLNW. In our method, only a member who updates requires recalculation. Specifically, the number of multiplications required for updating in EfficientAccWitUpdate is $\frac{1}{2}$ of LNWX, and the number of additions required for updating in EfficientAccWitUpdate is $\frac{nk+1}{2nk-1}$ of LNWX. Consequently, by incorporating the EfficientAccWitUpdate accumulator scheme into the zero-knowledge protocol, group signature, and blockchain, it is possible to realize a more efficient application.