Lattice-Based Accumulator with Constant Time List Update and Constant Time Verification

An accumulator is a cryptographic protocol that compresses a set of inputs into a short string of a certain size and can efficiently prove that the compressed set contains a particular input element. Accumulators have been actively studied in recent years and are used to streamline various protocols such as membership rosters, zero-knowledge proofs, group signatures, and blockchains. Libert et al. proposed a Merkle tree-based accumulator using lattice cryptography, one of the post-quantum cryptography. They proposed an accumulator with logarithmic time complexity for the verification algorithm. Ling et al. proposed an accumulator that satisfies logarithmic time updating lists. However, no algorithm has been proposed thus far that satisfies constant time updating lists and constant time verification based on the lattice-based accumulator. In this study, we propose an accumulator based on lattice that satisfies constant-time verification and constant-time updating lists for the first time. In our proposed accumulator, the bit length of the witness associated with each element is independent of the number of elements in the list. We developed techniques that use the Partial Fourier Recovery problem instead of the Merkle tree. We also prove that the proposed accumulator satisfies the security requirements of an accumulator scheme. Finally, to demonstrate that our proposed accumulator is more practical, we compared it with other lattice-based accumulators. The proposed accumulator scheme can be incorporated into membership list management, zero-knowledge proof, group signature, and blockchain to realize more efficient applications.