Compressed Zero-Knowledge Proofs for Lattice-Based Accumulator

Abstract

Abstract The lattice-based cryptographic accumulators, which enable short zero-knowledge arguments of membership, have numerous applications in post-quantum privacy-preserving protocols. However, most efficient quantum-safe zero-knowledge arguments are PCP-based systems and rely on non-falsifiable assumptions. For non-PCP-based constructions using the state-of-the-art techniques on compressing lattice-based zero-knowledge proofs, the concrete size of the resulting proof for accumulators with $2^{32}$ members is at least 500 KB. In this paper, we propose a compact non-PCP zero-knowledge proof for the lattice-based Merkle-tree, which leads to an efficient post-quantum cryptographic accumulator. The complexity of our construction is logarithmic in $l\cdot n_{s}$, where $l$ and $n_{s}$ denote the depth of the underlying Merkle-tree and the size of a node, respectively, and the concrete size is only $143.7\ $KB when $l=32$. In particular, we provide an improved lattice-based Bulletproof with efficient knowledge extraction, which allows large challenge space but small soundness slack. Furthermore, the amortized technique can be applied to the Bulletproof without breaking the knowledge soundness due to our improved knowledge extraction. As a direct application, we present a practical lattice-based ring signature, which can achieve logarithmical signing/verifying computational complexity with the number of the ring, while the state-of-the-art constructions (CRYPTO 21) have linear computational complexity.