Short Zero-Knowledge Proof of Knowledge for Lattice-Based Commitment

Abstract

Commitment scheme, together with zero-knowledge proof, is a fundamental tool for cryptographic design. Recently, Baum et al. proposed a commitment scheme (BDLOP), which is by far the most efficient lattice-based one and has been applied on several latest constructions of zero-knowledge proofs. In this paper, we propose a more efficient zero-knowledge proof of knowledge for BDLOP commitment opening with a shorter proof. There are a few technical challenges, and we develop some new techniques: First, we make an adaption of BDLOP commitment by evaluating the opening with the singular value rather than (Formula Presented) norm in order to get compact parameters. Then, we try to use the bimodal Gaussian technique to minimize the size of the proof. Finally, utilizing a modulus-switch technique, we can retain the size of the commitment.