研究成果

Range arguments are a type of zero-knowledge proofs that aim to prove that a prover's committed value falls within a specified range for a verifier. Previously, most range arguments were constructed based on the discrete logarithm (DLOG) assumption, and hence, exponentiation operation is required for proof generation and verification. In addition, it is generally known that splitting a zero-knowledge proof protocol into a preprocessing phase and an online phase makes computation after fixing the input efficient. Still, such protocol has yet to be known for range arguments. This paper proposes an efficient range arguments protocol with a preprocessing phase. Our proposal takes a new approach by using arithmetic circuits to express the constraints that the prover must prove. The prover (resp. verifier) can generate (resp. verify) a part of proof based on multiplication and addition operations instead of exponentiation operations. Our range argument is a generic construction that does not rely on any particular mathematical assumptions, which enables us to construct a post-quantum range argument. The implementation evaluation shows that the total computation time for the prover and verifier in the online phase is efficient compared to Bulletproofs, one of the state-of-the-art range proofs. Especially, the prover computation is efficient.