An Efficient Range Proof Based on Polynomial Commitment and Vector Inner Product Commitment

Abstract

We propose an efficient range proof scheme by constructing a polynomial commitment scheme and combining with the vector inner product commitment scheme (PolyCom-VecInnPro). Compared with the Bulletproof scheme proposed by BUNZB et al. in 2017, our scheme not only reduce the communication overhead, but also reduces the time complexity of proof generation. In addition, the scheme optimizes the verifification speed of evidence under the condition that it takes time to generate evidence and the length of evidence generation is the same, so it is a more practical blockchain range proof scheme. The paper also proves that the PolyCom-VecInnPro satisfifies perfect completeness, perfect honest-verififier zero knowledge and computational witness extended emulation.

Keywords: commitment to polynomial, commitment to vector inner product, zero knowledge proof, range proof