A Modified Zero-Knowledge Scheme from Bilinear Pairing for Securing Multiple Secret Values

Abstract

Zero-knowledge proof is a tool in cryptography that ensures the privacy of the users. In general, zero-knowledge (ZK) proves that a user (called the prover) knows one secret value to another (called the verifier) without revealing the secret value itself. This proof is used, for instance, in password verification or authentication process. The concept of ZK has been implemented in various fileds, including secure multi-party computation and blockchain technology. ZK proof could use pairing as the interactive function, through which the prover and verifier play their roles. ZK proof usually protects one secret, meaning the prover only certifies their knowledge of one single secret value. In this paper, we proposed a zero-knowledge scheme using a bilinear map which could help a user prove their knowledge related to multiple secret values to others. We also show that this scheme satisfies completeness and soundness properties, implying the proposed scheme is a proof of knowledge.