Improving Applicability, Efficiency and Security of Non-Membership Proof

Two new non-membership proof protocols are proposed in this paper, which prove that a committed message is not in a finite set. They are concrete proof protocols rather than abstract principles. The first is a completely general non-membership proof suitable for any application. The second is a much more efficient non-membership proof protocol for special applications. It is simpler, more efficient and more applicable than the existing concrete solution to non-membership proof. Except for possible mathematical assumptions needed for the employed commitment algorithm, our non-membership proof protocols themselves do not need any additional mathematical assumption, so are proofs instead of arguments. They are flexible solutions suitable for various secure commitment algorithm. Once a commitment algorithm is chosen and proved to be secure, the new non-membership proof scheme can adopt it and achieve formally provable security without any additional assumption. This is also an advantage over the existing solution.