Achieving High Efficiency in Membership Proof without Compromising or Weakening any Security Property

Membership proof shows that a secret committed message is in a finite set. In this paper, a general, flexible, universally verifiable and efficient solution to membership proof is proposed. It overcomes the drawbacks of the existing membership proof schemes. It achieves all the desired security properties in membership proof. Its most important advantage is very high efficiency. It transfers only O(1) integers in communication and costs a prover and a verifier only O(1) exponentiations respectively in computation. It overcomes the drawbacks of the existing membership proof schemes and does not compromise or Weaken any security property. It is universally verifiable and can be non-interactive. It is a general and flexible solution supporting any set and any secure commitment algorithm. Once a commitment algorithm is chosen and proved to be secure, the new membership proof protocol can adopt it and achieve formally provable security without any additional assumption.