Membership Proof Device With Split RSA and Zero-Knowledge Calculations
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Solution Overview
Problem
Existing membership proof methods using zero-knowledge proof algorithms, such as zk-SNARK and RSA accumulators, suffer from increased computational load and time due to hash and exponentiation operations, which hinder efficient and private user membership verification.
Innovation Solution
Perform exponentiation operations for RSA accumulator-based membership proof separately from zero-knowledge proof algorithms, using a commit-and-prove technique to verify user values, and employ a prime number exponentiation to ensure privacy, along with a fast proof of knowledge exponent (PoKE) technique to maintain privacy and reduce proof size.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If zero-knowledge proof algorithm (zk-SNARK) is used for membership proof, then user privacy is ensured, but computational load and time increase due to hash operations
Solution Approach 1:
The patent segments the membership proof process into two independent parts: (1) RSA accumulator-based membership proof calculation, and (2) zero-knowledge proof calculation. By separating these operations, the computationally intensive RSA exponentiation is performed independently before the ZK-proof, allowing the ZK-proof to verify membership without performing heavy hash operations on all user values, thus reducing overall proving time while maintaining privacy
Solution Approach 2:
The patent performs preliminary RSA accumulator-based membership proof calculation before generating the zero-knowledge proof. The prover first computes the membership proof value using RSA exponentiation on the user value and accumulated public values, then uses this pre-computed result in the ZK-proof generation. This preliminary action eliminates the need for repeated hash operations during ZK-proof verification, reducing computational load and time
2Reliability
If RSA accumulator-based membership proof is used, then membership verification is achieved, but computational load increases due to exponentiation operations
Solution Approach 1:
The patent extracts the computationally intensive RSA exponentiation operation from the zero-knowledge proof algorithm and performs it separately as a preliminary membership proof calculation. The prover computes the membership proof value using RSA exponentiation independently, then incorporates this pre-computed value into the ZK-proof. This extraction eliminates redundant exponentiation operations within the ZK-proof itself, reducing computational load while maintaining verification reliability
Solution Approach 2:
The patent changes the computational parameters by using RSA accumulator-based membership proof with pre-computed exponentiation results. Instead of performing exponentiation operations repeatedly during ZK-proof generation and verification, the system uses the pre-computed membership proof value as an input parameter to the ZK-proof, significantly reducing the number of expensive exponentiation operations required
Data Source
AI summary
Disclosed are a membership proof device and method for ensuring privacy. The disclosed membership proof method includes for ensuring privacy includes performing a first calculation for a user's membership proof using a zero-knowledge proof algorithm and performing a second calculation for the user's membership proof on a user value of the user using a Rivest-Shamir-Adleman (RSA) accumulator-based membership proof algorithm and transmitting results of the first and second calculations to a verifier.