Zero-Knowledge Subset Membership Proof for Dynamic Set Privacy
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Solution Overview
Problem
Existing zero-knowledge set membership proof solutions are inefficient in implementing membership proofs for dynamic subsets, as they require authorization and verification for predetermined entire sets, failing to protect the privacy of element values.
Innovation Solution
A method and apparatus that utilize user equipment and a verifier device to efficiently prove membership in a dynamic subset by calculating and verifying public values, random statements, and challenge values using elliptic curve groups and bilinear mappings, ensuring privacy of element values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If authorization and verification are performed for a pre-determined entire set S, then the proof process can be simplified, but membership proof for a dynamic subset S' cannot be efficiently implemented
Solution Approach 1:
The patent divides the original set S into multiple subsets S' based on different attributes or categories. Each subset can be independently proven, allowing the system to handle dynamic subset membership efficiently. The issuer issues evidence for specific subsets rather than requiring proof for the entire set, enabling flexible and efficient subset membership verification.
2Loss of information
If the issuer issues evidence for the entire set S, then the proof structure is simpler, but the privacy of specific element values in subset S' cannot be protected
Solution Approach 1:
The patent applies different proof mechanisms to different subsets S' based on their specific characteristics. Each subset can have customized proof construction methods that balance privacy protection and verification complexity appropriately. This allows elements with different privacy requirements to be handled differently within the same system.
Solution Approach 2:
The patent introduces random values and commitment mechanisms as intermediaries between the prover and verifier. These intermediaries enable the prover to demonstrate subset membership without directly revealing specific element values. The random challenges and responses act as mediators that preserve privacy while enabling verification.
3Loss of information
If existing ZKSM solutions are used for subset proof, then implementation is straightforward, but the proof process exposes specific element values
Solution Approach 1:
The patent implements a dynamic proof system where the subset S' can change based on different verification needs. The system adapts the proof construction to the specific subset being verified, using dynamic random challenges and responsive proof generation. This dynamic approach maintains confidentiality while preserving verification efficiency through optimized proof paths for different subsets.
Data Source
AI summary
Embodiments of this specification provide a zero-knowledge set membership proof method and apparatus. User equipment receives, from a verifier device, a subset S′ whose size is η in a set S; calculates two public values based on a parameter set disclosed by a third party, an element u, and an evidence σ, and sends the two public values to the verifier device to calculate a third public value; calculates η groups of random statements based on η groups of generated random numbers and the three public values, and sends the η groups of random statements to the verifier device; receives a random challenge c from the verifier device; and sends η groups of data proofs. The verifier device verifies whether the random statement, the challenge value, and the proof value satisfy a preset relationship, to determine whether the element u owned by the user equipment belongs to the subset S′.