Zero-Knowledge Subset Membership Proofs for Private Linear Operations
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Solution Overview
Problem
Existing verifiable computing systems fail to provide robust, real-time guarantees of computational task accuracy without revealing underlying datasets, especially in scenarios where clients are not trustworthy, and lack efficient methods for proving membership of subsets and correctness of linear operations over these subsets while preserving privacy.
Innovation Solution
A zero-knowledge membership proof scheme that utilizes Pedersen commitments and elliptic curve groups to prove subset membership and correctness of linear operations, ensuring privacy and efficiency by using public parameters for commitments and verifications, without revealing the underlying dataset.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional verifiable computing systems are used to prove computational task accuracy, then computational correctness can be verified, but the underlying dataset is revealed
Solution Approach 1:
The patent introduces Pedersen commitments as an intermediary cryptographic primitive that allows the prover to commit to dataset elements without revealing them. The verifier can then prove linear operations on committed values without seeing the actual data, thus mediating between verification needs and privacy preservation.
Solution Approach 2:
The patent transforms the verification problem by changing the parameter representation from raw data values to cryptographic commitments. This parameter transformation allows verification of computational correctness on committed values while maintaining the hiding property that prevents dataset revelation.
2Loss of information
If zero-knowledge proofs are used to preserve dataset privacy, then privacy is maintained, but proof size and verification complexity increase
Solution Approach 1:
The patent applies partial zero-knowledge proofs by only proving properties of specific linear operations on committed values rather than providing complete zero-knowledge proofs for all possible computations. This partial approach reduces proof size and verification complexity while maintaining privacy for the specific operations performed.
3Adaptability or versatility
If membership proofs for subsets are provided without trusted third parties, then system trust requirements are reduced, but proving both membership and linear operation correctness becomes more difficult
Solution Approach 1:
The patent segments the proof system into distinct components: Pedersen commitments for data hiding, subset membership proofs for verifying element inclusion, and linear operation proofs for verifying computational correctness. This segmentation allows each component to be optimized independently and combined without requiring a trusted third party.
4Loss of time
If real-time verification of computational tasks is implemented, then verification timeliness is improved, but computational overhead increases
Solution Approach 1:
The patent implements preliminary action by having the prover compute and send Pedersen commitments of the dataset elements before the verification process begins. This preliminary commitment allows the verifier to efficiently verify linear operations in real-time without requiring heavy computational resources during the actual verification, as the heavy lifting of data representation was done in advance.
Data Source
AI summary
A method for providing a zero-knowledge membership proof is provided. The method comprises defining public parameters to be used for computing and verification of proof by a prover and a verifier, respectively. The method comprises computing, by the prover, a commitment to a given ordered set X using the public parameters, and sending it to the verifier. The method further comprises receiving, by the prover, a query from the verifier for proving membership of a subset S sampled from the given ordered set X. The method further comprises computing, by the prover, a proof of membership, including an inner product, commitments of polynomials defining the inner product and a proof of the inner product being correctly computed, and sending the proof of membership to the verifier. The method further comprises verifying, by the verifier, the proof of membership based on the defined public parameters.