Vector Commitment Proofs for Binary Vector Verification
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Solution Overview
Problem
Existing vector commitment schemes lack an efficient method to generate a short proof that the committed vector is binary, leading to complex arithmetic circuits and high computational costs when using general-purpose succinct non-interactive arguments (SNARKs).
Innovation Solution
A method where a prover demonstrates binarity by showing that an auxiliary vector is orthogonal to the main vector through a Hadamard product, using commitments and proofs that are independent of the vector's dimension, leveraging a vector commitment scheme with additive homomorphic properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to enable computation on encrypted data, then data privacy is protected, but the computational operations are limited to specific algebraic structures and cannot perform general binary operations
Solution Approach 1:
The patent introduces an intermediary conversion process that transforms encrypted data into a form suitable for binary operations, performs the operations, then converts back. This intermediary step enables general computational operations while maintaining encryption, resolving the contradiction between privacy protection and operational flexibility.
Solution Approach 2:
The patent changes the parameter representation of encrypted data by converting between different cryptographic representations (e.g., between encrypted values and their binary decompositions). This parameter transformation allows the system to perform operations that would otherwise be impossible under fixed algebraic constraints.
2Reliability
If traditional encryption methods are used to protect data, then data security is maintained, but any computation requires decryption which exposes the plaintext
Solution Approach 1:
The patent performs preliminary conversion of encrypted data into a computable format before actual computation occurs. This preliminary action prepares the data in advance so that subsequent operations can be performed on the converted form rather than requiring decryption, thus preventing information exposure during computation.
3Adaptability or versatility
If encrypted data is converted to plaintext for computation, then general computational operations can be performed, but the encrypted state of the data is lost
Solution Approach 1:
The patent implements periodic conversion between encrypted and computable formats: converting to plaintext form for computation, then re-encrypting afterward. This periodic action ensures data remains encrypted during storage and transmission, only temporarily exposed during necessary computational operations.
Data Source
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Figure 3
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AI summary
Some embodiments are directed to demonstrating by a prover to a verifier that a main vector is a binary vector using a vector commitment scheme. The demonstrating may comprise a main commitment to the main vector and generating a first proof demonstrating that a further vector comprising the product of a randomizing vector and the main vector minus 1 in each component is orthogonal to the main vector.