Zero-Knowledge Statement Proof with Batched Discrete Log Commitments
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Solution Overview
Problem
Existing zero-knowledge proof systems, such as zkSNARKs, require computationally expensive elliptic curve point multiplications and special pairing-friendly curves, limiting their applicability to standard cryptographic sets like Bitcoin secp256k1, and increasing proof generation time and size.
Innovation Solution
A method using a zero-knowledge proof system that incorporates batched commitments to discrete logarithms of public elements in a finite group, avoiding explicit elliptic curve point multiplications, and utilizing augmented verification circuits for efficient proof generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing zero-knowledge proof systems (zkSNARKs) are used to prove statements, then proof validity can be verified, but the computational expense increases due to required elliptic curve point multiplications and special pairing-friendly curves
Solution Approach 1:
The patent extracts and removes the computationally expensive elliptic curve point multiplication operations from the zero-knowledge proof system. By using batched commitments to discrete logarithms in a finite group instead of explicit elliptic curve operations, the system maintains proof validity verification while eliminating the harmful computational overhead associated with pairing-friendly curves and point multiplications.
2Reliability
If existing zero-knowledge proof systems (zkSNARKs) are used to prove statements, then proof validity can be verified, but the proof generation time increases
Solution Approach 1:
The patent removes the time-consuming elliptic curve point multiplication operations from the proof generation process. By replacing these operations with batched commitments using discrete logarithms in a finite group, the system maintains the ability to verify proof validity while dramatically reducing the time required to generate proofs, as the finite group operations are computationally lighter than elliptic curve operations.
3Reliability
If existing zero-knowledge proof systems (zkSNARKs) are used to prove statements, then cryptographic security can be ensured, but the applicability to standard cryptographic sets like Bitcoin secp256k1 is limited
Solution Approach 1:
The patent creates a universal zero-knowledge proof system that works with standard cryptographic sets like Bitcoin secp256k1 by using batched commitments to discrete logarithms in a finite group. This approach is not limited to special pairing-friendly curves but can be applied to any standard cryptographic group, making the system universally applicable while maintaining cryptographic security through the mathematical properties of discrete logarithms.
4Reliability
If existing zero-knowledge proof systems (zkSNARKs) are used to prove statements, then proof verification is possible, but the proof size increases
Solution Approach 1:
The patent merges multiple commitment operations into a single batched commitment structure. Instead of creating separate proofs for each statement, the system combines multiple discrete logarithm commitments into a unified batched commitment, thereby reducing the overall proof size while maintaining the ability to verify each individual statement's validity through the shared commitment structure.
Data Source
AI summary
A method of providing proof that a statement is true keeping a secret input to the statement a secret, comprising: generating a proof using a public input, the secret input, and a proving key linked to an augmented verification circuit which comprises (i) a verification circuit arranged to receive the inputs, supply the secret input to a function circuit representing the statement to generate a function circuit output, and determine whether the public input corresponds to the function circuit output; and (ii) a multiplicative gate arranged to receive the secret input and a dummy value. The proof comprises a commitment to inputs of multiplicative gates of the augmented verification circuit, the commitment generated using a first vector comprising n components from a finite group of data elements. The secret input is a discrete logarithm of a public element of said finite group. The proof is transmitted to a verifying device.