Discrete-Log Zero-Knowledge Proofs for Composite Statement Verification
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Solution Overview
Problem
Existing zero-knowledge proof systems, such as zkSNARKs, are computationally demanding, require large proving keys, and rely on untested cryptographic assumptions, making them impractical for proving statements involving arbitrary cryptographic elliptic curve key operations, especially in blockchain applications.
Innovation Solution
A method that enables zero-knowledge proof by using discrete-log based protocols without bilinear pairing-friendly elliptic curves, employing homomorphic commitments and batched commitments to reduce proof size and computational expense, allowing efficient verification of composite statements involving arithmetic circuit satisfiability and public key validity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If zkSNARKs are used for zero-knowledge proof, then the proof provides strong cryptographic security, but the proof generation is extremely computationally demanding and requires large proving keys
Solution Approach 1:
The patent changes the cryptographic parameters by using discrete-log based protocols instead of bilinear pairing-friendly elliptic curves. This parameter change reduces the computational complexity of proof generation while maintaining security, as the system no longer relies on pairing operations that require large proving keys and extensive computation.
Solution Approach 2:
The patent extracts and removes the dependency on bilinear pairings from the zero-knowledge proof system. By taking out this complex cryptographic assumption, the system achieves more efficient proof generation without sacrificing the core security properties, as the security relies instead on more efficient discrete-log based cryptography.
2Reliability
If zkSNARKs are used for zero-knowledge proof, then the proof provides strong cryptographic security, but the system relies on untested cryptographic assumptions
Solution Approach 1:
The patent extracts and removes the dependency on bilinear pairings and pairing-friendly elliptic curves, which are considered untested cryptographic assumptions. The system replaces these with discrete-log based cryptography, which uses more well-studied and tested cryptographic primitives, thereby improving the reliability of the cryptographic assumptions.
3Productivity
If discrete-log based protocols without bilinear pairings are used, then proof generation becomes more efficient and security assumptions are more reliable, but the system must handle composite statements involving arithmetic circuit satisfiability and public key validity simultaneously
Solution Approach 1:
The patent merges multiple proof objectives into a single integrated approach. It combines arithmetic circuit satisfiability proofs with public key validity proofs into one unified zero-knowledge proof system. This merging is achieved by formulating both types of statements within the same discrete-log based protocol framework, allowing simultaneous verification without requiring separate proof systems.
Solution Approach 2:
The patent creates a universal zero-knowledge proof system that can handle multiple types of statements simultaneously. The discrete-log based protocol serves multiple functions: it can prove arithmetic circuit satisfiability, validate public key relationships, and handle composite statements involving both elements. This multi-functionality reduces overall system complexity by eliminating the need for specialized proof systems for different purposes.
Data Source
AI summary
A method relates to efficient zero knowledge verification of composite statements that involve both arithmetic circuit satisfiability and dependent statements about the validity of public keys (key-statement proofs) simultaneously. In one example, a computer-implemented method is provided for enabling zero-knowledge proof or verification of a statement (S) in which a prover proves to a verifier that a statement is true while keeping a witness (w) to the statement a secret. The method also relates to the reciprocal method employed by a verifier who verifies the proof. The method includes the prover sending to the verifier a set of data including a statement, which for a given function circuit output and an elliptic curve point, the function circuit input is equal to the corresponding elliptic curve point multiplier. The data includes individual wire commitments and/or a batched commitment for the circuit of the statement, an input and an output.