Zero-Knowledge Algorithm for Digital Asset Exchange Solvency
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Solution Overview
Problem
Current zero-knowledge proof systems are inefficient in verifying compound statements, particularly those involving both algebraic and Boolean functions, which are essential for proving solvency in digital asset exchanges and verifying anonymous digital certificates, as they require combining incompatible proof techniques like zkSNARKs and Sigma protocols, leading to computational inefficiencies and privacy concerns.
Innovation Solution
A system that generates zero-knowledge algorithms by combining zkSNARK and Sigma protocols, using commitments to secret values and algebraic functions, allowing for efficient proof of compound statements like knowledge of x such that AES(x)=y1 and gx=y2, while keeping x private, and proving solvency in digital asset exchanges without revealing private keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If zkSNARK and Sigma protocol are combined to prove compound statements, then proof capability is improved, but computational complexity increases
Solution Approach 1:
The patent segments the proof process into two distinct components: a zkSNARK component for proving algebraic statements (gx=y) and a Sigma protocol component for proving Boolean statements (H(y)=h). Each component operates independently with its own verification logic, allowing the system to handle compound statements by combining these segmented proofs rather than creating a monolithic complex proof system.
Solution Approach 2:
The patent introduces an intermediary public key y that serves as a bridge between the algebraic zkSNARK proof and the Boolean Sigma protocol proof. The public key y is generated algebraically from the private key x (gx=y) and then hashed (H(y)=h) to create the blockchain address. This intermediary structure allows both proof types to verify the same underlying relationship without direct interaction, reducing computational complexity.
2Reliability
If third-party auditors are used to verify exchange solvency, then verification capability is improved, but privacy protection deteriorates
Solution Approach 1:
The patent enables the exchange to perform self-verification of solvency through cryptographic proofs. The exchange generates zkSNARK proofs demonstrating that it controls sufficient private keys corresponding to public keys on the blockchain, and Sigma protocol proofs verifying the hashed addresses match user deposits. This self-service verification eliminates the need for third-party auditors while maintaining verification capability and protecting user privacy through zero-knowledge properties.
Solution Approach 2:
The patent replaces the mechanical system of third-party auditor verification with a cryptographic proof system. Instead of physical audits requiring trust in external entities, the system uses mathematical proofs (zkSNARKs and Sigma protocols) that provide cryptographic verification. This substitution maintains reliability through mathematical certainty while eliminating privacy loss associated with external auditors accessing sensitive exchange data.
3Reliability
If detailed transaction information is published on blockchain, then transparency is improved, but privacy protection deteriorates
Solution Approach 1:
The patent applies local quality by publishing only the hashed form H(y) of the public key on the blockchain rather than the full public key or transaction details. This localized transformation preserves the transparency needed for verification (anyone can verify the hash matches the claimed address) while protecting privacy (the actual public key and transaction information remain hidden). The exchange proves control over the pre-image of the hash through cryptographic proofs without revealing the pre-image itself.
Data Source
AI summary
Disclosed is a method, system, and computer program product for determining solvency of a digital asset exchange system. The method includes identifying a plurality of blockchain addresses corresponding to a plurality of users of a digital asset exchange system, generating a first commitment to an amount of digital assets corresponding to the plurality of blockchain addresses, and generating a second commitment to a balance of each user of the plurality of users. The method also includes generating a first component of a zero-knowledge algorithm that is configured to receive, as input, the first commitment. The method further includes generating, with at least one processor, a second component of the zero-knowledge algorithm that is configured to receive, as input, the second commitment. The method further includes determining that the digital asset exchange system is solvent based on the zero-knowledge algorithm.