Publicly Verifiable Zero-Knowledge Proofs with Compact Commitments
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Solution Overview
Problem
Existing zero knowledge proof systems generate large proof sizes, hindering their scalability and practical implementation in large-scale applications, and lack plausible post-quantum security, especially in non-interactive settings.
Innovation Solution
A non-interactive zero knowledge proof system is developed using a Fiat-Shamir transform from a non-succinct interactive line-point zero knowledge proof system, utilizing collision-resistant hash functions and vector oblivious linear evaluation protocols, with commitments generated via homomorphic encryption and Merkle tree optimizations to reduce proof size and ensure post-quantum security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing zero knowledge proof systems are used, then security and privacy are ensured, but proof size becomes large
Solution Approach 1:
The proof system is segmented into distinct components: commitment phase, challenge phase, and response phase. The proof itself is segmented into multiple messages (commitment, challenge, response) rather than a single large proof object, allowing for more efficient verification and smaller overall proof size while maintaining security
Solution Approach 2:
The patent transitions from traditional single-message proof structures to a multi-message interactive protocol structure, adding temporal and structural dimensions to the proof process. This dimensional change allows the proof to be distributed across multiple interaction rounds, reducing the size of individual proof components while maintaining overall security
2Loss of information
If traditional zero knowledge proof systems are used, then privacy is preserved, but scalability is hindered
Solution Approach 1:
The commitment phase is performed in advance before the challenge is issued. The prover commits to their witness and proof components beforehand, allowing the verifier to subsequently issue challenges without requiring the prover to recompute entire proofs. This preliminary action significantly improves scalability by reducing redundant computations
Solution Approach 2:
The proof system is designed as a dynamic interactive protocol where the verifier can adaptively issue challenges based on the commitment received. This dynamic structure allows the same commitment to serve multiple verification purposes and enables efficient batch verification, improving scalability while maintaining privacy
3Productivity
If non-interactive zero knowledge proof systems are implemented, then verification efficiency is improved, but post-quantum security is compromised
Solution Approach 1:
The patent introduces collision-resistant hash functions as intermediary components that bridge the interactive protocol and non-interactive verification. The Fiat-Shamir transformation uses hash functions as mediators to convert interactive challenges into non-interactive challenge generation, achieving both verification efficiency and post-quantum security through this intermediary mechanism
Solution Approach 2:
The patent replaces traditional cryptographic assumptions (such as factoring or discrete logarithm problems) with collision-resistant hash function assumptions, which are believed to be secure against quantum computers. This substitution of cryptographic primitives maintains security while enabling efficient non-interactive verification
Data Source
AI summary
A method for generating a proof of a statement related to private data without revealing the data to verifier parties. The method involves secure storage of private data and a statement at a prover party's computing device. The statement's validity is encoded as an arithmetic circuit's satisfiability. The method includes computing two vectors, A and B, with A containing random elements and B derived from the private data and the statement. A commitment to these vectors is generated, followed by a hash function to produce a value alpha. These elements are used in a line-point zero knowledge proof system to produce an output vector and a proof of knowledge, ensuring the statement's validity. The proof is stored and made accessible to verifier parties, maintaining the security of the private data.