Recursive Zero-Knowledge Proofs for Large Pre-Image Verification
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Solution Overview
Problem
Existing zero-knowledge proof systems are inefficient for proving knowledge of large pre-image values due to their monolithic approach, leading to high computational and memory requirements, and lack scalability.
Innovation Solution
The use of recursive SNARKs and proof-carrying data (PCD) to split computations into manageable subroutines, allowing incremental and scalable proof generation for proving knowledge of arbitrarily large pre-image values, with constant proof size and reduced memory requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a monolithic approach is used for zero-knowledge proof generation, then the proof can cover the entire pre-image value, but the computational and memory requirements become prohibitively high
Solution Approach 1:
The pre-image value is divided into multiple blocks, and the proof generation is segmented into multiple sequential steps. Each node processes a specific block and generates a proof for that block, rather than processing the entire pre-image at once. This segmentation reduces the computational and memory requirements for each individual proof generation step while maintaining the ability to prove knowledge of the complete pre-image value through composition of individual proofs.
2Reliability
If a monolithic approach is used for zero-knowledge proof generation, then the proof can cover the entire pre-image value, but the memory requirements become prohibitively high
Solution Approach 1:
The proof generation process is segmented across multiple nodes, each handling a specific block of the pre-image value. Each node only needs to store and process the memory requirements for its assigned block rather than the entire pre-image, significantly reducing individual memory requirements. The segmented proofs are then composed to form a complete proof of knowledge of the entire pre-image value.
3Productivity
If the proof size is reduced to improve efficiency, then computational demands decrease, but the ability to prove knowledge of large pre-images is compromised
Solution Approach 1:
The proof is segmented into multiple smaller proofs, each corresponding to a specific block of the pre-image value. Each individual proof is small and computationally efficient to generate and verify. The complete proof capability for large pre-images is achieved by composing these individual block proofs sequentially, where each proof verifies knowledge of its corresponding block, collectively proving knowledge of the entire large pre-image value.
4Adaptability or versatility
If the computation is split into subroutines to reduce memory requirements, then scalability improves, but the system complexity increases
Solution Approach 1:
The computation is segmented into multiple independent subroutine executions, each handling a specific block of the pre-image value. Each subroutine is relatively simple and can be executed independently by different nodes. The segmentation enables scalability by allowing additional nodes to be added to handle additional blocks. The overall system complexity is managed through the modular structure, where each node follows the same simple pattern of processing its assigned block and generating a corresponding proof.
Data Source
AI summary
A computer-implemented method for generating a zero-knowledge proof for proving knowledge of a pre-image value. A series of pre-image blocks is obtained which, when combined, form the pre-image value. A series of nodes are executed, wherein each node of the series is configured to: receive a respective current state and a respective current iteration counter; evaluate an instance of a predefined compression function, based on the respective current state, to compute a respective next state; increment the respective current iteration counter to generate a respective next iteration counter; determine, based on a respective next pre-image block of the series of pre-image blocks, that the predefined compression function instance has been evaluated correctly; and output a proof, wherein the proof attests to the predefined compression function instance being evaluated correctly. The proof generated by a final node of the series of nodes proves knowledge of the pre-image value.