Improving Blockchain Scalability Using a Perceptron Tree-Based Zero-Knowledge Proof Model
Abstract
This project proposes a method to enhance scalability and privacy protection in the Ethereum network using a Perceptron Tree-based Zero-Knowledge Proof (ZKP) model. The Perceptron Tree, a hybrid model combining the strengths of decision trees and perceptron neural networks, provides a compressed representation for transaction relationships, facilitating efficient verification. It addresses specific drawbacks of existing zk-SNARK and zk-STARK methods, consolidating multiple transactions into a single proof to reduce gas fees and decrease on-chain verification load.
Motivation
The significant increase in blockchain transactions has resulted in scalability limitations and privacy issues. Existing ZKP methods effectively validate individual transactions but fall short in analyzing inter-transaction relationships while maintaining privacy.
ZK-Rollups bundle multiple transactions off-chain into a single proof submitted to the Ethereum mainnet, improving throughput and reducing costs. However, current batching approaches verify transactions individually without leveraging inter-transaction patterns or relationships.
Existing privacy solutions generate separate ZK proofs for each transaction, limiting ZKP’s full potential. The proposed Perceptron Tree model overcomes these limitations by measuring the similarity among multiple transactions and compressing them into a unified proof, thus broadening ZKP applications.
Specification
1. Tree Construction
The system inputs a transaction dataset T = {x₁, x₂, …, xₙ} to construct a recursive tree.
- Each node classifies transaction data using a perceptron with a linear function:
f(x) = step(Wₐ·a + Wᵦ·b + θ)
where the step function is defined as:
step(z) = {
1, if z ≥ 0
0, if z < 0
}
- Tree construction recursively partitions nodes based on conditions like homogeneity (isPure) or maximum depth (maxDepth).
2. Relationship Similarity Calculation
Path Similarity
Measures similarity by the ratio of shared paths between two transactions within the tree:
sim_path(xᵢ, xⱼ) = d/D
Vector Space Similarity
Uses cosine similarity calculated from the feature vectors of each transaction:
sim_cos(xᵢ, xⱼ) = (xᵢ·xⱼ)/(‖xᵢ‖‖xⱼ‖)
3. ZKP Proof Generation
The process follows five key steps:
- Construct Perceptron Tree: Build a tree based on transaction set T and train perceptrons at each node.
- Calculate Node Commitments: Compute a commitment value Cₙ for each node n using weights Wₙ, bias bₙ, and hashes of left/right child nodes:
Cₙ = H(Wₙ, bₙ, Cₗₑₜₜ, Cᵣᵢₑₕₜ)
- Generate Path Proof: For a specific transaction xᵢ, demonstrate the classification path within the tree.
- Prove Similarity Threshold: Prove that the similarity between two transactions xᵢ and xⱼ exceeds a predefined threshold θ.
- Construct Final ZKP Proof: The final Zero-Knowledge Proof Π includes:
Π = {Cᵣₒₒₜ, path(xᵢ), sim(xᵢ, xⱼ)}
Where Cᵣₒₒₜ is the root commitment, path(xᵢ) is the path proof of xᵢ, and sim(xᵢ, xⱼ) is the similarity proof between transactions.
4. On-chain Verification
Smart contracts verify the submitted proof (Π) by checking:
- The Cᵣₒₒₜ commitment matches the pre-registered tree root hash
- The transaction xᵢ is correctly classified along the provided path(xᵢ)
- The similarity between two transactions meets the predefined threshold θ
Backward Compatibility
This proposal operates at the smart contract level, requiring no modifications to the existing Ethereum protocol or consensus algorithm. It can be implemented alongside existing transaction verification methods, allowing optional adoption without network upgrades.
Security Considerations
- Privacy Protection: Verifies transaction validity without revealing specific transaction details
- Tamper Resistance: Uses commitment values based on tree structures and weights to detect data tampering
- Replay Attack Prevention: Includes unique transaction IDs in proofs to avoid replay attacks
- Lightweight Verification: Ensures efficient, simple proof verification operations within smart contracts, minimizing gas fees
Development Status
This project is currently in research and development phase. Contributions and feedback are welcome.
License
Copyright and related rights waived via CC0.