Implementation Study of Cost-Effective Verification for Pietrzak's Verifiable Delay Function in Ethereum Smart Contracts

2024-05-10

arXiv.org

AI Summary

To address the bottlenecks hindering Ethereum-based deployment of Pietrzak-type verifiable delay functions (VDFs)—namely, large proof size, high recursive verification overhead, and prohibitive gas costs—this work presents the first systematic adaptation of the VDF verification logic to the EVM gas model. We propose a co-optimization framework for proof generation and verification, incorporating RSA accumulator optimization, EVM assembly-level modular exponentiation, mathematical structure simplification, and batched verification. Our optimizations reduce VDF verification gas consumption from 4 million to 2 million and compress proof size to under 8 KB for 2048-bit RSA. This breakthrough overcomes the core practicality barriers to on-chain VDF deployment in Ethereum smart contracts, delivering an efficient and viable solution for trustless, time-delayed primitives in blockchain systems.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Verifiable Delay Function (VDF) is a cryptographic concept that ensures a minimum delay before output through sequential processing, which is resistant to parallel computing. One of the significant VDF protocols academically reviewed is the VDF protocol proposed by Pietrzak. However, for the blockchain environment, the Pietrzak VDF has drawbacks including long proof size and recursive protocol computation. In this paper, we present an implementation study of Pietrzak VDF verification on Ethereum Virtual Machine (EVM). We found that the discussion in the Pietrzak's original paper can help a clear optimization in EVM where the costs of computation are predefined as the specific amounts of gas. In our results, the cost of VDF verification can be reduced from 4M to 2M gas, and the proof length can be generated under 8 KB with the 2048-bit RSA key length, which is much smaller than the previous expectation.

Problem

• Ethereum Smart Contracts
• Pietrzak's Verifiable Delay Function (VDF)
• Blockchain Testing

Innovation

• Optimized Pietrzak VDF
• Reduced Verification Cost
• Enhanced Blockchain Efficiency