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

TL;DR

This paper explores optimizing Pietrzak's Verifiable Delay Function verification on Ethereum, reducing gas costs and proof size, making VDF implementation more practical for blockchain applications.

Contribution

It provides a cost-effective verification method for Pietrzak VDF on Ethereum, optimizing gas usage and proof size based on original protocol insights.

Findings

VDF verification cost reduced from 4M to 2M gas

Proof size under 8 KB with 2048-bit RSA key

Optimization strategies based on EVM gas model

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.