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

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.