Implementation study of cost-effective verification for Pietrzak's VDF in Ethereum smart contract

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 a large proof size and recursive protocol computation. In this paper, we present an implementation study of Pietrzak's VDF verification on the Ethereum virtual machine (EVM). We found that the discussion in Pietrzak's original paper can help with a clear optimization in EVM, where the costs of computation are predefined as specific amounts of gas. In our results, the cost of VDF verification can be reduced from 4 M to 2 M gas, and the proof size can be generated under 8 KB with a 2048-bit RSA key length, which is much smaller than the previous expectation.