How hard are verifiable delay functions?

TL;DR

This paper introduces a new complexity class for verifiable delay functions (VDFs), situates it within existing complexity classes, and identifies a complete problem for this class, advancing theoretical understanding of VDFs.

Contribution

It defines a new complexity class for VDFs, proves its relation to CLS, and identifies a complete problem, deepening the theoretical framework of VDFs.

Findings

VDFs form a new complexity class within CLS

Relaxed-Sink-of-Verifiable-Line is complete for this class

Provides a theoretical foundation for analyzing VDF complexity

Abstract

Verifiable delay functions (VDF) are functions that take a specified number of sequential steps to be evaluated but can be verified efficiently. In this paper, we introduce a new complexity class that contains all the VDFs. We show that this new class $\mathbf{VDF}$ is a subclass of $\mathbf{CLS}$ (continuous local search) and Relaxed-Sink-of-Verifiable-Line is a complete problem for the class $\mathbf{VDF}$.