Introduction
Verifiable Delay Functions (VDF) were introducted by Boneh et al [BBBF18] in 2018. Informally, a VDF is a funtion that requires a specified number of step to compute its output, even with a large number of parallel processor, but the correctness of the output can be quickly verified. While there can be many functions that require a specified of step to compute its output, not all of them are qualified to become VDFs. For example, consider the function \(f(X)=\mathsf{SHA256}^t(X)=\mathsf{SHA256}(\mathsf{SHA256}(...(\mathsf{SHA256}(X))...))\). Calculating \(f(X)\) require \(t\) iterations, even on a parallel computer. However, verification would also require \(t\) iterations, thus the function \(f(X)\), while VDF verification time must be within \(O(poly(\log t))\). VDFs has found it application in many aspects [BBBF18]. We will highlight some of them later in the Application section.