VDF Algorithms
A VDF consists of three algorithms \( (\mathsf{Gen}, \mathsf{Eval}, \mathsf{Verify})\) where:
\((ek,vk) \leftarrow \mathsf{Gen}(1^{\lambda},t)\): This algorithm takes as input as a security parameter \( \lambda \), and outputs a public key pair \( (ek,vk)\).
\( (Y,\pi) \leftarrow \mathsf{Eval}(X,ek,t)\): This algorithm takes an input an evaluation key \(sk\), a value \(X\) a time parameter \(t\) and outputs a value \(Y \in \{0,1\}^{out(\lambda)} \) and a proof \( \pi \).
\( b \leftarrow \mathsf{Verify}(vk,X,Y,\pi,t)\): This algorithm takes an input a verification key \(vk \), a value \(X\), a value \(Y\), a proof \(\pi\), a time parameter \(t\) and outputs a bit \(b\) that determines whether \(Y=\mathsf{Eval}(X,ek)\). This algorithm run within time \(O(poly(\log t))\).