Properties
We require a VDF to have the following security properties:
Correctness: For all parameter \(x\),\(t\) and \((ek,vk) \leftarrow \mathsf{Gen}(1^{\lambda})\) if \((Y,\pi)=Eval(ek,X,t)\) then \(Verify(vk,X,Y,\pi,t)=1\)
Soundness: A VDF is sound if every algorithms \(A\) can solve the following problem with negligible probability in \(\lambda\): Given \(ev,vk\) output \(X,Y,\pi\) such that \((Y,\pi) \neq Eval(ek,X,t)\) and \(Verify(vk,X,Y,\pi,t)=1\).
Sequentiality: A VDF is \(t-\)sequentiality if for all algorithms \(A\) with at most \(O(\mathsf{poly}(t))\) parallel processors and runs within time \(O(\mathsf{poly}(t))\), the experiment \(ExpSeq*{VDF}^{A}(1^\lambda)\) is negilible in \(\lambda\), where \(ExpSeq*{VDF}^{A}(1^\lambda)\) is described as follows:
\(ExpSeq_{VDF}^{A}(1^\lambda)\):
- \((ek,vk) \leftarrow \mathsf{Gen}(1^{\lambda})\)
- \(X {\stackrel{$}{\leftarrow}} \{0,1\}^{in(\lambda)}\)
- \((Y,\pi) \leftarrow A(X,ek,vk)\)
- Return \((Y,\pi)==\mathsf{Eval}(X,ek,t)\)