### 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 $$(Y,\pi)==\mathsf{Eval}(X,ek,t)$$