This paper is concerned with the question, wether VDFs can be used to construct TLPs in a black-box manner, and the reverse question, if TLPs can be used to construct VDFs in a black-box manner. In this paper, we construct two ”worlds”: one where TLPs exist and VDFs do not, and another one where VDFs exist and TLPs do not. This provides strong evidence that the answer to both questions is negative.

This paper is concerned with the question whether Verifiable Delay Functions (VDFs), as introduced by Boneh et al. [CRYPTO 2018], can be constructed in the plain Random Oracle Model (ROM) without any computational assumptions. A first partial answer to this question is due to Mahmoody, Smith, and Wu [ICALP 2020], and rules out the existence of perfectly unique VDFs in the ROM. Building on this result, Guan, Riazanov, and Yuan [CRYPTO 2025] very recently demonstrated that even VDFs with computational uniqueness are impossible under a public-coin setup. However, the case of computationally unique VDFs with private-coin setup remained open. We close this gap by showing that even computationally expensive private-coin setup will not allow to construct VDFs in the ROM.

Let \( E \) be a non-Archimedean local field with residue characteristic \( p \), and let \( \ell \neq p \) be another prime number. Non-Abelian Lubin–Tate theory refers to the appearence of the local Langlands correspondence for \( \operatorname{GL}_n(E) \) within the \( \ell \)-adic cohomology of the Lubin–Tate perfectoid space. Building on a sketch provided in a paper by Yoichi Mieda (itself drawing on work by Drinfeld, Yoshida, and Weinstein), we investigate the geometry of this perfectoid space and define a rational subset admitting a certain formal model whose special fiber is isomorphic to the perfection of a Deligne–Lusztig variety. This connection elucidates links between aspects of the local Langlands correspondence for \( \operatorname{GL}_n(E) \) and Deligne–Lusztig theory, and enables an explicit description of certain components of the local Langlands correspondence for \( \operatorname{GL}_n(E) \). The necessary tools for this explicit description were developed by Yoichi Mieda.