Verifiable Isogeny Walks: Towards an Isogeny-Based Postquantum VDF

In this paper, we investigate the problem of constructing postquantum-secure verifiable delay functions (VDFs), particularly based on supersingular isogenies. Isogeny-based VDF constructions have been proposed before, but since verification relies on pairings, they are broken by quantum computers. We propose an entirely different approach using succinct non-interactive arguments (SNARGs), but specifically tailored to the arithmetic structure of the isogeny setting to achieve good asymptotic efficiency. We obtain an isogeny-based VDF construction with postquantum security, quasi-logarithmic verification, and requiring no trusted setup. As a building block, we also construct non-interactive arguments for isogeny walks in the supersingular graph over F-p2, which may be of independent interest.