Paper 2021/1289

Verifiable Isogeny Walks: Towards an Isogeny-based Postquantum VDF

Jorge Chavez-Saab and Francisco Rodríguez Henríquez and Mehdi Tibouchi

Abstract

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 Fp2 , which may be of independent interest.

Note: A typo in the statement of Theorem 2 has been addressed, which changes the complexities appearing in the appendix. The main results and complexities appearing in the body of the paper remain unchanged.