### Verifiable Isogeny Walks: Towards an Isogeny-based Postquantum VDF

Jorge Chavez-Saab, 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.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MINOR revision.Selected Areas in Cryptography – SAC 2021
Keywords
Isogeny-based cryptographyPostquantum cryptographyVerifiable delay functionsSupersingular elliptic curvesSNARGsVerifiable computation
Contact author(s)
jorgechavezsaab @ gmail com
Francisco rodriguez @ cinvestav mx
mehdi tibouchi @ normalesup org
History
2021-11-09: revised
See all versions
Short URL
https://ia.cr/2021/1289

CC BY

BibTeX

@misc{cryptoeprint:2021/1289,
author = {Jorge Chavez-Saab and Francisco Rodríguez Henríquez and Mehdi Tibouchi},
title = {Verifiable Isogeny Walks: Towards an Isogeny-based Postquantum VDF},
howpublished = {Cryptology ePrint Archive, Paper 2021/1289},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/1289}},
url = {https://eprint.iacr.org/2021/1289}
}

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