Post-quantum hash functions using $\mathrm{SL}_n(\mathbb{F}_p)$
Cryptography and Security
2024-08-26 v3 Group Theory
Abstract
We define new families of Tillich-Z\'emor hash functions, using higher dimensional special linear groups over finite fields as platforms. The Cayley graphs of these groups combine fast mixing properties and high girth, which together give rise to good preimage and collision resistance of the corresponding hash functions. We justify the claim that the resulting hash functions are post-quantum secure.
Cite
@article{arxiv.2207.03987,
title = {Post-quantum hash functions using $\mathrm{SL}_n(\mathbb{F}_p)$},
author = {Corentin Le Coz and Christopher Battarbee and Ramón Flores and Thomas Koberda and Delaram Kahrobaei},
journal= {arXiv preprint arXiv:2207.03987},
year = {2024}
}
Comments
18 pages, an appendix with a python/sage implementation of the hash functions