Post-quantum hash functions using $\mathrm{SL}_n(\mathbb{F}_p)$

Corentin Le Coz; Christopher Battarbee; Ramón Flores; Thomas Koberda; Delaram Kahrobaei

Paper 2022/896

Post-quantum hash functions using $\mathrm{SL}_n(\mathbb{F}_p)$

Corentin Le Coz

, Oppida, France

Christopher Battarbee, Sorbonne Université, France

Ramón Flores

, University of Seville

Thomas Koberda

, University of Virginia

Delaram Kahrobaei

, Queens College, CUNY, University of York, Initiatives for the Theoretical Sciences (ITS), CUNY Graduate Center

Abstract

We define new families of Tillich-Zémor 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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. arxiv.org
Keywords: Hash functions Post-quantum cryptography Group-based cryptography
Contact author(s): corentinlecoz @ outlook com
cb2036 @ york ac uk
ramonjflores @ us es
thomas koberda @ gmail com
dkahrobaei @ gc cuny edu
History: 2024-08-22: last of 2 revisions; 2022-07-08: received; See all versions
Short URL: https://ia.cr/2022/896
License: CC BY

BibTeX

@misc{cryptoeprint:2022/896,
      author = {Corentin Le Coz and Christopher Battarbee and Ramón Flores and Thomas Koberda and Delaram Kahrobaei},
      title = {Post-quantum hash functions using $\mathrm{{SL}}_n(\mathbb{F}_p)$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/896},
      year = {2022},
      url = {https://eprint.iacr.org/2022/896}
}