A Cryptographic Hash Function from Markoff Triples

Elena Fuchs; Kristin Lauter; Matthew Litman; Austin Tran

Paper 2021/983 Original: eprint.iacr.org/2021/983 ↗

A Cryptographic Hash Function from Markoff Triples

Elena Fuchs

Kristin Lauter

Matthew Litman

Austin Tran

Abstract

Cryptographic hash functions from expander graphs were proposed by Charles, Goren, and Lauter in [CGL] based on the hardness of finding paths in the graph. In this paper, we propose a new candidate for a hash function based on the hardness of finding paths in the graph of Markoff triples modulo p. These graphs have been studied extensively in number theory and various other fields, and yet finding paths in the graphs remains difficult. We discuss the hardness of finding paths between points, based on the structure of the Markoff graphs. We investigate several possible avenues for attack and estimate their running time to be greater than O(p). In particular, we analyze a recent groundbreaking proof in [BGS1] that such graphs are connected and discuss how this proof gives an algorithm for finding paths.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2021-07-23: last updated; 2021-07-23: published
Short URL: https://ia.cr/2021/983
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2021/983,
      author = {Elena Fuchs and Kristin Lauter and Matthew Litman and Austin Tran},
      title = {A Cryptographic Hash Function from Markoff Triples},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/983},
      year = {2021},
      url = {https://eprint.iacr.org/2021/983}
}