Tropical cryptography IV: Digital signatures and secret sharing with arbitrary access structure

Dima Grigoriev; Chris Monico; Vladimir Shpilrain

Paper 2026/095

Tropical cryptography IV: Digital signatures and secret sharing with arbitrary access structure

Dima Grigoriev, Universite de Lille

Chris Monico, Texas Tech University

Vladimir Shpilrain, The City College of New York

Abstract

We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring a given tropical matrix in a product of two matrices of given dimensions; this problem is known to be NP-complete. We also offer a secret sharing scheme with an arbitrary access structure where security of the shared secret is based on computational hardness of the same problem.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: digital signature tropical algebra factoring matrices
Contact author(s): dmitry grigoryev @ math univ-lille1 fr
c monico @ ttu edu
shpilrain @ yahoo com
History: 2026-02-24: revised; 2026-01-21: received; See all versions
Short URL: https://ia.cr/2026/095
License: CC BY

BibTeX

@misc{cryptoeprint:2026/095,
      author = {Dima Grigoriev and Chris Monico and Vladimir Shpilrain},
      title = {Tropical cryptography {IV}: Digital signatures and secret sharing with arbitrary access structure},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/095},
      year = {2026},
      url = {https://eprint.iacr.org/2026/095}
}