Ultra short signatures with Dragon $HFE_{LL'}$

Jacques Patarin; Jan Vacek; Alexandre Roullet

Paper 2026/404

Ultra short signatures with Dragon $HFE_{LL'}$

Jacques Patarin, Thales DIS France SAS, Meudon, France, Université Paris-Saclay, UVSQ, CNRS, Laboratoire de mathématiques de Versailles, 78000, Versailles, France

Jan Vacek, Thales DIS Czech Republic, s.r.o., Prague, Czech Republic, Université Paris-Saclay, UVSQ, CNRS, Laboratoire de mathématiques de Versailles, 78000, Versailles, France

Alexandre Roullet, Thales DIS France SAS, Meudon, France, Université Paris-Saclay, UVSQ, CNRS, Laboratoire de mathématiques de Versailles, 78000, Versailles, France

Abstract

We study HFE-based multivariate signatures with an $LL'$ perturbation. The resulting scheme $HFE_{LL'}$ gives short signatures, and its Dragon variant $D\text{-}HFE_{LL'}$ gives ultra-short signatures by separating the hash length from the number of signature variables. We discuss the relation with $\mathrm{HFE}^{\widehat{+}}$, the applicability of known attacks, and propose explicit parameter sets.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Post-quantum cryptography Multivariate cryptography Hidden Field Equations HFE LL’ perturbation Ultra-short signatures
Contact author(s): jacques patarin @ thalesgroup com
jan vacek @ thalesgroup com
alexandreroullet3 @ gmail com
History: 2026-08-17: last of 2 revisions; 2026-02-27: received; See all versions
Short URL: https://ia.cr/2026/404
License: CC BY

BibTeX

@misc{cryptoeprint:2026/404,
      author = {Jacques Patarin and Jan Vacek and Alexandre Roullet},
      title = {Ultra short signatures with Dragon ${HFE_}{{LL}'}$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/404},
      year = {2026},
      url = {https://eprint.iacr.org/2026/404}
}