An extension of Overbeck's attack with an application to cryptanalysis of Twisted Gabidulin-based schemes.

Alain Couvreur; Ilaria Zappatore

Paper 2023/997

An extension of Overbeck's attack with an application to cryptanalysis of Twisted Gabidulin-based schemes.

Alain Couvreur

, Computer Science Laboratory of the École Polytechnique

Ilaria Zappatore

, XLIM, Université de Limoges

Abstract

In this article, we discuss the decoding of Gabidulin and related codes from a cryptographic point of view, and we observe that these codes can be decoded solely from the knowledge of a generator matrix. We then extend and revisit Gibson and Overbeck attacks on the generalized GPT encryption scheme (instantiated with the Gabidulin code) for different ranks of the distortion matrix. We apply our attack to the case of an instantiation with twisted Gabidulin codes.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Published elsewhere. PQCrypto2023
Keywords: Code-based cryptography rank metric codes Gabidulin codes Overbeck attack twisted Gabidulin codes
Contact author(s): alain couvreur @ inria fr
ilaria zappatore @ unilim fr
History: 2023-06-27: approved; 2023-06-26: received; See all versions
Short URL: https://ia.cr/2023/997
License: CC BY

BibTeX

@misc{cryptoeprint:2023/997,
      author = {Alain Couvreur and Ilaria Zappatore},
      title = {An extension of Overbeck's attack with an application to cryptanalysis of Twisted Gabidulin-based schemes.},
      howpublished = {Cryptology ePrint Archive, Paper 2023/997},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/997}},
      url = {https://eprint.iacr.org/2023/997}
}