A Family of Nonlinear MDS Diffusion Layers over $\mathbb{F}_{2^{4n}}$

M.  R.  Mirzaee Shamsabad; S.  M.  Dehnavi

Paper 2021/008

A Family of Nonlinear MDS Diffusion Layers over $\mathbb{F}_{2^{4n}}$

M. R. Mirzaee Shamsabad and S. M. Dehnavi

Abstract

Nonlinear diffusion layers are less studied in cryptographic literature, up to now. In 2018, Liu, Rijmen and Leander studied nonlinear non-MDS diffusion layers and mentioned some advantages of them. As they stated, nonlinear diffusion layers could make symmetric ciphers more resistant against statistical and algebraic cryptanalysis. In this paper, with the aid of some special maps over the finite field $\mathbb{F}_{2^n}$, we examine nonlinear MDS mappings and present a family of $4 \times 4$ nonlinear MDS diffusion layers. Next, we determine the Walsh and differential spectrum as well as the algebraic degree of the proposed diffusion layers.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Nonlinear MDS diffusion layer Linear structure Algebraic degree Walsh spectrum Differential spectrum.
Contact author(s): dehnavism @ ipm ir
History: 2021-01-02: received
Short URL: https://ia.cr/2021/008
License: CC BY

BibTeX

@misc{cryptoeprint:2021/008,
      author = {M.  R.  Mirzaee Shamsabad and S.  M.  Dehnavi},
      title = {A Family of Nonlinear MDS Diffusion Layers over $\mathbb{F}_{2^{4n}}$},
      howpublished = {Cryptology ePrint Archive, Paper 2021/008},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/008}},
      url = {https://eprint.iacr.org/2021/008}
}