### 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.

Available format(s)
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Nonlinear MDS diffusion layerLinear structureAlgebraic degreeWalsh spectrumDifferential spectrum.
Contact author(s)
dehnavism @ ipm ir
History
Short URL
https://ia.cr/2021/008

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}
}

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