Cryptology ePrint Archive: Report 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.

Category / Keywords: secret-key cryptography / Nonlinear MDS diffusion layer. Linear structure. Algebraic degree. Walsh spectrum. Differential spectrum.