Geodesic
Construction of orthomorphic $\mathrm{MDS}$ matrices with primitive characteristic polynomial
Matematičeskie voprosy kriptografii, Tome 12 (2021), pp. 125-143

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Matrices having the Maximum Distance Separable property ($\mathrm{MDS}$ matrices) are a vital component for the design of symmetric-key algorithms to achieve the diffusion property. In a number of papers the construction and characterization of $\mathrm{MDS}$ matrices with a low implementation cost in the context of the so-called lightweight schemes were considered. However, small attention was paid to the influence of reducibility of the proposed $\mathrm{MDS}$ matrices; this property may be used by an adversary to exploit the nontrivial invariant subspaces associated to corresponding mappings. We propose some methods for constructing $\mathrm{MDS}$ matrices with primitive characteristic polynomial that provide better resistance against the so-called invariant subspaces attacks. 
@article{MVK_2021_12_a8,
     author = {O. C. Puente and R. A. de la Cruz Jim\'enez},
     title = {Construction of orthomorphic $\mathrm{MDS}$ matrices with primitive characteristic polynomial},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {125--143},
     publisher = {mathdoc},
     volume = {12},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MVK_2021_12_a8/}
}
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O. C. Puente; R. A. de la Cruz Jiménez. Construction of orthomorphic $\mathrm{MDS}$ matrices with primitive characteristic polynomial. Matematičeskie voprosy kriptografii, Tome 12 (2021), pp. 125-143. http://geodesic.mathdoc.fr/item/MVK_2021_12_a8/