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Experimental Methods for Constructing MDS Matrices of a Special Form

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Abstract

MDS matrices are widely used as a diffusion primitive in the construction of block type encryption algorithms and hash functions (such as AES and GOST 34.12-2015). The matrices with the maximum number of 1s and minimum number of different elements are important for more efficient realizations of the matrix-vector multiplication. The article presents a new method for the MDS testing of matrices over finite fields and shows its application to the (8 × 8)-matrices of a special form with many 1s and few different elements; these matrices were introduced by Junod and Vaudenay. For the proposed method we obtain some theoretical and experimental estimates of effectiveness. Moreover, the article comprises a list of some MDS matrices of the above-indicated type.

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Authors and Affiliations

  1. National Research University Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000, Russia

    M. I. Rozhkov & S. S. Malakhov

Authors
  1. M. I. Rozhkov
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  2. S. S. Malakhov
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Correspondence to M. I. Rozhkov or S. S. Malakhov.

Additional information

Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 2, pp. 115–128.

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Rozhkov, M.I., Malakhov, S.S. Experimental Methods for Constructing MDS Matrices of a Special Form. J. Appl. Ind. Math. 13, 302–309 (2019). https://doi.org/10.1134/S199047891902011X

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  • DOI: https://doi.org/10.1134/S199047891902011X

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