Lobachevskii Journal of Mathematics

, Volume 38, Issue 5, pp 880–883 | Cite as

Some classes of the MDS matrices over a finite field

  • A. V. BelovEmail author
  • A. B. Los
  • M. I. Rozhkov


The paper is presented some classes of MDS matrices of size 4 × 4 with the maximum number of units and minimal number of non unit elements. This class of matrices is widely used as diffuse maps when building block type algorithms and hash functions that provide protection against certain methods of analysis.

Keywords and phrases

MDS matrix MDS code 


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  1. 1.
    P. Junod and S. Vaudenay, “Perfect diffusion primitives for block ciphers building efficient MDS matrices,” Lect. Notes Comput. Sci. 3357, 84–99 (2004).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    D. Augot and M. Finiasz, “Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash functions,” in Proceedings of the IEEE International Symposiumon Information Theory, 2013, pp. 1551–1555.Google Scholar
  3. 3.
    K. C. Gupta and I. G. Ray, “On constructions of MDS matrices from companion matrices for lightweight cryptography,” Lect. Notes Comput. Sci. 8128, 29–43 (2013).CrossRefGoogle Scholar
  4. 4.
    G. Murtaza and N. Ikram, “New methods of generating MDS matrices,” in Proceedings of International Cryptology Workshop and Conference, 2008.Google Scholar
  5. 5.
    V. Markov and A. Nechaev, “Generalized BCH-theorem and linear recursive MDS-codes,” in Proceedings of 12th International Workshop on Algebraic and Combinatorial Coding Theory, 2010.Google Scholar
  6. 6.
    E. Couselo and S. Gonsales, V. Markov, and A. Nechaev, “Recursive MDS-codes and recursively differentiable quasigroup,” Discret.Mat. 10 (2), 3–29 (1988).Google Scholar
  7. 7.
    E. Couselo, S. Gonsales, V. Markov, and A. Nechaev, “The parameters of recursive MDS-codes,” Discret. Mat. 12 (4), 3–24 (2000).MathSciNetzbMATHGoogle Scholar
  8. 8.
    R. Lidl and H. Niederreiter, Introduction to Finite Fields ant their Applications (Cambridge Univ. Press, Cambridge, 1994).CrossRefzbMATHGoogle Scholar
  9. 9.
    E. Berlekamp, Algebraic Coding Theory (McGraw-Hill, New York, 1968).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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