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English version: Journal of Applied and Industrial Mathematics, 2019, 13:2, 302-309 |
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Volume 26, No 2, 2019, P. 115-128 UDC 519.688
Keywords: MDS matrix, MDS code. DOI: 10.33048/daio.2019.26.621 Mikhail I. Rozhkov 1 Received May 22, 2018 References[1] A. V. Anashkin, Complete description of a class of MDS-matrices over finite field of characteristic 2, Mat. Vopr. Kriptogr., 8, No. 4, 5–28, 2017 [Russian].[2] R. Lidl and H. Niederreiter, Finite Fields, Camb. Univ. Press, Cambridge, 1985. Translated under the title Konechnye polya, Mir, Moscow, 1988 [Russian]. [3] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977 (North-Holland Math. Libr., Vol. 16). Translated under the title Teoriya kodov, ispravlyayushchikh oshibki, Svyaz’, Moscow, 1979 [Russian]. [4] F. M. Malyshev, The duality of differential and linear methods in cryptography, Mat. Vopr. Kriptogr., 5, No. 3, 35–47, 2014 [Russian]. [5] F. M. Malyshev and D. I. Trifonov, Diffusion properties of XSLP-ciphers, Mat. Vopr. Kriptogr., 7, No. 3, 47–60, 2016 [Russian]. [6] M. Hall, Jr., Combinatorial Theory, Blaisdell, Waltham, MA, 1967. Translated under the title Kombinatorika, Mir, Moscow, 1970 [Russian]. [7] D. Augot and M. Finiasz, Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash functions, Proc. 2013 IEEE Int. Symp. Inf. Theory, Istanbul, Turkey, July 7–12, 2013, [8] A. V. Belov, A. B. Los, and M. I. Rozhkov, Some approaches to construct MDS matrices over a finite field, Commun. Appl. Math. Comp., 31, No. 2, 143–152, 2017. [9] A. V. Belov, A. B. Los, and M. I. Rozhkov, Some classes of the MDS matrices over a finite field, Lobachevskii J. Math., 38, No. 5, 880–883, 2017. [10] E. Couselo, S. González, V. Markov, and A. Nechaev, Recursive MDS-codes and recursive differentiable quasigroups, Discrete Math. Appl., 8, No. 3, 217–245, 1998. [11] E. Couselo, S. González, V. Markov, and A. Nechaev, Parameters of recursive MDS-codes, Discrete Math. Appl., 10, No. 5, 433–453, 2000. [12] K. C. Gupta and I. G. Ray, On constructions of MDS matrices from companion matrices for lightweight cryptography, in Security Engineering and Intelligence Informatics (Proc. CD-ARES 2013 Workshops: MoCrySEn SeCIHD, Regensburg, Germany, Sept. 2–6, 2013), pp. 29–43, Springer, Heidelberg, 2013 (Lect. Notes Comput. Sci., Vol. 8128). [13] K. C. Gupta and I. G. Ray, On constructions of circulant MDS matrices for lightweight cryptography, in Information Security Practice and Experience, (Proc. 10th Int. Conf., Fuzhou, China, May 5–8, 2014), [14] P. Junod and S. Vaudenay, Perfect diffusion primitives for block ciphers: Building efficient MDS matrices, Selected Areas in Cryptography (Rev. Sel. Pap. 11th Int. Conf., Waterloo, Canada, Aug. 9–10, 2004), [15] M. Matsui, On correlation between the order of S-boxes and the strength of DES, Advances in Cryptology – EUROCRYPT’94 (Proc. Workshop Theory Appl. Cryptogr. Tech., Perugia, Italy, May 9–12, 1994), pp. 366–375, Springer, Heidelberg, 1995 (Lect. Notes Comput. Sci., Vol. 950). |
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