Construction of MDS matrices combining the Feistel, Misty and Lai-Massey schemes
Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 2, pp. 57-74 Cet article a éte moissonné depuis la source Math-Net.Ru

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In cryptography maximum distance separable (MDS) matrices are an important structural element to provide the diffusion property in the block ciphers, stream ciphers and hash functions. To discover new kind of transformations that may generate a series of new MDS matrices which could be used in practice is not a trivial task. In this paper we propose new methods for constructing MDS matrices of size $4\times 4$ combining the well-known Feistel, Misty and Lai-Massey structures which are very attractive for the so-called lightweight schemes.
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R. R. Aulet; R. A. de la Cruz Jiménes. Construction of MDS matrices combining the Feistel, Misty and Lai-Massey schemes. Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 2, pp. 57-74. http://geodesic.mathdoc.fr/item/MVK_2021_12_2_a4/

[1] Anashkin A.V., “Complete description of a class of MDS-matrices over finite field of characteristic2”, Matematicheskie Voprosy Kriptografii, 8:4 (2017), 5–28 (in Russian)

[2] Adnan B., Mustafa C., Mehmet O., Feistel like construction of involutory binary matrices with high branch number, Cryptology ePrint Archive, Report 2016/751, https://eprint.iacr.org/2016/751

[3] Barreto P., Rijmen V., “The Khazad legacy-level block cipher”, First Open NESSIE Workshop Project, KU-Leuven, 2000

[4] Barreto P., Rijmen V., The WHIRLPOOL Hashing Function, Submission to the NESSIE Project, 2003 (May 2003)

[5] Borghoff J. et al., “PRINCE — A low-latency block cipher for pervasive computing applications”, ASIACRYPT 2012, Lect. Notes Comput. Sci., 7658, 2012, 208–225

[6] Boyar J., Matthews P., Peralta R., “Logic minimization techniques with applications to cryptology”, J. Cryptology, 26:2 (2013), 280-312

[7] Shannon C., “Communication theory of secrecy systems”, Bell Syst. Tech. J., 28:4 (1949), 656–715

[8] Burov D.A., Pogorelov B.A., “The influence of linear mapping reducibility on the choice of round constants”, Matematicheskie Voprosy Kriptografii, 8:2 (2017), 51–64

[9] Duval S., Leurent G., “MDS matrices with lightweight circuits”, IACR Trans. Symm. Cryptology, 2018, no. 2, 48-78

[10] Dygin D.M., Lavrikov I.V., Marshalko G.B., Rudskoy V.I., Trifonov D.I., Shishkin V.A., “On a new Russian encryption standard”, Matematicheskie Voprosy Kriptografii, 6:2 (2015), 29–34

[11] Glukhov M.M., Elizarov V.P., Nechaev A.A., Algebra, Textbook, 2nd, Lan, Sankt-Peterburg–M.–Krasnodar, 2015 (in Russian)

[12] Hong X., Lin T. Xuejia L., “On the recursive construction of MDS matrices for ligtweight Cryptography”, ISPEC 2014, Lect. Notes Comput. Sci., 8434, 2014, 552–563

[13] Heys H.M., Tavares S.E., “Avalanche characteristics of substitution-permutation encryption networks”, IEEE Trans. Computers, 44:9 (1995), 1131–1139

[14] Heys H.M., Tavares S.E., “Substitution-permutation networks resistant to differential and linear cryptanalysis”, J. Cryptology, 9 (1996), 1–19

[15] Gupta K.C., Ray I.G., “On constructions of MDS matrices from companion matrices for lightweight cryptography”, CD-ARES Workshops 2013, Lect. Notes Comput. Sci., 8128, 2013, 29-43

[16] Junod P., Vaudenay S., “Perfect diffusion primitives for block ciphers building efficient MDS matrices”, SAC 2004, Lect. Notes Comput. Sci., 3357, 2004, 84–99

[17] Guo J., Peyrin T., Poschmann A., “The PHOTON family of lightweight hash functions”, CRYPTO 2011, Lect. Notes Comput. Sci., 6841, 2011, 222–239

[18] Kranz T., Leander G., Stoffelen K., Wiemer F., “Shorter linear straight-line programs for MDS matrices”, IACR Trans. Symm. Cryptology, 2017, no. 4, 188–211

[19] Mahdi S., Mohsen M., Construction of lightweight MDS matrices from generalized Feistel structures, Cryptology ePrint Archive, Report 2018/1072, https://eprint.iacr.org/2018/1072

[20] Mahdi S., Mohammad D., Hamid M., Behnaz O., “On construction of involutory MDS matrices from Vandermonde matrices in $GF(2^q)$”, Designs, Codes and Cryptogr., 64 (2012), 287-308

[21] Piret G., Roche T., Carlet C., “PICARO — A block cipher allowing efficient higher-order side-channel resistance”, ACNS 2012, Lect. Notes Comput. Sci., 7341, 2012, 311–328

[22] Advanced Encryption Standard, Federal Information Processing Standard (FIPS) 197, NIST, November 2001

[23] Standaert F.-X., Piret G., Rouvroy G., Quisquater J.J., Legat J.-D., “An involutional cipher efficient for block encryption in reconfigurable hardware”, FSE 2004, Lect. Notes Comput. Sci., 3017, 2004, 279–298

[24] Shun Li, Siwei Sun, Chaoyun Li, Zihao Wei, Lei Hu, “Constructing low-latency involutory MDS matrices with lightweight circuits”, IACR Trans. Symm. Cryptology, 2019, no. 1, 84–117

[25] Watanabe D., Furuya S., Yoshida H., Takaragi K., Preneel B., “A new keystream generator MUGI”, FSE 2002, Lect. Notes Comput. Sci., 2365, 2002, 179–194