Latin squares and their applications in cryptography
Prikladnaâ diskretnaâ matematika, no. 3 (2012), pp. 47-52.

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This survey contains examples of Latin squares applications in cryptography.
Keywords: Latin square, quasigroups, cryptography.
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M. E. Tuzhilin. Latin squares and their applications in cryptography. Prikladnaâ diskretnaâ matematika, no. 3 (2012), pp. 47-52. http://geodesic.mathdoc.fr/item/PDM_2012_3_a5/

[1] Euler L., Recherches sur une nouvelle espèce de quarrés magiques, Middelburg, 1782

[2] Cayley A., “On Latin Squares”, Messenger of mathematics, 19 (1890), 135–137

[3] Touchard J., “Permutations, discordant with two given permutations”, Scripta Math., 19 (1953), 109–119 | MR

[4] Suschkewitsch A. K., “On the number of Latin Squares”, Trans. Amer. Math. Soc., 31 (1929), 204–214 | DOI | MR | Zbl

[5] Moufang R., “Zur Struktur von Alternativkoerpern”, Math. Ann., 110:1 (1935), 416–430 | DOI | MR

[6] McKay B. D., Wanless I. M., “On the number of Latin Squares”, Ann. Combin., 9:3 (2005), 335–344 | DOI | MR | Zbl

[7] Van Lint J. H., Wilson R. M., A Course in Combinatorics, Cambridge University Press, 1992 | MR

[8] Cheremushkin A. V., “Pochti vse latinskie kvadraty imeyut trivialnuyu gruppu avtostrofii”, Prikladnaya diskretnaya matematika, 2009, no. 3(5), 29–32

[9] Ozanam J., Récréations mathématiques et physiques, Paris, 1725

[10] Bose R. S., “On the applications of the properties of Galois fields to the problems of construction of Hyper-Graeco-Latin squares”, Indian J. Stat., 3:4 (1938), 323–338

[11] Nelder J., “Critical sets in latin squares”, CSIRO Division Math. Stats, Newsletter, 38 (1977), 4

[12] Laywine C. F., Mullen G. L., Discrete mathematics using Latin squares, Wiley, New York, 1998 | MR | Zbl

[13] Trithemius J., Polygraphiae, Trittelheim, 1518

[14] Bellaso G. B., Il vero modo di scrivere in cifra con facilità, prestezza, et securezza di Misser Giovan Battista Bellaso, gentil'huomo bresciano, Iacobo Britannico, Bressa, 1564

[15] Shannon C., “Communication Theory of Secrecy Systems”, Bell System Technical J., 28 (1949), 656–715 | MR | Zbl

[16] Massey J. L., Maurer U., Wang M., “Non-Expanding, Key-Minimal, Robustly-Perfect, Linear and Bilinear Ciphers”, Adv. Cryptology – EUROCRYPT' 87, Springer Verlag, Berlin–Heidelberg, 1988, 237–247

[17] Gligoroski D., Markovski S., Kocarev L., Gusev M., Edon80, http://www.ecrypt.eu.org/stream/edon80p3.html

[18] Lai X., Massey J., “A Proposal for a New Block Encryption Standard”, Adv. Cryptology – EUROCRYPT' 90, Springer Verlag, New York, 1991, 55–70 | MR

[19] Gligoroski D., Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations, http://eprint.iacr.org/2005/352.pdf

[20] Dènes J., Keedwell A. D., “A new Authentication Scheme based in Latin Squares”, Discrete Math., 106/107 (1992), 157–162 | DOI | MR

[21] Cooper J., Donovan D., Seberry J., “Secret Sharing Schemes Arising From Latin Squares”, Bulletin of the ICA, 12 (1994), 33–43 | MR | Zbl

[22] Chum C. S., Zhang X., “The Latin squares and the secret sharing schemes”, Groups Complex. Cryptol, 2 (2010), 175–202 | MR | Zbl

[23] Chum C. S., Hash functions, Latin squares and secret sharing schemes, ProQuest, New York, 2010

[24] Pal S. K., Bhardwaj D., Kumar R., Bhatia V., “A New Cryptographic Hash Function based on Latin Squares and Non-linear Transformations”, Adv. Comput. Conf. IACC, Patiala, 2009, 862–867

[25] Gligoroski D., Ødegård R.S., Mihova M., et al., “Cryptographic Hash Function Edon-R”, Proc. IWSCN, Trondheim, 2009, 1–9

[26] Dènes J., Dènes T., “Non-associative algebraic system in cryptology. Protection against “meet in the middle” attack”, Quasigroups and Related Systems, 8 (2001), 7–14 | MR | Zbl

[27] Glukhov M. M., “O primeneniyakh kvazigrupp v kriptografii”, Prikladnaya diskretnaya matematika, 2008, no. 2(2), 28–32

[28] Shcherbacov V. A., “Quasigroups in cryptology”, Comput. Sci. J. Moldova, 17:2(50) (2009), 193–228 | MR | Zbl

[29] Malykh A. E., Danilova V. I., “Ob istoricheskom protsesse razvitiya teorii latinskikh kvadratov i nekotorykh ikh prilozheniyakh”, Vestnik Permskogo universiteta, 2010, no. 4(4), 95–104