Subgroups of direct products of groups invariant under the action of permutations on factors

References

[1] Gorchinskiy Yu.N., “On homomorphisms of multibase universal algebras in connection with cryptographic applications”, Trudy Diskr. Mat., 1 (1997), 67–84 (in Russian).Suche in Google Scholar

[2] Lidl R., Niederreiter H., Finite Fields, Addison-Wesley Publ. Inc., 1983, 755 pp.10.1017/CBO9780511525926Suche in Google Scholar

[3] Pogorelov B. A., Pudovkina M. A., “On the distance from permutations to imprimitive groups for a fixed system of imprimitivity”, Discrete Math. Appl., 24:2 (2014), 95–108.10.1515/dma-2014-0010Suche in Google Scholar

[4] GOST R 34.12-2015 Information technology. Cryptographic data security. Block ciphers, Standartinform, Moscow, 2015 (in Russian)Suche in Google Scholar

[5] Hall M., The Theory of Groups, The Macmillan Company, New Yourk, 1959, 434 pp.Suche in Google Scholar

[6] Aoki, K., Kanda, T., Matsui, M., Moriai, S., Nakajima, J., Tokita, T., “Camellia: a 128-bit block cipher suitable for multiple platforms — design and analysis”, SAC’OO, Lect. Notes Comput. Sci., 2012 (2013), 39–56.10.1007/3-540-44983-3_4Suche in Google Scholar

[7] Barreto P., Rijmen V., “The Khazad legacy-level block cipher”, First Open NESSIE Workshop, Submission to NESSIE, 2000.Suche in Google Scholar

[8] Biham, E., Shamir, A., “Differential cryptanalysis of DES-like cryptosystems”, J. Cryptology, 4 (1991), 3–72.10.1007/3-540-38424-3_1Suche in Google Scholar

[9] Burov D.A., Pogorelov B.A., “An attack on 6 rounds of Khazad”, Matematicheskie Voprosy Kriptografii, 7:2 (2016), 35–46.10.4213/mvk181Suche in Google Scholar

[10] 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 (in Russian).10.4213/mvk223Suche in Google Scholar

[11] Daemen J., Rijmen V., The Rijndael block cipher, AES Proposal, 1999, 45 pp.10.1007/10721064_26Suche in Google Scholar

[12] Lai X., Massey J.L., Murphy S., “Markov ciphers and differential cryptanalysis”, EUROCRYPT’91, Lect. Notes Comput. Sci., 547 (1991), 17–38.10.1007/3-540-46416-6_2Suche in Google Scholar

[13] Leander G., Abdelraheem M., Alkhzaimi H., Zenner E., “A cryptanalysis of PRINT cipher: The invariant subspace attack”, CRYPTO’11, Lect. Notes Comput. Sci., 6841 (2011), 206–221.10.1007/978-3-642-22792-9_12Suche in Google Scholar

[14] Matsui M., “Linear cryptanalysis method for DES cipher”, EUROCRYPT’93, Lect. Notes Comput. Sci., 765 (1994), 386–397.10.1007/3-540-48285-7_33Suche in Google Scholar

[15] Courtois N., “The inverse S-box, non-linear polynomial relations and cryptanalysis of block ciphers”, AES’2004, Lect. Notes Comput. Sci., 3373 (2004), 170–188.10.1007/11506447_15Suche in Google Scholar

[16] Dixon J., Mortimer B, Permutation Groups, Springer, New York, 1996, 346 pp.10.1007/978-1-4612-0731-3Suche in Google Scholar

[17] Kwon D., Kim J., Park S., Sung S., “New block cipher: ARIA”, ICISC’03, Lect. Notes Comput. Sci., 2971 (2004), 432–445.10.1007/978-3-540-24691-6_32Suche in Google Scholar

[18] Mattarei S., “Inverse-closed additive subgroups of fields”, Isr. J. Math., 2007, №1, 343–347.10.1007/s11856-007-0050-6Suche in Google Scholar

[19] Nyberg K., “Differentially uniform mappings for cryptography”, EUROCRYPT’93, Lect. Notes Comput. Sci., 765 (1993), 55–64.10.1007/3-540-48285-7_6Suche in Google Scholar

[20] Remak R., “Uber die darstellung der endlichen gruppen als Untergruppen direkter produkte”, J. Reine Angew. Math., 1 (1930), 1–44.10.1515/crll.1930.163.1Suche in Google Scholar