Geodesic
Noncloseness of hyper-bent-function class under the general linear group action
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 2, pp. 5-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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Representations of Boolean functions by mappings of finite field extension to its simple subfield are considered. The effect of transforming the argument of hyper-bent-function by general linear group on properties of this function is studied. It is shown that the class of hyper-bent-functions is not closed under such transforms. 
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A. V. Ivanov. Noncloseness of hyper-bent-function class under the general linear group action. Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 2, pp. 5-26. http://geodesic.mathdoc.fr/item/MVK_2012_3_2_a0/

[1] Kuzmin A. S., Markov V. T., Nechaev A. A., Shishkov A. B., “Priblizhenie bulevykh funktsii monomialnymi”, Diskretnaya matematika, 18:1 (2006), 9–29 | MR | Zbl

[2] Kuzmin A. S., Nechaev A. A., Shishkin V. A., “Bent- i giper-bent-funktsii nad polem iz $2^l$ elementov”, Trudy po diskretnoi matematike, 9, FIZMATLIT, M., 2006, 86–111

[3] Logachev O. A., Salnikov A. A., Yaschenko V. V., “O svoistvakh summ Veilya na konechnykh polyakh i konechnykh abelevykh gruppakh”, Diskretnaya matematika, 11:2 (1999), 66–85 | MR | Zbl

[4] Logachev O. A., Salnikov A. A., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MNTsMO, M., 2004, 469 pp.

[5] Mak-Vilyams F. Dzh., Sloen N. Dzh., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979, 744 pp.

[6] Pogorelov B. A., “O maksimalnykh podgruppakh simmetricheskikh grupp, zadannykh na proektivnykh prostranstvakh nad konechnym polem”, Matematicheskie zametki, 26:1 (1974), 91–100 | MR | Zbl

[7] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, M., 2004, 424 pp.

[8] Tokareva N. N., Nelineinye bulevy funktsii: bent-funktsii i ikh obobscheniya, LAP LAMBERT Acad. Publ., Saarbrucken, Germany, 2011, 170 pp.

[9] Carlet C., Gaborit P., “Hyper-bent-functions and cyclic codes”, J. Comb. Theory. Ser. A, 113 (2006), 466–482 | DOI | MR | Zbl

[10] Carlitz L., Uchiyama S., “Bounds for exponential sums”, Duke Math. J., 24 (1957), 37–41 | DOI | MR | Zbl

[11] Dillon J. F., “A survey of bent functions”, The NSA Technical Journal, 1972, Special Issue, 191–215

[12] Dillon J. F., Elementary Hadamard difference sets, Ph. D. Thesis, Univ. of Maryland, 1974 | MR

[13] Gong G., Golomb S. W., “Transform domain analysis of DES”, IEEE Trans. Inf. Theory, 45:6 (1999), 2065–2073 | DOI | MR | Zbl

[14] Hou X.-D., “Cubic bent functions”, Discrete Mathematics, 189 (1998), 149–161 | DOI | MR | Zbl

[15] Langevin P., Leander G., “Classification of Boolean quartics forms in eight variables”, Boolean Functions in Cryptology and Information Security, 18 (2008), 139–147 | MR | Zbl

[16] Nyberg K., “Differentially uniform mappings for cryptography”, EUROCRYPT' 93, Lect. Notes Comput. Sci., 765, 1994, 55–64 | DOI | MR | Zbl

[17] Rothaus O. S., “On “bent” functions”, J. Comb. Theory. Ser. A, 20 (1976), 300–305 | DOI | MR | Zbl

[18] Youssef A., Gong G., “Hyper-bent functions”, EUROCRYPT' 2001, Lect. Notes Comput. Sci., 2045, 2001, 406–419 | DOI | MR | Zbl