Geodesic
On values of affinity level for almost all Boolean functions
Prikladnaâ diskretnaâ matematika, no. 3 (2010), pp. 17-21.

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In the current paper, we consider asymptotic form of values of one parameter of Boolean functions, namely affinity level (generalized affinity level). We prove that asymptotically (with $n\to\infty$) values of affinity level (generalized affinity level) for almost all Boolean functions are all in the segment $[n-\log_2n,n-\log_2n+1]$.
Keywords: affinity level, generalized affinity level, Boolean equations, cryptography. 
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     author = {O. A. Logachev},
     title = {On values of affinity level for almost all {Boolean} functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {17--21},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_3_a1/}
}
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O. A. Logachev. On values of affinity level for almost all Boolean functions. Prikladnaâ diskretnaâ matematika, no. 3 (2010), pp. 17-21. http://geodesic.mathdoc.fr/item/PDM_2010_3_a1/

[1] Logachev O. A., Salnikov A. A., Yaschenko V. V., “Korrelyatsionnaya immunnost i realnaya sekretnost”, Matematika i bezopasnost informatsionnykh tekhnologii, MTsNMO, M., 2004, 165–170

[2] Logachev O. A., Salnikov A. A., Yaschenko V. V., “Kombiniruyuschie $k$-affinnye funktsii”, Matematika i bezopasnost informatsionnykh tekhnologii, MTsNMO, M., 2004, 176–178

[3] Buryakov M. L., Logachev O. A., “O raspredelenii urovnya affinnosti na mnozhestve bulevykh funktsii”, Matematika i bezopasnost informatsionnykh tekhnologii, MTsNMO, M., 2005, 141–146

[4] Buryakov M. L., Logachev O. A., “Ob urovne affinnosti bulevykh funktsii”, Diskretnaya matematika, 17:4 (2005), 98–107 | MR | Zbl

[5] Logachev O. A., “Nizhnyaya otsenka urovnya affinnosti dlya pochti vsekh bulevykh funktsii”, Diskretnaya matematika, 20:4 (2008), 85–88 | MR | Zbl

[6] Buryakov M. L., “Asimptoticheskie otsenki urovnya affinnosti dlya pochti vsekh bulevykh funktsii”, Diskretnaya matematika, 20:3 (2008), 73–79 | MR | Zbl

[7] Buryakov M. L., Algebraicheskie, kombinatornye i kriptograficheskie svoistva parametrov affinnykh ogranichenii bulevykh funktsii, Dis. $\dots$ kand. fiz.-mat. nauk, M., 2007

[8] Logachev O. A., Salnikov A. A., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2004