Geodesic
On a new classification of Boolean functions
Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 2, pp. 159-168 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss a recent approach to the study of Boolean functions. The approach is based on a notion of $\Delta$-equivalence class, which is a set of Boolean functions having the same autocorrelation function. Such a classification has an apparently useful property: a substantial number of cryptographic characteristics of Boolean functions are the same within any $\Delta$-equivalence class. 
@article{MVK_2019_10_2_a13,
     author = {S. N. Fedorov},
     title = {On a new classification of {Boolean} functions},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {159--168},
     year = {2019},
     volume = {10},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a13/}
}
TY  - JOUR
AU  - S. N. Fedorov
TI  - On a new classification of Boolean functions
JO  - Matematičeskie voprosy kriptografii
PY  - 2019
SP  - 159
EP  - 168
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a13/
LA  - en
ID  - MVK_2019_10_2_a13
ER  - 
%0 Journal Article
%A S. N. Fedorov
%T On a new classification of Boolean functions
%J Matematičeskie voprosy kriptografii
%D 2019
%P 159-168
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a13/
%G en
%F MVK_2019_10_2_a13
S. N. Fedorov. On a new classification of Boolean functions. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 2, pp. 159-168. http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a13/

[1] E. K. Alekseev, “On some nonlinearity measures of Boolean functions”, Prikladnaya diskretnaya matematika, 2011, no. 2 (12), 5–16 (in Russian)

[2] Р”Рμ Ла РљСЂСѓСЃ РҐРёРјРμРЅРμСЃ Р . Рђ., КамловскиРNo Рћ. Р’., “РЎСѓРјРјС‹ РјРѕРґСѓР»РμРNo коэффициРμнтов Уолша-Адамара Р±СѓР»РμРІС‹С... функциРNo”, ДискрРμтная матРμматика, 27:4 (2015), 49–66 | DOI | MR | Zbl

[3] O. A. Logachev, A. A. Salnikov, S. V. Smyshlyaev, V. V. Yashchenko, Boolean functions in coding theory and cryptology, URSS, M., 2015, 576 pp. (in Russian) | MR

[4] Diskretnaya Matematika, 30:1 (2018), 39–55 (in Russian) | DOI | DOI | MR

[5] O. A. Logachev, S. N. Fedorov, V. V. Yashchenko, “On $\Delta$-equivalence of Boolean functions”, Discretnaya Matematika, 2018, no. 4, 29–40 (in Russian) | DOI | MR

[6] B. Chor, O. Goldreich, J. Håstad, J. Friedman, S. Rudich, R. Smolensky, “The bit extraction problem of t-resilient functions (Preliminary version)”, 26th Annu. Symp. Found. Comput. Sci., FOCS '85, IEEE Computer Soc., 1985, 396–407

[7] W. Meier, O. Staffelbach, “Nonlinearity criteria for cryptographic functions”, EUROCRYPT'89, Lect. Notes Comput. Sci., 434, 1990, 549–562 | DOI | MR | Zbl

[8] B. Preneel, W. V. Van Leekwijck, L. V. Van Linden, R. Govaerts, J. Vandewalle, “Propagation characteristics of Boolean functions”, EUROCRYPT'90, Lect. Notes Comput. Sci., 473, 1991, 161–173 | DOI | MR | Zbl

[9] T. Siegenthaler, “Correlation-immunity of nonlinear combining functions for cryptographic applications”, IEEE Trans. Inf. Theory, 30:5 (1984), 776–780 | DOI | MR | Zbl

[10] A. F. Webster, S. E. Tavares, “On the design of S-boxes”, CRYPTO '85, Lect. Notes Comput. Sci., 219, 1986, 523–534 | DOI

[11] X. M. Zhang, Y. Zheng, “GAC — the criterion for global avalanche characteristics of cryptographic functions”, J. Univ. Comput. Sci., 1:5 (1995), 316–333 | MR