On the maximal component algebraic immunity of vectorial Boolean functions
Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 2, pp. 88-99.

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The component algebraic immunity of vectorial Boolean functions is studied. We prove a theorem on the correspondence between the maximum component algebraic immunity of a function and its balancedness. Some relationship between the maximal component algebraic immunity and matrices of a special form is obtained. We construct several functions with maximal component algebraic immunity in case of few variables. Tab. 1, bibliogr. 8.
Keywords: component algebraic immunity, vectorial Boolean function, balancedness.
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D. P. Pokrasenko. On the maximal component algebraic immunity of vectorial Boolean functions. Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 2, pp. 88-99. http://geodesic.mathdoc.fr/item/DA_2016_23_2_a4/

[1] Armknecht F., Krause M., “Constructing single- and multi-output Boolean functions with maximal algebraic immunity”, Automata, Languages and Programming, Proc. 33rd Int. Colloq. ALP (Venice, Italy, July 10–14, 2006), Pt. II, Lect. Notes Comput. Sci., 4052, Springer-Verl., Berlin–Heidelberg, 2006, 180–191 | DOI | MR | Zbl

[2] Ars G., Faugère J.-C., “Algebraic immunities of functions over finite fields”, Boolean Functions: Cryptography and Applications, Proc. 1st Workshop BFCA (Mont-Saint-Aignan, France, March 7–8, 2005), Publ. Univ. Rouen Havre, Mont-Saint-Aignan, 2005, 21–38

[3] Carlet C., “On the algebraic immunities and higher order nonlinearities of vectorial Boolean functions”, Enhancing cryptographic primitives with techniques from error correcting codes, Proc. NATO Adv. Res. Workshop ACPTECC (Veliko Tarnovo, Bulgaria, Oct. 6–9, 2008), IOS Press, Amsterdam, 2009, 104–116 | MR

[4] Courtois N. T., Meier W., “Algebraic attacks on stream ciphers with linear feedback”, Advances in Cryptology – EUROCRYPT 2003, Proc. Int. Conf. Theory Appl. Cryptogr. Tech. (Warsaw, Poland, May 4–8, 2003), Lect. Notes Comput. Sci., 2656, Springer-Verl, Heidelberg, 2003, 345–359 | DOI | MR | Zbl

[5] Dalai D. K., Gupta K. C., Maitra S., “Results on algebraic immunity for cryptographically significant Boolean functions”, Progress in Cryptology – INDOCRYPT 2004, Proc. 5th Int. Conf. Cryptol. India (Chennai, India, Dec. 20–22, 2004), Lect. Notes Comput. Sci., 3348, Springer-Verl., Heidelberg, 2005, 92–106 | DOI | MR

[6] Feng K., Liao Q., Yang J., “Maximal values of generalized algebraic immunity”, Des. Codes Cryptogr., 50:2 (2009), 243–252 | DOI | MR

[7] Lidl R., Niederreiter H., Finite fields, Addison-Wesley, Reading, MA, 1983, 755 pp. | MR | Zbl

[8] Meier W., Pasalic E., Carlet C., “Algebraic attacks and decomposition of Boolean functions”, Advances in Cryptology – EUROCRYPT 2004, Proc. Int. Conf. Theory Appl. Cryptogr. Tech. (Interlaken, Switzerland, May 2–6, 2004), Lect. Notes Comput. Sci., 3027, Springer-Verl., Berlin, 2005, 474–491 | DOI | MR