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English version: Journal of Applied and Industrial Mathematics, 2016, 10:2, 257263 

Volume 23, No 2, 2016, P. 8899 UDC 519.7
Keywords: component algebraic immunity, vectorial Boolean function, balancedness. DOI: 10.17377/daio.2016.23.495 Denis P. Pokrasenko ^{1} Received 29 May 2015 References[1] F. Armknecht and M. Krause, Constructing single and multioutput Boolean functions with maximal algebraic immunity, in Automata, Languages and Programming (Proc. 33rd Int. Colloq. ALP, Venice, Italy, July 10–14, 2006), Pt. II, pp. 180–191, Springer, Heidelberg, 2006 (Lect. Notes Comput. Sci., Vol. 4052).[2] G. Ars and J.C. Faugère, Algebraic immunities of functions over finite fields, in Boolean Functions: Cryptography and Applications (Proc. 1st Workshop BFCA, Mont SaintAignan, France, Mar. 7–8, 2005), pp. 21–38, Publ. Univ. Rouen Havre, Mont SaintAignan, 2005. [3] C. Carlet, On the algebraic immunities and higher order nonlinearities of vectorial Boolean functions, in Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes (Proc. NATO Adv. Res. Workshop ACPTECC, Veliko Tarnovo, Bulgaria, Oct. 6–9, 2008), pp. 104–116, IOS Press, Amsterdam, 2009. [4] N. T. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in E. Biham, ed., Advances in Cryptology — EUROCRYPT 2003 (Proc. Int. Conf. Theory Appl. Cryptogr. Tech., Warsaw, Poland, May 4–8, 2003), pp. 345–359, Springer, Heidelberg, 2003 (Lect. Notes Comput. Sci., Vol. 2656). [5] D. K. Dalai, K. C. Gupta, and S. Maitra, Results on algebraic immunity for cryptographically significant Boolean functions, in A. Canteaut and K. Viswanathan, eds., Progress in Cryptology — INDOCRYPT 2004 (Proc. 5th Int. Conf. Cryptol. India, Chennai, India, Dec. 20–22, 2004), pp. 92–106, Springer, Heidelberg, 2005 (Lect. Notes Comput. Sci., Vol. 3348). [6] K. Feng, Q. Liao and J. Yang, Maximal values of generalized algebraic immunity, Des. Codes Cryptogr., 50, No. 2, 243–252, 2009. [7] R. Lidl and H. Niederreiter, Finite Fields, AddisonWesley, Reading, MA, USA, 1983. [8] W.Meier, E. Pasalic, and C. Carlet, Algebraic attacks and decomposition of Boolean functions, in C. Cachin and J. L. Camenisch, eds., Advances in Cryptology — EUROCRYPT 2004 (Proc. Int. Conf. Theory Appl. Cryptogr. Tech., Interlaken, Switzerland, May 2–6, 2004), pp. 474–491, Springer, Berlin, 2005 (Lect. Notes Comput. Sci., Vol. 3027). 

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