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An upper bound for the nonlinearity of some Boolean functions with maximal possible algebraic immunity. (Russian. English summary) Zbl 1468.94969

Summary: An estimation for the nonlinearity of Dalai’s Boolean functions with the maximal algebraic immunity in even number of variables is given. It is proved that the estimation is achieved.

MSC:

94D10 Boolean functions
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)

Citations:

Zbl 1202.94179
Full Text: MNR

References:

[1] Courtois N. and Meier W., “Algebraic attacks on stream ciphers with liner feedback”, LNCS, 2656, 2003, 345-359 · Zbl 1038.94525
[2] Meier W., Pasalic E., and Carlet C., “Algebraic attacks and decomposition of Boolean functions”, LNCS, 3027, 2004, 474-491 · Zbl 1122.94041
[3] Dalai D.K., Maitra S., and Sarkar S., “Basic theory in construction of Boolean functions with maximum possible annihilator immunity”, Designs, Codes and Cryptography, 40:1 (2006), 41-58 · Zbl 1202.94179 · doi:10.1007/s10623-005-6300-x
[4] Lobanov M. S., “Tochnoe sootnoshenie mezhdu nelineinostyu i algebraicheskoi immunnostyu”, Diskretnaya matematika, 18:3 (2006), 152-159 · Zbl 1121.94020 · doi:10.4213/dm67
[5] Li Ch., A survey on construction of Boolean function with optimum algebraic immunity (AI),
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