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On the secondary constructions of resilient and bent functions. (English) Zbl 1062.94036
Feng, Keqin (ed.) et al., Coding, cryptography and combinatorics. Basel: Birkhäuser (ISBN 3-7643-2429-5/hbk). Progress in Computer Science and Applied Logic 23, 3-28 (2004).
Summary: We first give a survey of the known secondary constructions of Boolean functions, which lead to resilient functions achieving the best possible trade-offs between resiliency order, algebraic degree and nonlinearity (that is, achieving T. Siegenthaler’s bound [IEEE Trans. Inf. Theory 30, 776–780 (1984; Zbl 0554.94010)] and P. Sarkar and S. Maitra’s bound [CRYPTO 2000, Lect. Notes Comput. Sci. 1880, 515–532 (2000; Zbl 0995.94532)]. We introduce and study a general secondary construction of Boolean functions. This construction includes as particular cases the known secondary constructions previously recalled. We apply this construction to design more numerous functions achieving optimum trade-offs between the three characteristics (and additionally having no linear structure). We conclude the paper by indicating generalizations of our construction to Boolean and vectorial functions, and by relating it to a known secondary construction of bent functions.
For the entire collection see [Zbl 1047.94002].

MSC:
94A60 Cryptography
94D10 Boolean functions
06E30 Boolean functions
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