Perfect algebraic immune functions
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
A new method to construct Boolean functions with good cryptographic properties
Information Processing Letters
Secondary constructions of Boolean functions with maximum algebraic immunity
Cryptography and Communications
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In this paper, three constructions of balanced Boolean functions with optimal algebraic immunity are proposed. It is checked that, at least for small numbers of input variables, these functions have good behavior against fast algebraic attacks as well. Other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are also analyzed. Lower bounds on the nonlinearity are proved, which are similar to the best bounds obtained for known Boolean functions resisting algebraic attacks and fast algebraic attacks. Moreover, it is checked that for the number n of variables with 5 ≤ n ≤ 19, the proposed n-variable Boolean functions have in fact very good nonlinearity.