Abstract

Algebraic immunity and balancedness have been widely investigated as important cryptographic properties .
Boolean functions with high algebraic immunity can resist algebraic attacks. So, Boolean functions which achieve maximum algebraic immunity and balancedness are our research objects. In this paper, we present a method to study the algebraic immunity of balanced Boolean functions on 4-variable from the rank of matrix, and indicate that all 4-variable balanced Boolean functions with algebraic degree not less than 2 have maximum algebraic immunity. Finally, we introduce two classes balanced functions on even variables which don't achieve maximum algebraic immunity.

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