Journal of Mathematics Research
Analysis of Algebraic Immunity for Balanced Boolean Function On 4-Variable
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.
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.
This work is licensed under a Creative Commons Attribution 3.0 License.
Journal of Mathematics Research ISSN 1916-9795 (Print) ISSN 1916-9809 (Online)
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