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1. Symmetric Boolean Functions Depending on an Odd Number of Variables With Maximum Algebraic Immunity.

Author

Na Li and Wen-Feng Qi

Subjects
BOOLEAN algebra, INFORMATION theory, MATHEMATICAL analysis, MATHEMATICAL functions, MATHEMATICAL variables, EQUATIONS, ALGEBRA, DIFFERENTIAL equations, LINEAR algebra
Abstract

To resist algebraic attacks, Boolean functions should possess high algebraic immunity. In 2003, Courtois and Meier showed that the algebraic immunity of an n-variable Boolean function is upper bounded by [n/2]. And then several papers studied how to find symmetric Boolean functions with maximum algebraic immunity. In this correspondence, we prove that for each odd n, there is exactly one trivially balanced n-variable symmetric Boolean function achieving the maximum algebraic immunity. [ABSTRACT FROM AUTHOR]

Published
2006
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