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Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables

Na Li·Wen-feng Qi
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Abstract

To resist algebraic attack, a Boolean function should possess good algebraic immunity (AI). Several papers constructed symmetric functions with the maximum algebraic immunity $\lceil \frac{n}{2}\rceil $. In this correspondence we prove that for each odd $n$, there is exactly one trivial balanced $n$-variable symmetric Boolean function achieving the algebraic immunity $\lceil \frac{n}{2}\rceil $. And we also obtain a necessary condition for the algebraic normal form of a symmetric Boolean function with maximum algebraic immunity.

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Na Li, Wen-feng Qi. 2005-11-29. Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables. https://arxiv.org/abs/cs/0511099

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