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

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

2005-11-29

arxiv.org/abs/cs/0511099v1

Computer Science

Cryptography and Security

Scientific paper

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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