Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables
<|reference_start|>Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables: 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.<|reference_end|>
@article{li2005symmetric,
    title={Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number
  of Variables},
    author={Na Li and Wen-feng Qi},
    journal={arXiv preprint arXiv:cs/0511099},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0511099},
    primaryClass={cs.CR}
}