奇数元具有最大代数免疫性的对称布尔函数
Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables
摘要：
为了抵抗代数攻击，布尔函数必须具有良好的代数免疫性。几篇论文构造了具有最大代数免疫的对称函数$\lceil \frac{n}{2}\rceil $。在这一通信中，我们证明了，对于每一个奇数$n$，只有一个平凡的平衡$n$变量对称布尔函数实现代数免疫$\lceil \frac{n}{2}\rceil $。并给出了具有最大代数免疫度的对称布尔函数的代数范式的一个必要条件。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
