In cryptography, rotation symmetric Boolean functions (RSBFs) have very significant research value. In this paper, based on the knowledge of integer splitting, a new class of even-variable RSBFs with optimal algebraic immunity (AI) was constructed. The new functions have a nonlinearity of \(2^{n-1}-\left( {\begin{array}{c}n-1\\ k\end{array}}\right) +2^{k-3}(k-3)(k-2) \), which is the highest among all existing RSBFs with optimal AI as well as existing nonlinearity. The algebraic degree of our new construction is as well the highest. Additionally, the results indicate that within the computing capacity of computer, the new class of even-variable RSBFs have almost optimal fast algebraic immunity (FAI).

在密码学中，旋转对称布尔函数（RSBF）具有非常重要的研究价值。在本文中，基于整数分裂的知识，构造了一类具有最优代数免疫（AI）的偶变量RSBF。新函数的非线性为\(2^{n-1}-\left( {\begin{array}{c}n-1\\ k\end{array}}\right) +2^{k- 3}(k-3)(k-2) \)，这是所有现有的具有最优 AI 以及现有非线性的 RSBF 中最高的。我们新建筑的代数次数也是最高的。此外，结果表明，在计算机的计算能力范围内，新型偶变量 RSBF 具有几乎最佳的快速代数免疫 (FAI)。