Initial results on the rotation symmetric bent-negabent functions
Initial results on the rotation symmetric bent-negabent functions
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DOI：
10.1109/iwsda.2015.7458419
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
Sumanta Sarkar;T. Cusick
中科院分区：
文献类型：
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作者：
Sumanta Sarkar;T. Cusick
我们在文献中首次研究了旋转对称布尔函数类中的负布尔函数。我们推导出一个矩阵来分析旋转对称负布尔函数的负性质。该矩阵的维数比负哈达玛矩阵小得多。我们证明，即使 n ≤ 8，也不存在弯曲的旋转对称负函数。根据这个数值结果，我们证明不存在既弯曲又负的 2 次旋转对称布尔函数。
For the first time in the literature, we investigate the negabent Boolean functions in the class of rotation symmetric Boolean functions. We derive a matrix to analyze the negabent property of rotation symmetric negabent Boolean functions. The dimension of this matrix is much smaller than the nega-Hadamard matrix. We show that for even n ≤ 8, there is no rotation symmetric negabent function which is also bent. Taking the cue from this numerical results, we prove that there is no rotation symmetric Boolean function of degree 2 which is both bent and negabent.