Initial Results on the Rotation Symmetric Bent-Negabent Functions

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.