Abstract
We study the negabent Boolean functions which are symmetric. The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called a negabent function. For a bent function, the absolute spectral values are the same under the Hadamard-Walsh transform. Unlike bent functions, negabent functions can exist on odd number of variables. Moreover, all the affine functions are negabent.
We prove that a symmetric Boolean function is negabent if and only if it is affine.
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Sarkar, S. (2009). On the Symmetric Negabent Boolean Functions. In: Roy, B., Sendrier, N. (eds) Progress in Cryptology - INDOCRYPT 2009. INDOCRYPT 2009. Lecture Notes in Computer Science, vol 5922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10628-6_9
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DOI: https://doi.org/10.1007/978-3-642-10628-6_9
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