Investigations on bent and negabent functions via the nega-Hadamard transform
Gangopadhyay, Aditi Kar
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Parker, et al. considered a new style of discrete Fourier transform, called nega-Hadamard transform. We prove several results regarding its behaviior on combinations of Boolean functions and use this theorry to derive several results on negabentness (that is, flat nega-spactrum) of concatenations, and partially symmetric functions. We derive the uppoer bound (n/2) for the algebraic dgree of a negabent function on n variables.. Further, a characterization of of bent-negabent functions is obtained within a subclass if the Maiorana-McFarland set. We develop a technique to construct bent-negabent Boolean functions by using a complete mappig polynomials. Using this technique, we demonstrate for each l > 2, there exist bent-negabent funcitions on n = 12l variable with algebraic degree n/4 + 1 = 3l + 1. It is also demonstrated that there exist bent nega-bent functions on eight variables with algebraic degrees 2, 3, and 4. Simple proofs of several previously known facts are obtained as immediate consequences of our work.
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Gangopadhyay, Sugata; Pasalic, Enes; Stanica, Pantelimon (2012);In this paper, we consider the spectra of Boolean functions with respect to the action of unitary transforms obtained by taking tensor products of the Hadamard kernel, denoted by H, and the nega–Hadamard kernel, denoted ...
Stanica, Pantelimon; Chaturvedi, Ankita; Gangopadhyay, Aditi Kar; Gangopadhyay, Sugata; Maitra, Subhamoy (2010);In this paper, we start developing a detailed theory of nega-Hadamard transforms. Consequently, we derive several results on negabentness of concatenations and partially symmetric functions. We also obtain a characterization ...
Schafer, Neil Brendan. (Monterey, California: Naval Postgraduate School, 2009-09);Boolean bent functions have desirable cryptographic properties in that they have maximum nonlinearity, which hardens a cryptographic function against linear cryptanalysis attacks. Furthermore, bent functions are extremely ...