Generalized Bent Functions - Some General Construction Methods and Related Necessary and Sufficient Conditions

Abstract

In this article we present a broader theoretical framework useful in studying the properties of so-called generalized bent functions. We give the sufficient conditions (and in many cases also necessary) for generalized bent functions when these functions are represented as a linear combination of: generalized bent; Boolean bent; and a mixture of generalized bent and Boolean bent functions. These conditions are relatively easy to satisfy and by varying the variables that specify these linear combinations many different classes of generalized bent functions can be derived. In particular, based on these results, we provide some generic construction methods of these functions and demonstrate that some previous methods are just special cases of the results given in this article.

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Acknowledgments

Samir Hodžić is supported in part by the Slovenian Research Agency (research program P1-0285 and Young Researchers Grant) and Enes Pasalic is supported in part by the Slovenian Research Agency (research program P3-0384 and research project J1-6720).

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Correspondence to S. Hodžić.

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Hodžić, S., Pasalic, E. Generalized Bent Functions - Some General Construction Methods and Related Necessary and Sufficient Conditions. Cryptogr. Commun. 7, 469–483 (2015). https://doi.org/10.1007/s12095-015-0126-9

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Keywords

  • Generalized boolean functions
  • Generalized bent functions
  • Walsh-Hadamard transform

Mathematics Subject Classification (2010)

  • 94A60
  • 11T71