Abstract
Hyper-bent functions as a subclass of bent functions attract much interest and it is elusive to completely characterize hyper-bent functions. Most of known hyper-bent functions are Boolean functions with Dillon exponents and they are often characterized by special values of Kloosterman sums. In this paper, we present a method for characterizing hyper-bent functions with Dillon exponents. A class of hyper-bent functions with Dillon exponents over \(\mathbb {F}_{2^{2m}}\) can be characterized by a Boolean function over \(\mathbb {F}_{2^m}\), whose Walsh spectrum takes the same value twice. Further, we show several classes of hyper-bent functions with Dillon exponents characterized by Kloosterman sum identities and the Walsh spectra of some common Boolean functions.
Y. Qi – Part of this work was done when he was a postdoctor in Peking University and Aisino Corporation Inc.
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Acknowledgements
This work was supported by the Natural Science Foundation of China (Grant No.10990011, 11401480 & No. 61272499).
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Tang, C., Qi, Y. (2014). Constructing Hyper-Bent Functions from Boolean Functions with the Walsh Spectrum Taking the Same Value Twice. In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_5
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