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 hyperbent functions with Dillon exponents over (formula presented) can be characterized by a Boolean function over 𝔽2m, 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.
CITATION STYLE
Tang, C., & Qi, Y. (2014). Constructing hyper-bent functions from boolean functions with the walsh spectrum taking the same value twice. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8865, 60–71. https://doi.org/10.1007/978-3-319-12325-7_5
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