Cryptology ePrint Archive: Report 2014/524

Constructing hyper-bent functions from Boolean functions with the Walsh spectrum taking the same value twice

Chunming Tang and Yanfeng Qi

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.

Category / Keywords: foundations / Bent function, hyper-bent function, Dillon exponents, Walsh-Hadamard transform, Kloosterman sums

Date: received 5 Jul 2014, last revised 7 Jul 2014

Contact author: tangchunmingmath at 163 com

Available format(s): PDF | BibTeX Citation

Note: Accepted by SETA 2014

Version: 20140707:101340 (All versions of this report)

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