Paper 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.

Note: Accepted by SETA 2014

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Bent functionhyper-bent functionDillon exponentsWalsh-Hadamard transformKloosterman sums
Contact author(s)
tangchunmingmath @ 163 com
History
2014-07-07: revised
2014-07-07: received
See all versions
Short URL
https://ia.cr/2014/524
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2014/524,
      author = {Chunming Tang and Yanfeng Qi},
      title = {Constructing hyper-bent functions from Boolean functions with the Walsh spectrum taking the same value twice},
      howpublished = {Cryptology ePrint Archive, Paper 2014/524},
      year = {2014},
      note = {\url{https://eprint.iacr.org/2014/524}},
      url = {https://eprint.iacr.org/2014/524}
}
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