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
-
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},
url = {https://eprint.iacr.org/2014/524}
}
