Paper 2013/166 Original: eprint.iacr.org/2013/166 ↗
On generalized semi-bent (and partially bent) Boolean functions
Abstract
In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and $\sigma_f$, the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that $\sigma_f = 2^{2n + s}$ for every $s$-plateaued generalized Boolean function in $n$ variables. Two classes of generalized semi-bent Boolean functions are constructed.% and it is demonstrated that their SSMI is over generalized $s$-plateaued Boolean functions is $2^{2n + s}$. We have constructed a class of generalized semi-bent functions in $(n+1)$ variables from generalized semi-bent functions in $n$ variables and identify a subclass of it for which $\sigma_f$ and $\triangle_{f}$ both have optimal value. Finally, some construction on generalized partially bent Boolean functions are given.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2013-03-28: last updated
- 2013-03-28: published
- Short URL
- https://ia.cr/2013/166
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2013/166,
author = {Brajesh Kumar Singh},
title = {On generalized semi-bent (and partially bent) Boolean functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/166},
year = {2013},
url = {https://eprint.iacr.org/2013/166}
}