Paper 2013/493
A new class of semi-bent quadratic Boolean functions
Chunming Tang and Yanfeng Qi
Abstract
In this paper, we present a new class of semi-bent quadratic Boolean functions of the form $f(x)=\sum_{i=1}^{\lfloor\frac{m-1}{2}\rfloor}Tr^n_1(c_ix^{1+4^{i}})$ $~(c_i\in \mathbb{F}_4$,$n=2m)$. We first characterize the semi-bentness of these quadratic Boolean functions. There exists semi-bent functions only when $m$ is odd. For the case: $m=p^r$, where $p$ is an odd prime with some conditions, we enumerate the semi-bent functions. Further, we give a simple characterization of semi-bentness for these functions with linear properties of $c_i$. In particular, for a special case of $p$, any quadratic Boolean function $f(x)=\sum_{i=1}^{\frac{p-1}{2}}Tr^{2p}_1(c_ix^{1+4^{i}})$ over $\mathbb{F}_{2^{2p}}$ is a semi-bent function.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Semi-bent functionBoolean functionm-sequencecyclotomic polynomialbent function
- Contact author(s)
- tangchunmingmath @ 163 com
- History
- 2013-08-15: received
- Short URL
- https://ia.cr/2013/493
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/493, author = {Chunming Tang and Yanfeng Qi}, title = {A new class of semi-bent quadratic Boolean functions}, howpublished = {Cryptology {ePrint} Archive, Paper 2013/493}, year = {2013}, url = {https://eprint.iacr.org/2013/493} }