Paper 2012/037 Original: eprint.iacr.org/2012/037 ↗
Some results on $q$-ary bent functions
Abstract
Kumar et al.(1985) have extended the notion of classical bent Boolean functions in the generalized setup on $\BBZ_q^n$. They have provided an analogue of classical Maiorana-McFarland type bent functions. In this paper, we study the crosscorrelation of a subclass of such generalized Maiorana-McFarland (\mbox{GMMF}) type bent functions. We provide a construction of quaternary ($q = 4$) bent functions on $n+1$ variables in terms of their subfunctions on $n$-variables. Analogues of sum-of-squares indicator and absolute indicator of crosscorrelation of Boolean functions are defined in the generalized setup. Further, $q$-ary functions are studied in terms of these indictors and some upper bounds of these indicators are obtained. Finally, we provide some constructions of balanced quaternary functions with high nonlinearity under Lee metric.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2012-04-22: last updated
- 2012-01-29: published
- Short URL
- https://ia.cr/2012/037
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/037,
author = {Deep Singh and Maheshanand Bhaintwal and Brajesh Kumar Singh},
title = {Some results on $q$-ary bent functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/037},
year = {2012},
url = {https://eprint.iacr.org/2012/037}
}