Paper 2012/396
On second-order nonlinearity and maximum algebraic immunity of some bent functions in $\cP S^+$
Brajesh Kumar Singh
Abstract
In this paper, by modifying a subclass of bent functions in $\mathcal P S_{ap}$, we construct another subclass of bent functions in $\mathcal P S^+$ with maximum algebraic degree. We demonstrate that the algebraic immunity of the constructed functions is maximum. The result is proved by using the well known conjecture proposed by Tu and Deng (Des. Codes Cryptogr. 60(1), pp. 1-14, 2011) which has been proved recently by Cohen and Flori (http://eprint.iacr.org/ 2011/400.pdf). Finally, we identify a class of $\cD_0$ type bent functions constructed by modifying Dillon functions whose lower bound on second-order nonlinearity is very high.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Boolean functionbent functionalgebraic immunityDillon functions$\cD_0$ type bentssecond-order nonlinearities.
- Contact author(s)
- bksingh0584 @ gmail com
- History
- 2012-07-23: received
- Short URL
- https://ia.cr/2012/396
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2012/396,
author = {Brajesh Kumar Singh},
title = {On second-order nonlinearity and maximum algebraic immunity of some bent functions in $\cP S^+$},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/396},
year = {2012},
url = {https://eprint.iacr.org/2012/396}
}
