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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2012/396}},
      url = {https://eprint.iacr.org/2012/396}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.