Paper 2011/452

The Good lower bound of Second-order nonlinearity of a class of Boolean function

Manish Garg and Sugata Gangopadhyay

Abstract

In this paper we find the lower bound of second-order nonlinearity of Boolean function $f_{\lambda}(x) = Tr_{1}^{n}(\lambda x^{p})$ with $p = 2^{2r} + 2^{r} + 1$, $\lambda \in \mathbb{F}_{2^{r}}^{*}$ and $n = 5r$. It is also demonstrated that the lower bound obtained in this paper is much better than the lower bound obtained by Iwata-Kurosawa \cite{c14}, and Gangopadhyay et al. (Theorem 1, \cite{c12}).

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functionHigher-order derivativesSecond-order nonlinearitWalsh-spectrum
Contact author(s)
manishiitr8 @ gmail com
manishiitr12 @ gmail com
History
2011-08-20: received
Short URL
https://ia.cr/2011/452
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/452,
      author = {Manish Garg and Sugata Gangopadhyay},
      title = {The Good lower bound of Second-order nonlinearity of a class of Boolean  function},
      howpublished = {Cryptology ePrint Archive, Paper 2011/452},
      year = {2011},
      note = {\url{https://eprint.iacr.org/2011/452}},
      url = {https://eprint.iacr.org/2011/452}
}
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