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

Manish Garg; Sugata Gangopadhyay

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 $f_{λ} (x) = T r_{1}^{n} (λ x^{p})$ with $p = 2^{2 r} + 2^{r} + 1$ , $λ \in F_{2^{r}}^{*}$ and $n = 5 r$ . 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 function Higher-order derivatives Second-order nonlinearit Walsh-spectrum
Contact author(s): manishiitr8 @ gmail com
manishiitr12 @ gmail com
History: 2011-08-20: received
Short URL: https://ia.cr/2011/452
License: 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},
      url = {https://eprint.iacr.org/2011/452}
}