Paper 2012/186

Third-order nonlinearities of some biquadratic monomial Boolean functions

Brajesh Kumar Singh

Abstract

In this paper, we estimate the lower bounds on third-order nonlinearities of some biquadratic monomial Boolean functions of the form $Tr_1^n(\lambda x^d)$ for all $x \in \mathbb F_{2^n}$, where $\lambda \in \BBF_{2^n}^{*}$, \begin{itemize} \item [{(1)}]$d = 2^i + 2^j + 2^k + 1$, $i, j, k$ are integers such that $ i > j > k \geq 1$ and $n > 2 i$. \item [{(2)}] $d = 2^{3\ell} + 2^{2\ell} + 2^{\ell} + 1$, $\ell$ is a positive integer such that $\gcd (i, n) = 1$ and $n > 6$. \end{itemize}

Note: Dear sir, Some typos errors are removed here. Thank you.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functionsWalsh-Hadamard spectrumThird-order nonlinearitiesLinearized polynomial
Contact author(s)
bksingh0584 @ gmail com
History
2012-04-11: received
Short URL
https://ia.cr/2012/186
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/186,
      author = {Brajesh Kumar Singh},
      title = {Third-order nonlinearities of some biquadratic monomial Boolean functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/186},
      year = {2012},
      url = {https://eprint.iacr.org/2012/186}
}
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