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
-
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} }