## Cryptology ePrint Archive: Report 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}

Category / Keywords: Boolean functions, Walsh-Hadamard spectrum, Third-order nonlinearities, Linearized polynomial

Date: received 8 Apr 2012, last revised 8 Apr 2012

Contact author: bksingh0584 at gmail com

Available format(s): PDF | BibTeX Citation

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