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 $T{r}_1^n(\lambda x^d)$ for all $x\in {\mathbb{F}}_{2^n}$, where $\lambda \in {\text{BBF}}_{2^n}^{\ast }$, \begin{itemize} \item [{(1)}]$$, $$ are integers such that $$ and $$. \item [{(2)}] $$, $$ is a positive integer such that $$ and $$. \end{itemize}

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