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International Association for Cryptologic Research (IACR)
Abstract
In this paper, we estimate the lower bounds on third-order
nonlinearities of some biquadratic monomial Boolean functions of the
form Tr1nβ(Ξ»xd) for all xβF2nβ, where
\lambda \in \BBF_{2^n}^{*},
\begin{itemize}
\item [{(1)}]d=2i+2j+2k+1, i,j,k
are integers such that i>j>kβ₯1 and n>2i.
\item [{(2)}] d=23β+22β+2β+1, β
is a positive integer such that gcd(i,n)=1 and n>6.
\end{itemize
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