IACR News item: 11 April 2012
Brajesh Kumar Singh
ePrint Report
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}
Additional news items may be found on the IACR news page.